data/data.json

[
    {
        "Misconception":"when students don't understand how to represent proportional relationships.",
        "Misconception ID":"MaE01",
        "Topic":"Number sense",
        "Example Number":1,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise A)",
        "Incorrect Answer":"1\/3",
        "Correct Answer":"1\/4",
        "Question image":"MaE1-Ex1Q",
        "Learner Answer image":"MaE1-Ex1LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students don't understand how to represent proportional relationships.",
        "Misconception ID":"MaE01",
        "Topic":"Number sense",
        "Example Number":2,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise C)",
        "Incorrect Answer":"2\/1",
        "Correct Answer":"2\/3",
        "Question image":"MaE1-Ex2Q",
        "Learner Answer image":"MaE1-Ex2LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students don't understand how to represent proportional relationships.",
        "Misconception ID":"MaE01",
        "Topic":"Number sense",
        "Example Number":3,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise D)",
        "Incorrect Answer":"2\/2",
        "Correct Answer":"1\/2",
        "Question image":"MaE1-Ex3Q",
        "Learner Answer image":"MaE1-Ex3LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students don't understand how to represent proportional relationships.",
        "Misconception ID":"MaE01",
        "Topic":"Number sense",
        "Example Number":4,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise E)",
        "Incorrect Answer":"3\/1",
        "Correct Answer":"3\/4",
        "Question image":"MaE1-Ex4Q",
        "Learner Answer image":"MaE1-Ex4LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"Students misunderstand proportional relationships, not realizing parts must be equal in size.",
        "Misconception ID":"MaE02",
        "Topic":"Number sense",
        "Example Number":1,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise C)",
        "Incorrect Answer":"1\/5",
        "Correct Answer":"1\/4",
        "Question image":"MaE2-Ex1Q",
        "Learner Answer image":"MaE2-Ex1LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"Students misunderstand proportional relationships, not realizing parts must be equal in size.",
        "Misconception ID":"MaE02",
        "Topic":"Number sense",
        "Example Number":2,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise D)",
        "Incorrect Answer":"1\/7",
        "Correct Answer":"1\/6",
        "Question image":"MaE2-Ex2Q",
        "Learner Answer image":"MaE2-Ex2LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"Students misunderstand proportional relationships, not realizing parts must be equal in size.",
        "Misconception ID":"MaE02",
        "Topic":"Number sense",
        "Example Number":3,
        "Question":"What part is shaded?\nWrite a Fraction\n(Exercise F)",
        "Incorrect Answer":"1\/7",
        "Correct Answer":"1\/6",
        "Question image":"MaE2Ex3Q",
        "Learner Answer image":"MaE2Ex3LA",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"Students misunderstand proportional relationships, not realizing parts must be equal in size.",
        "Misconception ID":"MaE02",
        "Topic":"Number sense",
        "Example Number":4,
        "Question":"Reduce 24\/36 to lowest terms",
        "Incorrect Answer":"24\/36=12\/18=5\/9",
        "Correct Answer":"2\/3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. 2006\np. 4",
        "Explanation":""
    },
    {
        "Misconception":"when students misunderstand numerical exponent patterns, resorting to computation instead of recognizing generalizable patterns.",
        "Misconception ID":"MaE03",
        "Topic":"Number sense",
        "Example Number":1,
        "Question":"What digit is in the one\u2019s place of the number: (2^9)(3^4)(5^6)",
        "Incorrect Answer":"The result must end in zero",
        "Correct Answer":"(2^9)(3^4)(5^6)=648000000\nThere is a zero in the ones place",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Slavit, D. 2006\np. 3, 5\n",
        "Explanation":"The value of (2^9)(3^4)(5^6) is computed and the value of the one\u2019s place identified. However, students could also identify a factor of 10 present in the product, either through initial computation or by an examination of the factors, and recognize that the value of the product must end in zero."
    },
    {
        "Misconception":"when students misunderstand numerical exponent patterns, resorting to computation instead of recognizing generalizable patterns.",
        "Misconception ID":"MaE03",
        "Topic":"Number sense",
        "Example Number":2,
        "Question":"Evaluate: (2^9)(3^4)(5^6)=",
        "Incorrect Answer":"2^9 = 2+2+2+2+2+2+2+2+2=18\n3^4=3+3+3+3=12\n5^6=5+5+5+5+5+5=30\n18*12*30=6480",
        "Correct Answer":"648000000",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Slavit, D. 2006\np. 3, 5\nModifiqu\u00e9 la pregunta y respuesta de estudiante",
        "Explanation":"The learners confuse the exponent with a factor and add the base instead of multiplying it by itself. "
    },
    {
        "Misconception":"when students misunderstand numerical exponent patterns, resorting to computation instead of recognizing generalizable patterns.",
        "Misconception ID":"MaE03",
        "Topic":"Number sense",
        "Example Number":3,
        "Question":"5^-2=?",
        "Incorrect Answer":"5^-2=5*10^-2",
        "Correct Answer":"0.05",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Farah (1993)\np.11",
        "Explanation":"The learner has the wrong idea that \"we can write any number in the form of a power of 10, by writing the base times ten at the negative number. This rule applies always to negative powers. Another example is: 15^-6=15*10^-6\""
    },
    {
        "Misconception":"when students misunderstand numerical exponent patterns, resorting to computation instead of recognizing generalizable patterns.",
        "Misconception ID":"MaE03",
        "Topic":"Number sense",
        "Example Number":4,
        "Question":"Evaluate: 9^3-5^4 =",
        "Incorrect Answer":"9^3-5^4=9+9+9-(5+5+5+5)=27-20=7",
        "Correct Answer":"104",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, Sarah B., 2011\np. 238",
        "Explanation":"The lerner interpreted the exponents as factors and added repeatedly instead of multiplying"
    },
    {
        "Misconception":"when students misunderstand algebraic terms and equations involving exponents, such as numerical bases raised to algebraic powers, or algebraic expressions raised to numerical or algebraic powers.",
        "Misconception ID":"MaE04",
        "Topic":"Number sense",
        "Example Number":1,
        "Question":"(z -4)^2=",
        "Incorrect Answer":"(z -4)^2=\n(z-4)(z+4)=z^2+4z-4z-16=z^2-16",
        "Correct Answer":"z^2-8z+16",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Pinchback (1991)",
        "Explanation":"This example shows the lack of understanding that algebra students have regarding exponents. This learner for example, interpreted the expression (z-4)^2 as (z-4)(z+4) "
    },
    {
        "Misconception":"when students misunderstand algebraic terms and equations involving exponents, such as numerical bases raised to algebraic powers, or algebraic expressions raised to numerical or algebraic powers.",
        "Misconception ID":"MaE04",
        "Topic":"Number sense",
        "Example Number":2,
        "Question":"(z -4)^2=",
        "Incorrect Answer":"(z-4)^2=(z+2)(z-2)",
        "Correct Answer":"z^2-8z+16",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Pinchback (1991)",
        "Explanation":"This example shows the lack of understanding that algebra students have regarding exponents. This learner for example, interpreted the expression (z-4)^2 as (z+2)(z-2)"
    },
    {
        "Misconception":"when students misunderstand algebraic terms and equations involving exponents, such as numerical bases raised to algebraic powers, or algebraic expressions raised to numerical or algebraic powers.",
        "Misconception ID":"MaE04",
        "Topic":"Number sense",
        "Example Number":3,
        "Question":"Write an algebraic expression to represent: \n\"Four times a number\"",
        "Incorrect Answer":"x^4",
        "Correct Answer":"4x",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stacey and MacGregor, 1997b\np. 3",
        "Explanation":"The learner confused an exponent with a factor"
    },
    {
        "Misconception":"when students misunderstand algebraic terms and equations involving exponents, such as numerical bases raised to algebraic powers, or algebraic expressions raised to numerical or algebraic powers.",
        "Misconception ID":"MaE04",
        "Topic":"Number sense",
        "Example Number":4,
        "Question":"Fold this piece of paper in half and then open it up. How many regions were made? Can you describe how many regions there would be for any number of folds?",
        "Incorrect Answer":"2 regions folding once",
        "Correct Answer":"Regions=2^n",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford and Langrall, 2000\np. 7, 12",
        "Explanation":"Learners oversimplified the interpretation of the geometric function"
    },
    {
        "Misconception":"when Students think longer numerals mean larger numbers, misunderstanding place value",
        "Misconception ID":"MaE05",
        "Topic":"Number sense",
        "Example Number":1,
        "Question":"Fill in the blank with >, < or =\n0.04 __ 0.5",
        "Incorrect Answer":"0.04 > 0.5",
        "Correct Answer":"0.04 < 0.5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006\np. 141",
        "Explanation":"When Tonya compares two decimals, she appears to focus primarily on the \"size\" of the numeral and thinks that a numeral with an additional place is for a greater number because the numeral is longer. She does not compare product values of digits, she does not consider face value times place value of a digit when comparing two decimals. In short, she does not compare the total values of the numbers shown."
    },
    {
        "Misconception":"when Students think longer numerals mean larger numbers, misunderstanding place value",
        "Misconception ID":"MaE05",
        "Topic":"Number sense",
        "Example Number":2,
        "Question":"Fill in the blank with >, < or =\n0.9 __ 0.01",
        "Incorrect Answer":"0.9 < 0.01",
        "Correct Answer":"0.9 > 0.01",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006\np. 141",
        "Explanation":"The learner does not compare the total values of the numbers shown."
    },
    {
        "Misconception":"when Students think longer numerals mean larger numbers, misunderstanding place value",
        "Misconception ID":"MaE05",
        "Topic":"Number sense",
        "Example Number":3,
        "Question":"Fill in the blank with >, < or =\n0.001 __ 0.02",
        "Incorrect Answer":"0.001 > 0.02",
        "Correct Answer":"0.001 < 0.02",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006\np. 140",
        "Explanation":""
    },
    {
        "Misconception":"when Students think longer numerals mean larger numbers, misunderstanding place value",
        "Misconception ID":"MaE05",
        "Topic":"Number sense",
        "Example Number":4,
        "Question":"Fill in the blank with >, < or =\n0.2 __ 0.03",
        "Incorrect Answer":"0.2 < 0.03",
        "Correct Answer":"0.2 > 0.03",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006\np. 140",
        "Explanation":""
    },
    {
        "Misconception":"when students inaccurately simplify fractions by guessing instead of dividing",
        "Misconception ID":"MaE06",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"Find an equivalent fraction for 3\/8. If possible, simplify.",
        "Incorrect Answer":"3\/8=1\/4",
        "Correct Answer":"3\/8 can't be written in lower terms\nEquivalent fraction: 3\/8=6\/16",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students inaccurately simplify fractions by guessing instead of dividing",
        "Misconception ID":"MaE06",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"Reduce 4\/9",
        "Incorrect Answer":"4\/9=2\/3",
        "Correct Answer":"4\/9 can't be reduced",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students inaccurately simplify fractions by guessing instead of dividing",
        "Misconception ID":"MaE06",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"How does subtracting 1\/3 from 2\/5 compare with subtracting 1\/10 from 2\/5? Which set of fractions will produce a larger difference? Explain your answer.",
        "Incorrect Answer":"It seems that 1\/10 is smaller than 1\/3, so subtracting 1\/10 from 2\/5 should produce a larger difference",
        "Correct Answer":"2\/5-1\/3=6\/15-5\/15=1\/15\n2\/5-1\/10=4\/10-1\/10=3\/10\n3\/10>1\/15\nSubtracting 1\/10 from 2\/5 produces a larger difference",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Johanning (2011),\np. 98-99",
        "Explanation":"The learner estimated instead of solving both subtractions to compare the results"
    },
    {
        "Misconception":"when students inaccurately simplify fractions by guessing instead of dividing",
        "Misconception ID":"MaE06",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"Write 3 5\/6 as an improper fraction.",
        "Incorrect Answer":"3 5\/6=3+1=4",
        "Correct Answer":"23\/6",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006)\np. 4",
        "Explanation":"The learner estimated 5\/6 = 1"
    },
    {
        "Misconception":"when students simplify just one of the terms in a fraction, either the numerator or the denominator",
        "Misconception ID":"MaE07",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"Simplify the fraction 4\/8",
        "Incorrect Answer":"4\/8=2\/8",
        "Correct Answer":"4\/8=1\/4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner simplified the numerator, but not the denominator"
    },
    {
        "Misconception":"when students simplify just one of the terms in a fraction, either the numerator or the denominator",
        "Misconception ID":"MaE07",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"Simplify the fraction 6\/8",
        "Incorrect Answer":"6\/8=3\/8",
        "Correct Answer":"6\/8=3\/4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner simplified the numerator, but not the denominator"
    },
    {
        "Misconception":"when students simplify just one of the terms in a fraction, either the numerator or the denominator",
        "Misconception ID":"MaE07",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"Simplify 4\/6",
        "Incorrect Answer":"4\/6=1\/6",
        "Correct Answer":"4\/6=2\/3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner simplified the numerator, but not the denominator"
    },
    {
        "Misconception":"when students simplify just one of the terms in a fraction, either the numerator or the denominator",
        "Misconception ID":"MaE07",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"Simplify the fraction 7\/7",
        "Incorrect Answer":"7\/7=1\/7",
        "Correct Answer":"7\/7=1",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner simplified the numerator, but not the denominator"
    },
    {
        "Misconception":"when students incorrectly add or subtract fractions by summing both numerators and denominators separately",
        "Misconception ID":"MaE08",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"4\/5+2\/3=",
        "Incorrect Answer":"4\/5+2\/3=6\/8",
        "Correct Answer":"22\/15",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":"The learner added the numerator and the denominators"
    },
    {
        "Misconception":"when students incorrectly add or subtract fractions by summing both numerators and denominators separately",
        "Misconception ID":"MaE08",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"1\/4+2\/3=",
        "Incorrect Answer":"1\/4+2\/3=3\/7",
        "Correct Answer":"11\/12",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":"The learner added the numerator and the denominators"
    },
    {
        "Misconception":"when students incorrectly add or subtract fractions by summing both numerators and denominators separately",
        "Misconception ID":"MaE08",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"Find the sum of 5\/12 and 3\/8",
        "Incorrect Answer":"5\/12+3\/8=(5+3)\/(12+8)=8\/20",
        "Correct Answer":"19\/24",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006)\np. 3",
        "Explanation":"The learner added the numerator and the denominators"
    },
    {
        "Misconception":"when students incorrectly add or subtract fractions by summing both numerators and denominators separately",
        "Misconception ID":"MaE08",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"Subtract 3\/5 from 8",
        "Incorrect Answer":"8-3\/5=(8-3)\/(8-5)=5\/3",
        "Correct Answer":"7 2\/5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006)\np. 3",
        "Explanation":"The learner converted 8 into 8\/8 and then subtracted the numerators and denominators, incurring in 2 MaEs in this case: 8 and 13"
    },
    {
        "Misconception":"when students find common denominators but wrongly keep the original numerators unchanged",
        "Misconception ID":"MaE09",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"Add 1\/2+1\/4=?",
        "Incorrect Answer":"1\/2 = 1\/4\n+      +\n1\/4 = 1\/4\n ----     ----\n          2\/4",
        "Correct Answer":"3\/4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner did not find a correct equivalent fraction for 1\/2 expressed as fourths"
    },
    {
        "Misconception":"when students find common denominators but wrongly keep the original numerators unchanged",
        "Misconception ID":"MaE09",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"Add 2\/5+1\/2=?",
        "Incorrect Answer":"2\/5 = 2\/10\n+         +\n1\/2 = 1\/10\n----     ----\n          3\/10",
        "Correct Answer":"9\/10",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner incorrectly made 1\/2 equal to 1\/10, failed to change 1\/2 into an equivalent form in tenths"
    },
    {
        "Misconception":"when students find common denominators but wrongly keep the original numerators unchanged",
        "Misconception ID":"MaE09",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"Add 3\/5+1\/3=?",
        "Incorrect Answer":"3\/5 = 3\/15\n+        +\n1\/3 = 1\/15\n ----     ----\n           4\/15",
        "Correct Answer":"14\/15",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students find common denominators but wrongly keep the original numerators unchanged",
        "Misconception ID":"MaE09",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"Add 3\/4+1\/2=?",
        "Incorrect Answer":"3\/4=3\/4\n1\/2=1\/4\n3\/4+1\/4=4\/4",
        "Correct Answer":"5\/4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":"The learner is able to determine the least common denominator, and she uses it when changing two factions so they will have the same denominator. However, she merely copies the original numerator. Apparently, she is able to add like fractions correctly."
    },
    {
        "Misconception":"when students subtract mixed numbers incorrectly, avoiding regrouping and just subtracting the smaller from the larger number",
        "Misconception ID":"MaE10",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"Solve x+1\/3=7",
        "Incorrect Answer":"x+1\/3=7\nx=7-1\/3=6\/3=2",
        "Correct Answer":"x=6 2\/3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J.  2006\np. 6",
        "Explanation":"The learner did not find an equivalent fraction for 7 and instead, subtracted 1 from 7 and left the denominator without changing"
    },
    {
        "Misconception":"when students subtract mixed numbers incorrectly, avoiding regrouping and just subtracting the smaller from the larger number",
        "Misconception ID":"MaE10",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"Solve 8 1\/3-2\/3",
        "Incorrect Answer":"8 1\/3-2\/3=4 1\/2",
        "Correct Answer":"7 2\/3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students subtract mixed numbers incorrectly, avoiding regrouping and just subtracting the smaller from the larger number",
        "Misconception ID":"MaE10",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"Solve 6-1 1\/4=",
        "Incorrect Answer":"6-1 1\/4=5 1\/4",
        "Correct Answer":"4 3\/4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students subtract mixed numbers incorrectly, avoiding regrouping and just subtracting the smaller from the larger number",
        "Misconception ID":"MaE10",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"Subtract 1\/3 from 1",
        "Incorrect Answer":"1 \n   -     1\/3\n-------------\n        1 1\/3",
        "Correct Answer":"2\/3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly subtract mixed numbers by separately subtracting wholes, numerators, and denominators to form a new fraction",
        "Misconception ID":"MaE11",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"6 2\/3-3 1\/6=",
        "Incorrect Answer":"6 2\/3-3 1\/6=(6-3)+(2-1)\/(6-3)=3 1\/3",
        "Correct Answer":"7\/2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly subtract mixed numbers by separately subtracting wholes, numerators, and denominators to form a new fraction",
        "Misconception ID":"MaE11",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"4 5\/8-1 3\/4=",
        "Incorrect Answer":"4 5\/8-1 3\/4=(4-1)+(5-3)\/(8-4)=3 2\/4",
        "Correct Answer":"23\/8",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly subtract mixed numbers by separately subtracting wholes, numerators, and denominators to form a new fraction",
        "Misconception ID":"MaE11",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"5 3\/8-2 2\/3=",
        "Incorrect Answer":"5 3\/8-2 2\/3=(5-3)+(3-2)\/(8-3)=3 1\/5",
        "Correct Answer":"65\/24",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":"Chuck is subtracting by first finding the difference between the two whole numbers and recording that difference as the new whole number. He then finds the difference between the two numerators and records that difference as the new numerator. Finally, he finds the difference between the two denominators and records that number as the new denominator."
    },
    {
        "Misconception":"when students wrongly subtract mixed numbers by separately subtracting wholes, numerators, and denominators to form a new fraction",
        "Misconception ID":"MaE11",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"7 2\/5-4 7\/10=",
        "Incorrect Answer":"7 2\/5-4 7\/10=(7-4)+(7-2)\/(10-5)=3 5\/5",
        "Correct Answer":"27\/10",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"When students multiply the numerator of the first fraction by the denominator of the second fraction, they write down only the unit digit of this product and mistakenly save the tens digit for later use, then they multiply the denominator of the first fraction by the numerator of the second one and add the saved tend digit, obtaining an integer number instead of a fraction.",
        "Misconception ID":"MaE12",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"4\/5*3\/4=",
        "Incorrect Answer":"4\/5*3\/4=166",
        "Correct Answer":"3\/5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"When students multiply the numerator of the first fraction by the denominator of the second fraction, they write down only the unit digit of this product and mistakenly save the tens digit for later use, then they multiply the denominator of the first fraction by the numerator of the second one and add the saved tend digit, obtaining an integer number instead of a fraction.",
        "Misconception ID":"MaE12",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"2\/3*4\/6=",
        "Incorrect Answer":"2\/3*4\/6=132",
        "Correct Answer":"4\/9",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"When students multiply the numerator of the first fraction by the denominator of the second fraction, they write down only the unit digit of this product and mistakenly save the tens digit for later use, then they multiply the denominator of the first fraction by the numerator of the second one and add the saved tend digit, obtaining an integer number instead of a fraction.",
        "Misconception ID":"MaE12",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"1\/2*3\/8=",
        "Incorrect Answer":"1\/2*3\/8=68",
        "Correct Answer":"3\/16",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"When students multiply the numerator of the first fraction by the denominator of the second fraction, they write down only the unit digit of this product and mistakenly save the tens digit for later use, then they multiply the denominator of the first fraction by the numerator of the second one and add the saved tend digit, obtaining an integer number instead of a fraction.",
        "Misconception ID":"MaE12",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"2\/3*4\/6=",
        "Incorrect Answer":"2\/3*4\/6=132",
        "Correct Answer":"4\/9",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly scale both numerator and denominator by the same whole number, effectively multiplying the fraction by 1 instead of the intended whole number",
        "Misconception ID":"MaE13",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"2\/3*3=",
        "Incorrect Answer":"2\/3*3=(2*3)\/(3*3)=6\/9",
        "Correct Answer":"6\/3=2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 173",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly scale both numerator and denominator by the same whole number, effectively multiplying the fraction by 1 instead of the intended whole number",
        "Misconception ID":"MaE13",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"1\/4*6=",
        "Incorrect Answer":"1\/4*6=(1*6)\/(4*6)=6\/24",
        "Correct Answer":"6\/4=3\/2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 173",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly scale both numerator and denominator by the same whole number, effectively multiplying the fraction by 1 instead of the intended whole number",
        "Misconception ID":"MaE13",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"4\/5*2=",
        "Incorrect Answer":"4\/5*2=(4*2)\/(5*2)=8\/10",
        "Correct Answer":"8\/5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 173",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly scale both numerator and denominator by the same whole number, effectively multiplying the fraction by 1 instead of the intended whole number",
        "Misconception ID":"MaE13",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"3\/8*4=",
        "Incorrect Answer":"3\/8*4=(3*4)\/(8*4)=12\/32",
        "Correct Answer":"12\/8=3\/2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 173",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly divide fractions by splitting numerators and denominators into separate divisions, ignoring remainders",
        "Misconception ID":"MaE14",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"4\/6\u00f72\/2=?",
        "Incorrect Answer":"4\/6\u00f72\/2=2\/3",
        "Correct Answer":"8\/12",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 174",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly divide fractions by splitting numerators and denominators into separate divisions, ignoring remainders",
        "Misconception ID":"MaE14",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"6\/8\u00f72\/8=?",
        "Incorrect Answer":"6\/8\u00f72\/8=3\/1",
        "Correct Answer":"3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 174",
        "Explanation":"The learner got a correct answer, however he did not apply the correct algorithm"
    },
    {
        "Misconception":"when students wrongly divide fractions by splitting numerators and denominators into separate divisions, ignoring remainders",
        "Misconception ID":"MaE14",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"6\/10\u00f72\/4=?",
        "Incorrect Answer":"6\/10\u00f72\/4=3\/2",
        "Correct Answer":"6\/5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 174",
        "Explanation":"When Linda divides with fractions, her answers are sometimes correct, but frequently they are not. She does not appear to be using good number sense and estimating skills. If she were, she might think, for example, \"How many halves (2\/4) are in about one half (6\/10)? There should be about one, not one and one half (3\/2).\""
    },
    {
        "Misconception":"when students wrongly divide fractions by splitting numerators and denominators into separate divisions, ignoring remainders",
        "Misconception ID":"MaE14",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"7\/5\u00f73\/2=?",
        "Incorrect Answer":"7\/5\u00f73\/2=2\/2",
        "Correct Answer":"14\/15",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 174",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly invert the dividend instead of the divisor when dividing fractions, misunderstanding the 'invert and multiply' rule.",
        "Misconception ID":"MaE15",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"2\/3\u00f73\/8=?",
        "Incorrect Answer":"2\/3\u00f73\/8=3\/2*3\/8=9\/16",
        "Correct Answer":"16\/9",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 175",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly invert the dividend instead of the divisor when dividing fractions, misunderstanding the 'invert and multiply' rule.",
        "Misconception ID":"MaE15",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"2\/5\u00f71\/3=?",
        "Incorrect Answer":"2\/5\u00f71\/3=5\/2*1\/3=5\/6",
        "Correct Answer":"6\/5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 175",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly invert the dividend instead of the divisor when dividing fractions, misunderstanding the 'invert and multiply' rule.",
        "Misconception ID":"MaE15",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"3\/4\u00f71\/5=?",
        "Incorrect Answer":"3\/4\u00f71\/5=4\/3*1\/5=4\/15",
        "Correct Answer":"15\/4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 175",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly invert the dividend instead of the divisor when dividing fractions, misunderstanding the 'invert and multiply' rule.",
        "Misconception ID":"MaE15",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"5\/8\u00f72\/3=?",
        "Incorrect Answer":"5\/8\u00f72\/3=8\/5*2\/3=16\/15",
        "Correct Answer":"15\/16",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 175",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly position the decimal point left of the sum, assuming units and tenths combine separately",
        "Misconception ID":"MaE16",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"0.8+0.4=",
        "Incorrect Answer":".8\n+ .4\n-------\n     .12",
        "Correct Answer":"0.8+0.4=1.2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly position the decimal point left of the sum, assuming units and tenths combine separately",
        "Misconception ID":"MaE16",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"6.7+8.5=",
        "Incorrect Answer":"6.7\n+ 8.5\n-------\n14.12",
        "Correct Answer":"15.2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly position the decimal point left of the sum, assuming units and tenths combine separately",
        "Misconception ID":"MaE16",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"0.6+0.9=",
        "Incorrect Answer":".6\n+.9\n-------\n0.15",
        "Correct Answer":"0.6+0.9 = 1.5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly position the decimal point left of the sum, assuming units and tenths combine separately",
        "Misconception ID":"MaE16",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"0.5+0.8=",
        "Incorrect Answer":".5\n+.8\n------\n.13",
        "Correct Answer":"0.5+0.8=1.3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly drop extra decimal digits directly into their answer when subtracting uneven decimals",
        "Misconception ID":"MaE17",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"60-1.35=?",
        "Incorrect Answer":"60    \n- 1.35\n-----------\n59.35",
        "Correct Answer":"58.65",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly drop extra decimal digits directly into their answer when subtracting uneven decimals",
        "Misconception ID":"MaE17",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"24.8-2.26=?",
        "Incorrect Answer":"24.8\n-   2.26\n-----------\n 22.66",
        "Correct Answer":"22.54",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly drop extra decimal digits directly into their answer when subtracting uneven decimals",
        "Misconception ID":"MaE17",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"$4-$.35",
        "Incorrect Answer":"$ 4 \n-  $  .35\n-----------\n$ 4.35",
        "Correct Answer":"$3.65",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly drop extra decimal digits directly into their answer when subtracting uneven decimals",
        "Misconception ID":"MaE17",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"87-0.31=?",
        "Incorrect Answer":"87  \n-   .31\n---------\n87.31",
        "Correct Answer":"86.69",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students are unsure of the correct sign when adding positive and negative numbers",
        "Misconception ID":"MaE18",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"-8+6=",
        "Incorrect Answer":"-8+6=2",
        "Correct Answer":"-2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students are unsure of the correct sign when adding positive and negative numbers",
        "Misconception ID":"MaE18",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"5+-9=",
        "Incorrect Answer":"5+-9=4",
        "Correct Answer":"-4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students are unsure of the correct sign when adding positive and negative numbers",
        "Misconception ID":"MaE18",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"7+-2=",
        "Incorrect Answer":"7+-2=-5",
        "Correct Answer":"5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students are unsure of the correct sign when adding positive and negative numbers",
        "Misconception ID":"MaE18",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"4+-3=",
        "Incorrect Answer":"4+-3=7",
        "Correct Answer":"1",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse signs of operations and signs of numbers, inappropriately applying the rule \"two negatives make a positive\".",
        "Misconception ID":"MaE19",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"-6+-8=",
        "Incorrect Answer":"-6+-8=2",
        "Correct Answer":"-14",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse signs of operations and signs of numbers, inappropriately applying the rule \"two negatives make a positive\".",
        "Misconception ID":"MaE19",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"-8+-3=",
        "Incorrect Answer":"-8+-3=5",
        "Correct Answer":"-11",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse signs of operations and signs of numbers, inappropriately applying the rule \"two negatives make a positive\".",
        "Misconception ID":"MaE19",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"-4+-3=",
        "Incorrect Answer":"-4+-3=7",
        "Correct Answer":"-7",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse signs of operations and signs of numbers, inappropriately applying the rule \"two negatives make a positive\".",
        "Misconception ID":"MaE19",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"-2+-5=",
        "Incorrect Answer":"-2+-5=7",
        "Correct Answer":"-7",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly position the decimal in multiplication by counting from the left, not the right",
        "Misconception ID":"MaE20",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"6.7*3=?",
        "Incorrect Answer":"6.7\nx 3\n-------\n2.01",
        "Correct Answer":"20.1",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 182",
        "Explanation":"In her answer, Marsha places the decimal point by counting over from the left instead of from the right in the product. She frequently gets the correct answer, but much of the time her answer is not the correct product."
    },
    {
        "Misconception":"when students wrongly position the decimal in multiplication by counting from the left, not the right",
        "Misconception ID":"MaE20",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"21.8*.4=?",
        "Incorrect Answer":"21.8\nx .4\n-------\n87.2",
        "Correct Answer":"8.72",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 176",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly position the decimal in multiplication by counting from the left, not the right",
        "Misconception ID":"MaE20",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"4.35*2.3=?",
        "Incorrect Answer":"4.35\nx 2.3\n----------\n1305\n870\n-------\n100.05",
        "Correct Answer":"10.005",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 176",
        "Explanation":""
    },
    {
        "Misconception":"when students wrongly position the decimal in multiplication by counting from the left, not the right",
        "Misconception ID":"MaE20",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"4.5*0.1=?",
        "Incorrect Answer":"4.5\nx 0.1\n---------\n45.",
        "Correct Answer":"0.45",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students fail to regroup in subtraction, mistakenly subtracting the larger number from the smaller",
        "Misconception ID":"MaE21",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"253-179=",
        "Incorrect Answer":"253\n- 179\n----------\n 126",
        "Correct Answer":"74",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006\np. 72",
        "Explanation":""
    },
    {
        "Misconception":"when students fail to regroup in subtraction, mistakenly subtracting the larger number from the smaller",
        "Misconception ID":"MaE21",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"Find the difference between 100 and 40.",
        "Incorrect Answer":"100\n- 40\n---------\n140",
        "Correct Answer":"100-40=60",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush (2011)\np. 258\n El ejemplo de los c\u00edrculos inscritos en un cuadrado",
        "Explanation":""
    },
    {
        "Misconception":"when students fail to regroup in subtraction, mistakenly subtracting the larger number from the smaller",
        "Misconception ID":"MaE21",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"Solve: \n  241-96=",
        "Incorrect Answer":"241\n-96\n-------\n255",
        "Correct Answer":"145",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students fail to regroup in subtraction, mistakenly subtracting the larger number from the smaller",
        "Misconception ID":"MaE21",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"A television station charges $1,089 for a sixty-second commercial and $325 for a fifteen-second commercial. \nThe television station also sells 10 minutes of commercial time for a total of $10,000. \nHow much will an advertiser save if they purchase the 10-minute block of commercials instead of 7 sixty-second commercials and 12 fifteen-second commercials?",
        "Incorrect Answer":"(1,089*7)+(12*325) = 7,623+3,900=11,523\n10,000\n-11,523\n-----------\n-1,523",
        "Correct Answer":"The advertiser will save $1,523.00",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush. 2011\np. 249-251",
        "Explanation":""
    },
    {
        "Misconception":"when students extend quotients with remainders as decimals, if division isn't exact within the dividend's digits",
        "Misconception ID":"MaE22",
        "Topic":"Number Operations",
        "Example Number":1,
        "Question":"2.57\u00f73=?",
        "Incorrect Answer":"[Image]",
        "Correct Answer":"0.8567",
        "Question image":"",
        "Learner Answer image":"MaE22-Ex1LA",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 183",
        "Explanation":"Ted has incorrect quotients because of the way he handles reminders. Id division does not \"come out even\" when taken as far as digits given in the dividend, Ted writes the reminder as an extension of the quotient. He may believe this is the same as writing R2 after the quotient for a division problem with whole numbers."
    },
    {
        "Misconception":"when students extend quotients with remainders as decimals, if division isn't exact within the dividend's digits",
        "Misconception ID":"MaE22",
        "Topic":"Number Operations",
        "Example Number":2,
        "Question":"9.35\u00f7.7=?",
        "Incorrect Answer":"[Image]",
        "Correct Answer":"13.357",
        "Question image":"",
        "Learner Answer image":"MaE22-Ex2LA",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 183",
        "Explanation":""
    },
    {
        "Misconception":"when students extend quotients with remainders as decimals, if division isn't exact within the dividend's digits",
        "Misconception ID":"MaE22",
        "Topic":"Number Operations",
        "Example Number":3,
        "Question":"38.6\u00f74=?",
        "Incorrect Answer":"[Image]",
        "Correct Answer":"9.65",
        "Question image":"",
        "Learner Answer image":"MaE22-Ex3LA",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 177",
        "Explanation":"Some students, having studied division with decimals, try to add digits to the quotient when dividing whole numbers; after taking as far as digits given in the dividend, they write the reminder as an extension of the quotient after a decimal point."
    },
    {
        "Misconception":"when students extend quotients with remainders as decimals, if division isn't exact within the dividend's digits",
        "Misconception ID":"MaE22",
        "Topic":"Number Operations",
        "Example Number":4,
        "Question":"8.24\u00f75=?",
        "Incorrect Answer":"[Image]",
        "Correct Answer":"1.648",
        "Question image":"",
        "Learner Answer image":"MaE22-Ex4LA",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 177",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse fixed scaling (absolute) with ratio comparisons (relative) in proportional relationships.",
        "Misconception ID":"MaE23",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"At ARCO, gas sells for $1.13 per gallon. This is 5 cents less per gallon than gas at Chevron. How much does 5 gallons of gas cost at Chevron?",
        "Incorrect Answer":"($1.13\/gallon)*(5 gallons)=$5.65\n$5.65-$0.05=$5.60",
        "Correct Answer":"$1.13+$0.05=$1.18\n5 gallons*$1.18\/gallon=$5.90\n5 gallons cost $5.9 at Chevron",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kilpatrick, J., Swafford, J. O., & Findell, B. (2001)\np. 125",
        "Explanation":"The learner thought about the proportionality relative to the cost of the gas at ARCO, focusing on specific numbers and keywords such as $1.13, 5 cents, less, and 5 gallons, rather than the relationships among the quantities"
    },
    {
        "Misconception":"when students confuse fixed scaling (absolute) with ratio comparisons (relative) in proportional relationships.",
        "Misconception ID":"MaE23",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"Adrian has conquered only 6 giants in his new video game, Giant Trouble, but this is only two-fifths of the giants that he must conquer. How many giants are there in the new video game?",
        "Incorrect Answer":"6\u00f71\/5=30 giants\nThere are six giants conquered, and since the number of giants is being divided into fifths, then there must be thirty giants",
        "Correct Answer":"6\u00f72\/5=30\/2=15\n15 giants",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006) \np. 5",
        "Explanation":"The student divided the six giants into fifths; his result was 30 giants"
    },
    {
        "Misconception":"when students confuse fixed scaling (absolute) with ratio comparisons (relative) in proportional relationships.",
        "Misconception ID":"MaE23",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"Which of the following drinks, C or D, will have a stronger apple taste?\na) Drink C: 3 cups apple, 5 cups water\nb) Drink D: 5 cups apple, 7 cups water",
        "Incorrect Answer":"b), because it has 5 apple, not 3",
        "Correct Answer":"b), because 5\/7>3\/5. The concentration of apple is bigger in drink D",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Lamon 2012\n(no link)",
        "Explanation":"The learners compared the drinks with a relative proportion, not absolute, which was the correct way to do it in this case"
    },
    {
        "Misconception":"when students confuse fixed scaling (absolute) with ratio comparisons (relative) in proportional relationships.",
        "Misconception ID":"MaE23",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"Consider two marigolds that were 8 inches and 12 inches tall two weeks ago and 11 inches and 15 tall inches now. Write a ratio to represent the growth of each one and tell: Which plant grew more compared to its initial height?",
        "Incorrect Answer":"Each plant grew the same, 3 inches",
        "Correct Answer":"The shorter plant grew 3\/8 of its original height, while the larger plant grew less, just 3\/12 of its original height",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kilpatrick, J., Swafford, J. O., & Findell, B. 2001\np. 264",
        "Explanation":"The learner compared how each plant grew relatively to the plant itself (relative proportion), but the instruction was to write a ratio to represent the growth of each plant and compare them"
    },
    {
        "Misconception":"when students struggle to understand that ratios can compare same or different units",
        "Misconception ID":"MaE24",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"To bake donuts, Mariah needs 8 cups of flour to bake 14 donuts. Using the same recipe, how many donuts can she bake with 12 cups of flour?",
        "Incorrect Answer":"I am counting... I am trying to divide 14 by 8... I got 1.75 and I times (multiplied) by 12.\n1.75*12 you get... 350+175, so... 35.0+17.5=53\n53 donuts",
        "Correct Answer":"In this case, it is intended to find the unit value to relate donuts to cups of flour, then calculate the amount needed with the proportional method, observing the correct units involved:\n(14 donuts)\/(8 cups)=(1.75 donuts)\/(1 cup)\n(1.75 donuts\/cup)*(12 cups)=21 donuts\n21 donuts",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Singh, 2000\np. 16-17",
        "Explanation":"She did not try to construct a relationship between 8 cups and 12 donuts as 1 1\/2 times more, which is an important criterion in multiplicative reasoning. She relied heavily on  algorithmic procedures and utilized additive reasoning"
    },
    {
        "Misconception":"when students struggle to understand that ratios can compare same or different units",
        "Misconception ID":"MaE24",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"If 4 cents can buy 6 sweets, how many can 10 cents buy?",
        "Incorrect Answer":"4\/6=0.66\nThis makes no sense\n4 cents buy 6 sweets and 8 cents buy 12 sweets and 6 cents buy 9 sweets. You see, 6 is between 4 and 8, so 4 cents you buy 6 sweets, 6 cents 9 sweets,\n8 cents 12 sweets, 10 cents 15 sweets, 12 cents 18 sweets. There is a pattern: 3,6,9, 12... 15 sweets",
        "Correct Answer":"(4 cents)\/(6 sweets) = (10 cents)\/(? sweets)\n(10 cents)*(6 sweets)\/(4 cents) = 60\/4 sweets = 15 sweets",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Singh, P. (2000).",
        "Explanation":"Karen tried to solve this task utilizing the formal method of unit analysis, (find the rate for one and multiplying to get the rate for many). She divided 4 by 6 and obtained 0.66 which did not make sense to her. She seemed confused about this outcome and abandoned it. She then used a method which was more meaningful to her. She spent quite some time writing on her paper and used her fingers occasionally in doing calculations. After some time working on it, she said: \"15 sweets. 4 cents buy 6 sweets and 8 cents buy 12 sweets and 6 cents buy 9 sweets. You see, 6 is between 4 and 8, so 4 cents you buy 6 sweets, 6 cents 9 sweets,\n8 cents 12 sweets, 10 cents 15 sweets, 12 cents 18 sweets. There is a pattern\n3,6,9, 12... 15 sweets\". Karen only found the pattern, but never considered the units in the ratios"
    },
    {
        "Misconception":"when students struggle to understand that ratios can compare same or different units",
        "Misconception ID":"MaE24",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"These two rectangles are the same shape. Find h",
        "Incorrect Answer":"16\n9 divided by 3 is 3 and 6 divide by 3 is 2. I divided by 3, because 9 can't go into 24. Then:\n3 cm-2 cm\n6-4\n9-6\n12-8\n15-10\n18-12\n21-14\n24-16\nThis one can't be solved with the proportions procedure, because we can't make a ratio of cm to cm",
        "Correct Answer":"(6 cm)\/(9 cm)=(h cm)\/(24 cm)\nh=(6 cm)*(24 cm)\u00f7(9 cm)=16 cm",
        "Question image":"MaE24-Ex3Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Singh, 2000\np. 13",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to understand that ratios can compare same or different units",
        "Misconception ID":"MaE24",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"In baking a cake, for every 8 eggs, one needs 18 cups of flour. If Mary has 4 cups of flour, how many eggs does she need?",
        "Incorrect Answer":"1.5 eggs\n[The learner answered without computing, not relating the number of cakes to the number of eggs]",
        "Correct Answer":"1.78 eggs with 4 cups",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Sigh, 2000\np. 18",
        "Explanation":"The learner used the unit method and computed 18 divided by 8 to match 1 cup with the number of eggs. She did it mentally and obtained 2.25 (which was actually 1 egg with 2.25 cups). When she multiplied 2.25 by 4 she found the result of 18 puzzling. \"That can't be!\" she said. Then she utilized the scalar method and computed a division of 18 by 4 which was 4.5. She  wrote: 4.5 cups with 2 eggs, 4 cups with 1.5 eggs [as both cups and eggs are lesser by 1\/2]. She utilized the additive strategy"
    },
    {
        "Misconception":"when students struggle to apply correct operations on ratios expressed as fractions",
        "Misconception ID":"MaE25",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"If 5 quarters can buy 100 candies, how many quarters can buy 80 candies? Express the quantities as ratios and solve.",
        "Incorrect Answer":"1q --> 20 c\n2q --> 40 c\n3q --> 60 c\n4q --> 80 c\nThere's no ratio in this problem",
        "Correct Answer":"Ratio: (5 quarters\/100 candies)=(? quarters\/80 candies)\n4 quarters",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ojose. B. 2015\np. 4",
        "Explanation":"The learner obtained the correct answer at the end, but she did it by writing a sequence, with an iterative method, not by understanding the ratio"
    },
    {
        "Misconception":"when students struggle to apply correct operations on ratios expressed as fractions",
        "Misconception ID":"MaE25",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"3:2=24:x\nFind the value of x",
        "Incorrect Answer":"32=24x\n32\/24=x\nx=4\/3",
        "Correct Answer":"x=16",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kilpatrick, J., Swafford, J. O., & Findell, B. 2011, p. 265",
        "Explanation":"The learner did not identify that 3:2 is the same as 3\/2 and 24:x is another ratio, the learner just removed the : in both cases\n"
    },
    {
        "Misconception":"when students struggle to apply correct operations on ratios expressed as fractions",
        "Misconception ID":"MaE25",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"If 5\/8=x\/24 then find x",
        "Incorrect Answer":"x = 5*8\u00f724\n40\u00f724=40\/24=20\/12=10\/6",
        "Correct Answer":"x=15",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006) \np. 6",
        "Explanation":"The learner did not identify the ratio and did not apply the algorithm of a proportional ratio to solve it\n"
    },
    {
        "Misconception":"when students struggle to apply correct operations on ratios expressed as fractions",
        "Misconception ID":"MaE25",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"Reduce: (3+4)\/2",
        "Incorrect Answer":"4\u00f72+3=5",
        "Correct Answer":"7\/2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006) \np. 7",
        "Explanation":"The learner did not see the operation as a complex ratio or an addition of fractions with a common denominator, but instead saw it as a set of operations that can be solved in any order"
    },
    {
        "Misconception":"when students misunderstand how to identify and use equivalent forms of ratios, including fractions and decimals",
        "Misconception ID":"MaE26",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"Express \"2\/3 dollars per balloon\" with equivalent integer numbers.",
        "Incorrect Answer":"$0.67 per balloon",
        "Correct Answer":"$3 dollars per 9 balloons",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kilpatrick, J., Swafford, J. O., & Findell, B. 2011\np. 263-264",
        "Explanation":"The learner interpreted 2\/3 as a division, rather than a ratio"
    },
    {
        "Misconception":"when students misunderstand how to identify and use equivalent forms of ratios, including fractions and decimals",
        "Misconception ID":"MaE26",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"Represent (1\/3)*a as a ratio",
        "Incorrect Answer":"1\/3a",
        "Correct Answer":"a\/3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006) \np. 6",
        "Explanation":"The learner did not recognize that one third of any number produces a ratio, instead seems to think that the fraction implies a division and got confused on how to represent it"
    },
    {
        "Misconception":"when students misunderstand how to identify and use equivalent forms of ratios, including fractions and decimals",
        "Misconception ID":"MaE26",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"Greg conducts a survey of 100 classmates to determine their favorite fruits. The results of the survey are shown in a circle graph that contains the following data: \nOrange - 17%\nApple - 36%\nGrape - 15%\nBanana - 23%\nKiwi - 9%\nWhich two fruits represent 2\/5 of the students' favorites?",
        "Incorrect Answer":"I guess grapes and Kiwi",
        "Correct Answer":"Orange and Banana (17%+23%=40%=2\/5)",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush 2011\np. 188",
        "Explanation":"Students had to understand that 2\/5 converts to 40% and then add to find the two fruits whose percentage totaled 40%. One interesting finding was that some students found the two fruits whose sum was approximately 25% (grapes and kiwi) or 50% (apples and grapes) of the total. Perhaps this meant that they believed that 25% or 50% was  equivalent to 2\/5. This was categorized as not understanding the value of a fraction and not understanding the size of a ratio"
    },
    {
        "Misconception":"when students misunderstand how to identify and use equivalent forms of ratios, including fractions and decimals",
        "Misconception ID":"MaE26",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"You had a picture on your computer and you made it 3\/4 (75%) of its original size. You changed your mind and now you want it back to its original size again. What fraction of its present size should you tell the computer to make it in order to restore its original size?",
        "Incorrect Answer":"To get it at 3\/4 you had to do 75% of the original. So that means you took off 25% of its size. To get it back, you should enlarge it 25% by setting the number at 125%, or 1.25",
        "Correct Answer":"4\/3 (the inverse of 3\/4)",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Lamon 2012\n(no link)",
        "Explanation":""
    },
    {
        "Misconception":"when students lack unitization skills, unable to treat ratios as composite units to solve problems systematically.",
        "Misconception ID":"MaE27",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"John used exactly 15 cans to paint 18 chairs. How many chairs can he paint with 25 cans?",
        "Incorrect Answer":"810 chairs\n18+18+18=54 cans. 20 cans-162 chairs [she got this by multiplying it by 3] 25 cans-810 chairs [The algorithmic procedures on her working paper were: 162+162+162+162+162= 810]",
        "Correct Answer":"(15 cans)\/(18 chairs)=(25 cans)\/(? chairs)\n(25*18)\u00f715=30\n30 chairs",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Singh, 2000\np. 17",
        "Explanation":"Alice was not able to construct a composite unit consisting of 15 to 18. Her reasoning seemed to be based on additive reasoning rather than multiplicative reasoning where each subsequent ratio is added on to the previous one. She was not able to unite a sequence of counting acts into composite units. Her 'adding' iteration was schematized as a ratio unit of 1 can to 18 chairs, where for each  additional can, she added 18 chairs"
    },
    {
        "Misconception":"when students lack unitization skills, unable to treat ratios as composite units to solve problems systematically.",
        "Misconception ID":"MaE27",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"To bake 6 cakes, you need 15 eggs. Using the same recipe, how many eggs do you need to bake 4 cakes?",
        "Incorrect Answer":"In 2, 4, 6 there are three and all are times 2. Then 15 divides 3 because 1,2,3, got three. 2 cakes - 5 eggs, 4 cakes - 10 eggs, and 6 cakes you need 15 eggs\n[The teacher asked: How do you know that for 2 cakes you need 5 eggs? The student replied: Because I divided 6 cakes and 15 eggs by 3. Because in 2, 4, 6 there are one, two, three, so I divided by 3]",
        "Correct Answer":"(15 eggs)\/(6 cakes)=2.5 eggs\/cake\n(2.5 eggs\/cake)*(4 cakes)=10 eggs\n10 eggs",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Singh, 2000\np. 10",
        "Explanation":""
    },
    {
        "Misconception":"when students lack unitization skills, unable to treat ratios as composite units to solve problems systematically.",
        "Misconception ID":"MaE27",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"Adrian has conquered only 6 giants in his new video game, Giant Trouble, but this is only two-fifths of the giants that he must conquer. How many giants are there in the new video game?",
        "Incorrect Answer":"6 2\/5 = 32\/5, then there are 32 giants\n32 giants",
        "Correct Answer":"(6 giants)\/(2\/5 total)=(? giants)\/(1 total)\n6\u00f7(2\/5)=30\/2=15\n15 giants in total",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J. (2006)\np. 5",
        "Explanation":"The learners did not compare the ratio, instead only arranged the numbers in a familiar form and then applied an algorithm that they believe fits the form"
    },
    {
        "Misconception":"when students lack unitization skills, unable to treat ratios as composite units to solve problems systematically.",
        "Misconception ID":"MaE27",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"Last Saturday, Rachel shelled walnuts. She was paid $5.00 for the day, plus an additional $0.10 for each cup of walnuts she shelled. If Rachel earned a total of $17.00, how many QUARTS of walnuts did Rachel shell? Show all work.",
        "Incorrect Answer":"17-5=12\n12\u00f75=2.4\n2.4 quarts",
        "Correct Answer":"$17-$5=$12\nShe earned $12 for the walnuts she shelled\n($0.10)\/(1 cup)=($12)\/(? cup)\n12\u00f70.10=120 cups\n(4 quarts)\/(1 cup)=((? quarts)\/(120 cups)\n4*120=480\n480 quarts",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 240-241",
        "Explanation":"The learners showed the inability to unitize when converting between cups and quarts\n"
    },
    {
        "Misconception":"when students fail to see ratios as relationships between two quantities",
        "Misconception ID":"MaE28",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"Bart is publicity painter. In the last few days, he had to paint Christmas decorations on several store windows. Yesterday, he made a drawing of a 56 cm high Father Christmas on the door of a bakery. He needed 6 ml paint.  Now he is asked to make an enlarged version of the same drawing on a supermarket window. This copy should be 168 cm high. How much paint will Bart approximately need to do this?",
        "Incorrect Answer":"You need more data, for instance the width",
        "Correct Answer":"54 ml",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"De Bock, D., Van Dooren, W., Verschaffel, L., & Janssens, D. (2002)\np. 8",
        "Explanation":"The learner did not recognize the ratio of the height of the figure to the amount of paint needed"
    },
    {
        "Misconception":"when students fail to see ratios as relationships between two quantities",
        "Misconception ID":"MaE28",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"Samer has 35 red glass balls in a bag and 25 green glass balls. \nWhat is the ratio of the red glass balls to the green ones in\nthe simplest form?",
        "Incorrect Answer":"35 and 25",
        "Correct Answer":"7\/5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Khasawneh 2022\np. 6",
        "Explanation":""
    },
    {
        "Misconception":"when students fail to see ratios as relationships between two quantities",
        "Misconception ID":"MaE28",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"Samer has 35 red glass balls in a bag and 25 green glass balls.\nWhat is the ratio of the green balls to all glass balls in the bag in the simplest form?",
        "Incorrect Answer":"25 and 60",
        "Correct Answer":"5\/12",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Khasawneh 2022\np. 6",
        "Explanation":""
    },
    {
        "Misconception":"when students fail to see ratios as relationships between two quantities",
        "Misconception ID":"MaE28",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"Eric has 12 cups of lemonade that tastes exactly the same as Brody\u2019s (3 cups of water for 2 cups of lemon juice). He needs a larger amount of lemonade. He pours one more cup of water and one more cup of lemon juice. Does his lemonade still taste the same? Why or why not?",
        "Incorrect Answer":"Since 4\/3 = 1.33 and 3\/2 = 1.5, the ratios are very close, so the lemonade will taste the same",
        "Correct Answer":"Eric's lemonade will not taste the same anymore, because he did not add the water and lemon in the same proportions",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"JiYeong I, 2018",
        "Explanation":"Students added 1 to each term of the given ratio. Treating a ratio as a single quantifiable, non-fraction, value. This shows their lack of understanding that a ratio is a relationship of two or more quantities, not quantities themselves"
    },
    {
        "Misconception":"when students incorrectly apply a single proportion formula to all percentage problems: (smaller value)\/(larger value) = (x\/100)",
        "Misconception ID":"MaE29",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"Jim correctly solved 88% of 50 test items. How many items did he have correct?",
        "Incorrect Answer":"(50\/88)=(x\/100)\n57 items",
        "Correct Answer":"44 items",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 187",
        "Explanation":"Sara successfully solved percent problems when the class first solved them, but as different types of problems were encountered, she began to have difficulty. Sara is solving correctly the proportion she writes for the problem. However, she uses a procedure that often does not accurately represent the ratios described in the problem. She is using the following proportion for every problem encountered:\n(lesser number in the problem)\/(greater number in the problem)=x\/100"
    },
    {
        "Misconception":"when students incorrectly apply a single proportion formula to all percentage problems: (smaller value)\/(larger value) = (x\/100)",
        "Misconception ID":"MaE29",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"Brad earned $400 during the summer and saved $240 from his earnings. What percent of his earnings did he spend?",
        "Incorrect Answer":"(240\/400)=(x\/100)\n60%",
        "Correct Answer":"40%",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 187",
        "Explanation":"Sara is solving correctly the proportion she writes for the problem. However, she uses a procedure that often does not accurately represent the ratios described in the problem. She is using the following proportion for every problem encountered:\n(lesser number in the problem)\/(greater number in the problem)=x\/100"
    },
    {
        "Misconception":"when students incorrectly apply a single proportion formula to all percentage problems: (smaller value)\/(larger value) = (x\/100)",
        "Misconception ID":"MaE29",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"The taffy sale brought in a total of $750, but 78% of this was used for expenses. How much money was used for expenses?",
        "Incorrect Answer":"(78\/750)=(x\/100)\n$10.4",
        "Correct Answer":"$585",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 187",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly apply a single proportion formula to all percentage problems: (smaller value)\/(larger value) = (x\/100)",
        "Misconception ID":"MaE29",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"Barbara received a gift of money on her birthday. She spent 80% of the money on a watch. The watch cost her $20. How much money did she receive as a birthday gift?",
        "Incorrect Answer":"(20\/80)=(x\/100)\n$25",
        "Correct Answer":"$400",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 187",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to discern the three types of percent problems, relying solely on \"percent times a number equals percentage\" rule",
        "Misconception ID":"MaE30",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":1,
        "Question":"Fifteen percent of what number is 240?",
        "Incorrect Answer":"240*0.15=36.00\n36",
        "Correct Answer":"1600",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 188",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to discern the three types of percent problems, relying solely on \"percent times a number equals percentage\" rule",
        "Misconception ID":"MaE30",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":2,
        "Question":"What percent of 40 is 28?",
        "Incorrect Answer":"40*.28=11.20\n11.2",
        "Correct Answer":"70%",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 192",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to discern the three types of percent problems, relying solely on \"percent times a number equals percentage\" rule",
        "Misconception ID":"MaE30",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":3,
        "Question":"Seventy is 14% of what number?",
        "Incorrect Answer":"70*.14=9.8\n9.8",
        "Correct Answer":"500",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 192",
        "Explanation":"Steve's solutions are correct when he is finding the percent of a specified number. However, his solutions are incorrect when the percent is known and he needs to find a number or when he needs to find what percent one number is of a specified number. "
    },
    {
        "Misconception":"when students struggle to discern the three types of percent problems, relying solely on \"percent times a number equals percentage\" rule",
        "Misconception ID":"MaE30",
        "Topic":"Ratios and proportional reasoning",
        "Example Number":4,
        "Question":"What percent of 125 is 25?",
        "Incorrect Answer":"125*.25=32.25\n31.25",
        "Correct Answer":"20%",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)\np. 192",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly assume the commutative and associative properties apply to subtraction and division, akin to the \"Switch-Around Rule.\"",
        "Misconception ID":"MaE31",
        "Topic":"Properties of number and operations",
        "Example Number":1,
        "Question":"Write the \u201cSwitch-Around Rule\u201d in your own words, and give examples to show if it\u2019s always, sometimes, or rarely true.",
        "Incorrect Answer":"The switch-around rule says 2-1=1 and 1-2=1",
        "Correct Answer":"The switch-around rule is not always true, it applies only for addition and multiplication. For example: 7+3=10 and 3+7=10, but 7-3=4 and 3-7=-4, it's not the same",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Schifter et al, (2008)",
        "Explanation":"Many of the children interpret the switch-around rule to apply to other operations, even though the rule was written \u201cwhen two numbers are added together.\u201d Some children consider addition, subtraction, multiplication, and division; others addition and subtraction; and some specify that the switch-around rule is about addition."
    },
    {
        "Misconception":"when students incorrectly assume the commutative and associative properties apply to subtraction and division, akin to the \"Switch-Around Rule.\"",
        "Misconception ID":"MaE31",
        "Topic":"Properties of number and operations",
        "Example Number":2,
        "Question":"Find the missing number:\n23=2+5+__+4+6",
        "Incorrect Answer":"23=7+__+10\n23=17+__\nIt's the same if I do 23-17 or 23+17, it's the switch-around rule\n23+17=40",
        "Correct Answer":"23=7+__+10\n23=17+__\n23-17=6\n6 is the missing number",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Warren (2003)",
        "Explanation":"The learner did not realize that 17 had to be subtracted from 23 in order to find the correct answer. This misconception is related to the belief that commutative and associative properties are true for subtraction and division, or in other words, that the \"Switch-Around Rule\" is always true."
    },
    {
        "Misconception":"when students incorrectly assume the commutative and associative properties apply to subtraction and division, akin to the \"Switch-Around Rule.\"",
        "Misconception ID":"MaE31",
        "Topic":"Properties of number and operations",
        "Example Number":3,
        "Question":"True or false?\n2\u00f73=3\u00f72",
        "Incorrect Answer":"True, because of the switch-around rule",
        "Correct Answer":"False. Commutative and associative properties are not true for division",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Warren (2003)",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly assume the commutative and associative properties apply to subtraction and division, akin to the \"Switch-Around Rule.\"",
        "Misconception ID":"MaE31",
        "Topic":"Properties of number and operations",
        "Example Number":4,
        "Question":"Sarah shares $15.40 among some of her friends. She gives the same amount to each person.\n(a) How many people might there be and how much would each receive? (Give at least 3 answers)\n(b) Explain in writing how to work out more answers.",
        "Incorrect Answer":"3*5= 15, so 3 friends can share the money but I don't know what to do with the 40 cents, because there's no way to share evenly 40 cents with 3 people. Since 3 times 5 is the same as 5 times 3, 15.4 shared by 3 has to be the same as 15.4 shared by 5, then we can also share the 15.4 dollars with 5 people, but we ignore the 40 cents.",
        "Correct Answer":"You can share $15.40 among 2, 4, and 7 people:\n$15.4\u00f72= $7.70\n$15.4\u00f74= $3.85\n$15.4\u00f77= $2.20\nThis way, everyone gets the same amount. You can give more answers if you divide 15.40 by more numbers",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Warren (2003)",
        "Explanation":"The learner believes that 3\u00f74=4\u00f73. Plus, the student did not realize that dividing 0.40 by 3 is not the same as dividing 4 by 3"
    },
    {
        "Misconception":"when students mistakenly add two negative numbers, yielding a positive sum, particularly in equations with variables",
        "Misconception ID":"MaE32",
        "Topic":"Properties of number and operations",
        "Example Number":1,
        "Question":"x+1-3+1-1+2-1=6 in the context of putting blocks in and out of a bag",
        "Incorrect Answer":"That\u2019s putting in 4 and taking out 5.\nx+4-5=6\nx=6-5-4\nx=6+9=15",
        "Correct Answer":"x=7",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Tierney & Monk (2008)\np. 189",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly add two negative numbers, yielding a positive sum, particularly in equations with variables",
        "Misconception ID":"MaE32",
        "Topic":"Properties of number and operations",
        "Example Number":2,
        "Question":"Simplify:\n3(6x-4)+2(3x-3)",
        "Incorrect Answer":"18x-12+6x-6=24x+18",
        "Correct Answer":"24x-18",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, S. (2011)\np.192",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly add two negative numbers, yielding a positive sum, particularly in equations with variables",
        "Misconception ID":"MaE32",
        "Topic":"Properties of number and operations",
        "Example Number":3,
        "Question":"The temperature on a chosen date last year was 5 and the temperature on the corresponding day this year is -3. Write an equation and calculate the change in temperature.",
        "Incorrect Answer":"T2-T1=-3-5=8\nThe temperature increased 8 degrees.",
        "Correct Answer":"T2-T1=-3-5=-8\nThere was a decrease of 8 degrees in the temperature",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Peled & Carraher (2008)\np. 312",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly add two negative numbers, yielding a positive sum, particularly in equations with variables",
        "Misconception ID":"MaE32",
        "Topic":"Properties of number and operations",
        "Example Number":4,
        "Question":"-8-3=x",
        "Incorrect Answer":"x=11",
        "Correct Answer":"x=-11",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bishop et. al. (2016)\np. 87",
        "Explanation":""
    },
    {
        "Misconception":"when students interchange minuend and subtrahend, reversing subtraction order, causing calculation errors, especially in equations or expressions",
        "Misconception ID":"MaE33",
        "Topic":"Properties of number and operations",
        "Example Number":1,
        "Question":"Solve for n:\n13n+196=391",
        "Incorrect Answer":"13n+196=391\n13n=196-391\n13n=-195\nn=-15",
        "Correct Answer":"15",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"L Linchevski, N Herscovics (1996)\np. 46",
        "Explanation":"The learner tried to use inverse operations, but did the subtracction in reverse order."
    },
    {
        "Misconception":"when students interchange minuend and subtrahend, reversing subtraction order, causing calculation errors, especially in equations or expressions",
        "Misconception ID":"MaE33",
        "Topic":"Properties of number and operations",
        "Example Number":2,
        "Question":"Solve for n:\n5n+12=3n+24",
        "Incorrect Answer":"5n+12=3n+24\n5n+12\u22125n=3n+24\u22125n\n12=\u22122n+24\n12\u221224=\u22122n+24\u221224\n\u221212=\u22122n\nn=-12\/-2\nn=6",
        "Correct Answer":"n=6",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"L Linchevski, N Herscovics (1996)\np. 46",
        "Explanation":"The learner tried to use inverse operations, but did the subtracction in reverse order. However, the learner got the correct answer. This demonstrates how sometimes incorrect methods can still lead to the correct answer."
    },
    {
        "Misconception":"when students interchange minuend and subtrahend, reversing subtraction order, causing calculation errors, especially in equations or expressions",
        "Misconception ID":"MaE33",
        "Topic":"Properties of number and operations",
        "Example Number":3,
        "Question":"Solve for n:\n16n-215=265",
        "Incorrect Answer":"16n-215-265=0\n16n=265-215=50\nn=50\/16\nn=3.125",
        "Correct Answer":"n=30",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"L Linchevski, N Herscovics (1996)\np. 46",
        "Explanation":"The learner tried to use reverse operations, but got confused with the negative signs and inverted the operation"
    },
    {
        "Misconception":"when students interchange minuend and subtrahend, reversing subtraction order, causing calculation errors, especially in equations or expressions",
        "Misconception ID":"MaE33",
        "Topic":"Properties of number and operations",
        "Example Number":4,
        "Question":"Solve for n:\n19n+67-11n-48=131",
        "Incorrect Answer":"19n+67-11n-48=131\n(11n-19n)+(67-48)=131\n8n-21=131\n8n=131+21\nn=72",
        "Correct Answer":"n=14",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"L Linchevski, N Herscovics (1996)\np. 52",
        "Explanation":"The learner added 19n + 11n instead of subtracting, and for the subtraction 67-48, took the bigger numbers minus the smaller ones, rather than correctly subtracting: 8-7 = 1 in the units place and 6-4 = 2 in the tens place. Plus, the learner did not finish solving the equation for n"
    },
    {
        "Misconception":"when students incorrectly perform operations from left to right, neglecting the proper order of operations",
        "Misconception ID":"MaE34",
        "Topic":"Properties of number and operations",
        "Example Number":1,
        "Question":"Solve: 5+6*10=",
        "Incorrect Answer":"5+6*10=11*10=110",
        "Correct Answer":"65",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Linchevski, L., & Livneh, D. 1999\np. 7",
        "Explanation":"The learner just solved the operations left to right, ignoring the priority of multiplication over addition"
    },
    {
        "Misconception":"when students incorrectly perform operations from left to right, neglecting the proper order of operations",
        "Misconception ID":"MaE34",
        "Topic":"Properties of number and operations",
        "Example Number":2,
        "Question":"Solve: 17-3*5=",
        "Incorrect Answer":"17-3*5=14*5=70",
        "Correct Answer":"2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Linchevski, L., & Livneh, D. 1999\np. 7",
        "Explanation":"The learner just solved the operations left to right, ignoring the priority of multiplication over addition"
    },
    {
        "Misconception":"when students incorrectly perform operations from left to right, neglecting the proper order of operations",
        "Misconception ID":"MaE34",
        "Topic":"Properties of number and operations",
        "Example Number":3,
        "Question":"Evaluate the following expression for y = 3:\n5y-24\u00f7y+10",
        "Incorrect Answer":"5(3)-24\/3+10=15-24\/3+10=-9\/3+10=-3+10=7",
        "Correct Answer":"17",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 219",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly perform operations from left to right, neglecting the proper order of operations",
        "Misconception ID":"MaE34",
        "Topic":"Properties of number and operations",
        "Example Number":4,
        "Question":"Read the following phrase:\n\"three more than twice n\"\nWrite an expression to represent the phrase\nEvaluate the expression you wrote when  n = 31",
        "Incorrect Answer":"2n*3\n6",
        "Correct Answer":"2n+3\n65",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 173",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to represent key aspects and relationships in patterns, as seen in attempts like graphical representations missing key components",
        "Misconception ID":"MaE35",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"On one side of a scale there are 3 pots of jam and a 100-ounce weight. The scale is balanced. What is the weight of 1 pot of jam?",
        "Incorrect Answer":"[Pictorial representation of a scale but nothing more]",
        "Correct Answer":"Schematic representation of the problem, including the scale, plus the data provided: 3 pots of jam, 100-, 200- and 500- ounnce weights.",
        "Question image":"",
        "Learner Answer image":"MaE35-Ex1LA",
        "Correct Answer image":"",
        "Source":"Scheuermann and van Garderen (2008)\np. 3",
        "Explanation":"Susan did generate a representation, which to some degree related to the corresponding problem. She noticed that several components were missing. For this problem, she had to include the weights and the pots of jam, but she only represented the scale."
    },
    {
        "Misconception":"when students struggle to represent key aspects and relationships in patterns, as seen in attempts like graphical representations missing key components",
        "Misconception ID":"MaE35",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"Kyle and Andrew have the same number of candies. Kyle has a bowl of candies and 4 additional candies. Andrew has 14 candies. How many candies are in Kyle's bowl?",
        "Incorrect Answer":"[Graphical representation of Kyle's candies with one bowl and 4 candies aside; also, Andrew's candies represented with 14 dots but nothing else].",
        "Correct Answer":"[A pictorial representation of Kyle's candies with one bowl having 10 pieces in it and 4 aside, representing the 4 additional candies. On the other side, Andrew's candies represented with 14 dots or candy shapes and matching the 4 separated candies from Kyle's with 4 from Andrew's, chowing so that there are 10 in Kyle's bowl because both kids have the same amount of candies, which is 14]",
        "Question image":"",
        "Learner Answer image":"MaE35-Ex2LA",
        "Correct Answer image":"MaE35-Ex2CA",
        "Source":"Scheuermann and van Garderen  (2008)\np. 5",
        "Explanation":"Michael understood what representations were and how to use them, although Michael could depict accurate representations of the relationships in the problems, he was not consistently identifying or depicting all the relationships."
    },
    {
        "Misconception":"when students struggle to represent key aspects and relationships in patterns, as seen in attempts like graphical representations missing key components",
        "Misconception ID":"MaE35",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"Joe rod his bike 2 miles to the bus station. He then boarded a bus that took him 12.5 miles. When he got off the bus, he walked 1 more mile to get to his friend's house. How far did Joe travel in all?",
        "Incorrect Answer":"[The learner drew a bike and a bus station, writing \"2 miles\" in between]",
        "Correct Answer":"A schematic representation including the bike, the bus station and the data provided in the statement: 2 miles by bike, 12.5 miles by bus, and 1 mile walked.",
        "Question image":"",
        "Learner Answer image":"MaE35-Ex3LA",
        "Correct Answer image":"",
        "Source":"Scheuermann and van Garderen  (2008)\np. 4",
        "Explanation":"Michael's representation is related to the problem, however he missed some key components to better illustrate the data of the problem and its solution."
    },
    {
        "Misconception":"when students struggle to represent key aspects and relationships in patterns, as seen in attempts like graphical representations missing key components",
        "Misconception ID":"MaE35",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"Cody has 24 marbles. Joseph has 3 equal bags of marbles and 9 individual marbles. After Joseph took 9 marbles out of his bags and gave them to Ariana, Joseph and Cody had the same amount of marbles. How many marbles were in each of Joseph's bags?",
        "Incorrect Answer":"[Graphic representation: Nine marbles taken out of the bag, Joseph and Cody's marbles are depicted as being equal sets, additional 9 marbles are shown as being removed]",
        "Correct Answer":"The same pictorial representation provided by the learner, but including as well the return of 9 marbles taken out of the bag, division of the 24 marbles into 3 equal sets.",
        "Question image":"",
        "Learner Answer image":"MaE35-Ex4LA",
        "Correct Answer image":"MaE35-Ex4CA",
        "Source":"Scheuermann and van Garderen  (2008)\np. 7",
        "Explanation":"The laerner's representation is missing the return of 9 marbles taken out of the bag, and the division of the 24 marbles into 3 equal sets."
    },
    {
        "Misconception":"when students struggle to accurately represent problems using graphical notation, misunderstanding the purpose of the representation",
        "Misconception ID":"MaE36",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"Logan and Luis had the same amount of marbles after Logan gave 12 individual marbles to Haley. Logan had 5 equal bags. Luis had 3 marbles. How many marbles were in one of Logan's bags?",
        "Incorrect Answer":"[Graphic representation: The learner drew 4 lines of circles trying to represent the marbles only. On the first line, he drew 12, on the second line he drew 3, on the third line he drew 5, and on the fourth line he drew 3 again. There's no representation for the bags, nor labels to specify the marbles that belong to Logan or Luis.]",
        "Correct Answer":"Inferring that Logan's bags have equal amounts of marbles, each bag should have 3 (15 marbles in total, because 12+3=15 -12 he gave to Haley, plus 3 he was left with). An accurate representation would contain a drawing to represent each of Logan's bag, the 12 individual marbles he gave to Haley and the 3 marbles that both Logan and Luis had after the sharing.",
        "Question image":"",
        "Learner Answer image":"MaE36-Ex1LA",
        "Correct Answer image":"",
        "Source":"Scheuermann and van Garderen (2008)\np. 4 ",
        "Explanation":"The learner did not understand the purpose of the representation, drawinng only some marbles but with no relationship with the problem"
    },
    {
        "Misconception":"when students struggle to accurately represent problems using graphical notation, misunderstanding the purpose of the representation",
        "Misconception ID":"MaE36",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"The cafeteria staff prepares three kinds of sandwiches for the bus trip. They make 100 of each kind. How many sandwiches do they make all together?",
        "Incorrect Answer":"[The learner represented the problem with a bar graph, labeled on the vertical axis with numbers 1, 2, 3, 4, 5, 6. The first graph size is 4, the second bar seems to be size 6, the third bar is size 4, the fourth bar is size 3 and there are 4 more bars which sizes are not clear and their shapes are irregular. The learner wrote scribbles instead of a label on the x-axis]",
        "Correct Answer":"[A graphic representation of three spots containing 100 sandwiches each, like: {100 tuna sandwiches} {100 jam sandwiches} {100 peanut butter sandwiches}]",
        "Question image":"",
        "Learner Answer image":"MaE36-Ex2LA",
        "Correct Answer image":"",
        "Source":"Scheuermann and van Garderen (2008)\np. 3",
        "Explanation":"The Bar graph provided by the learner does not contain any information found in the problem and is a poor choice of representation"
    },
    {
        "Misconception":"when students struggle to accurately represent problems using graphical notation, misunderstanding the purpose of the representation",
        "Misconception ID":"MaE36",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"Leroy bought some pants for a total cost of $24.03. The sales tax was $1.53. What was the price of the pants without the sales tax?",
        "Incorrect Answer":"[The student drew a paint (\"pants\" spelled incorrectly) can to represent the mathematics problem]",
        "Correct Answer":"[A drawing of some pants or jeans labeled \"$24.03\" and \"Tax $1.53\" and a representation in the diagram of the division with decimals: 24.03\u00f71.53=15.7 the prices without the tax was $15.7]",
        "Question image":"",
        "Learner Answer image":"MaE36-Ex3LA",
        "Correct Answer image":"",
        "Source":"Scheuermann and van Garderen (2013)\np. 3",
        "Explanation":"The learner does not understand the purpose of the representation and drew a paint can instead of pants"
    },
    {
        "Misconception":"when students struggle to accurately represent problems using graphical notation, misunderstanding the purpose of the representation",
        "Misconception ID":"MaE36",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"Marcus is at the music store buying guitar strings for his band. If there are 3 guitar players in the band, and each guitar has 6 strings, how many things should Marcus buy?",
        "Incorrect Answer":"[The learner's answer is a graphic representation of only a guitar with 6 strings]",
        "Correct Answer":"A diagram of 3 guitars with 6 strings each, or 3 sets of 6 strings each, like:\n||||||   ||||||   ||||||",
        "Question image":"",
        "Learner Answer image":"MaE36-Ex4LA",
        "Correct Answer image":"MaE36-Ex4CA",
        "Source":"Scheuermann and van Garderen (2013)\np. 4",
        "Explanation":"The learner's picture represents the guitar, but seems to misunderstand the purpose of representinng the problem, because the student drew only one guitar and did not relate it to the problem."
    },
    {
        "Misconception":"when students struggle to interpret graph scales accurately",
        "Misconception ID":"MaE37",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"The bar graph below [graph showing two bars, the bar at the left side represents 8125 and the one at the right represents 8625. The y-axis starts at 0 but it has a break sign that takes the axis to 8000, increasing by 125 until 9250. On the x-axis the column on the left side is labeled with 1 and the bar at the right side is labeled with 2. The x- axis name is \"Day\" and the y-axis name is \"Number of people\". The title of the graph is \"Circus Attendance\"] shows attendance at a circus over two days.\nHow many MORE people attended the circus on Day 2 than on Day 1?\nExplain why it appears that three times as many people attended the circus on Day 2 as on Day 1.",
        "Incorrect Answer":"It increases by small numbers making it look bigger than big numbers",
        "Correct Answer":"500 more people attended the circus on Day 2 than on Day 1\nIt appears that three times as many people attended the circus on Day 2 as in Day 1, because the graph has a break in the scale and is misleading",
        "Question image":"MaE37-Ex1Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 207 - 208",
        "Explanation":"The learner miss interprets the graph-scale and is not able to provide a numeric response"
    },
    {
        "Misconception":"when students struggle to interpret graph scales accurately",
        "Misconception ID":"MaE37",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"Use your ruler to solve this problem.\nOn the grid below [an empty cartesian plane is provided, that goes from -6 to 6 on each of the axes, increasing by one], graph the points (-2,4), (3,4), (2,2) and (-3,2)\nNow connect the points in the order listed above to make a polygon. Write the name of the polygon you drew.",
        "Incorrect Answer":"Learners plotted the ordered pairs (-2, 0), (3, 0), and (0, 4) [The graph only shows the dots of the ordered pairs, which are not connected to make the shape as requested]",
        "Correct Answer":"A quadrilateral or parallelogram [the correct graph contains the dots of the ordered pairs plotted and lines connecting the dots in the same order as the ordered pairs are provided, making the shape of a quadrilateral]",
        "Question image":"MaE37Ex2Q",
        "Learner Answer image":"MaE37-Ex2LA",
        "Correct Answer image":"MaE37-Ex2CA",
        "Source":"Bush, 2011\np. 243",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to interpret graph scales accurately",
        "Misconception ID":"MaE37",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"The bar graph below [graph showing two bars, the bar at the left side represents 8125 and the one at the right represents 8625. The y-axis starts at 0 but it has a break sign that takes the axis to 8000, increasing by 125 until 9250. On the x-axis the column on the left side is labeled with 1 and the bar at the right side is labeled with 2. The x- axis name is \"Day\" and the y-axis name is \"Number of people\". The title of the graph is \"Circus Attendance\"] shows attendance at a circus over two days.\nHow many MORE people attended the circus on Day 2 than on Day 1?\nExplain why it appears that three times as many people attended the circus on Day 2 as on Day 1.",
        "Incorrect Answer":"The graph starts at 8,000",
        "Correct Answer":"500 more people attended the circus on Day 2 than on Day 1\nIt appears that three times as many people attended the circus on Day 2 as in Day 1, because the graph has a break in the scale and is misleading",
        "Question image":"MaE37-Ex3Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 207 - 208",
        "Explanation":"The learner has difficulty interpreting the graph-scale and is only able to identify the number at which the graph seems to start\n"
    },
    {
        "Misconception":"when students struggle to interpret graph scales accurately",
        "Misconception ID":"MaE37",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"Use your ruler to solve this problem.\nOn the grid below, graph the points (-2,4), (3,4), (2,2) and (-3,2)\n[An empty cartesian plane is provided, that goes from -6 to 6 on each of the axes, increasing by one]\nNow connect the points in the order listed above to make a polygon. Write the name of the polygon you drew.",
        "Incorrect Answer":"Learners plotted the ordered pairs (2,-1), (4,2), (2,4), (-2,4), (-3,2), and (-2,-1) [The Graph only shows the ordered pairs, no shape]",
        "Correct Answer":"A quadrilateral or parallelogram",
        "Question image":"MaE37-Ex4Q",
        "Learner Answer image":"MaE37-Ex4LA",
        "Correct Answer image":"MaE37-Ex4CA",
        "Source":"Bush, 2011\np. 243",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to grasp the concept that a linear function represents a consistent rate of change",
        "Misconception ID":"MaE38",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"Water is being pumped into a swimming pool. The graph indicates that the pool held 6 gallons of water after 3 minutes, 10 gallons after 5 minutes, and 18 gallons after 9 minutes. Find the slope of the line.",
        "Incorrect Answer":"[The learner counted 3 boxes along the base of the stair step and 2 boxes along the side of the stair step and recorded the slope as 2\/3. She repeated this procedure, using the points (3,6) and (5,10). She found the run by counting 2 boxes along the base of her second stair step, and she apparently determined the rise by rounding the number of boxes along the side of the stair step to 1 box. She recorded a second slope of 1\/2.]\nIt has different amounts on the sides and the rise and the runs, the slope for this line changed.\n[The learner is then asked to draw a line with a slope that did not change. She plotted a point on the graph, went up 4 and over 2, plotted a new point, went up 4 and over 2, plotted a point, and then connected the points.]",
        "Correct Answer":"The slope is 2 gallons\/min",
        "Question image":"",
        "Learner Answer image":"MaE38-Ex1LA",
        "Correct Answer image":"",
        "Source":"Lobato, 2010\np. 66",
        "Explanation":"This process suggests that she did not connect linearity and proportionality. Instead, she apparently associated slope with the idea of stairs of identical size rather than with a ratio that is invariant despite changes in particular \u201crise\u201d and \u201crun\u201d values."
    },
    {
        "Misconception":"when students struggle to grasp the concept that a linear function represents a consistent rate of change",
        "Misconception ID":"MaE38",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"The clown walks 10 centimeters in 4 seconds. How far will the frog walk in 8 seconds if the frog travels at the same speed as the clown?",
        "Incorrect Answer":"Clown: 10\/4\nFrog: 20\/8\nThe frog is actually going faster than the clown because is going farther. Both numbers on the frog\u2019s \u201cside\u201d of the proportion are bigger than the corresponding numbers on the clown\u2019s side",
        "Correct Answer":"For this linear function, we use the slope to calculate the distance the frog walks: 20 cm",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Lobato, 2010\np. 66",
        "Explanation":"This is a case of univariate reasoning and an example of whole number reasoning, as students don't conceive that something in the situation remains the same while the distance and time values are changing, not connecting thence linearity with proportionality"
    },
    {
        "Misconception":"when students struggle to grasp the concept that a linear function represents a consistent rate of change",
        "Misconception ID":"MaE38",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"From the graph presented, which group is growing faster at the age of 14?\n[The graph represents the age of boys and girls on the x-axis and their average weight in kilograms, on the y-axis. The graph goes from 0 to 16 on the x-axis and from 0 to 70 on the y-axis. There are two lines: one dashed line representing the Boy's average weight in kilograms, in function of their age in years, and one solid line representing the Girl's average weight in kilograms, in function of their age in years. Both lines start resembling a straight line, but start changing into a curve-shape at 11 years]",
        "Incorrect Answer":"Em, I wrote Girls. Because they weigh more than boys and this means that they could be taller than \u2026they could be eating more. Yeah, I know [that the gradient is steeper] but it is not an area it is just for one point",
        "Correct Answer":"The boys are growing faster, because at the given point the line is steeper for boys than for girls",
        "Question image":"MaE38-Ex3Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Hadjidemetriou, C. & Williams, J.\n\np. 11",
        "Explanation":"The graph represents the age of boys and girls on the x-axis and their average weight in kilograms, on the y-axis. The learner interpreted that the group that is growing faster is the one that is heavier on the graph.\nThe learner interpreted that the group that is growing faster is the one that is heavier on the graph at the given age of 14, her argument was: \"I just thought that cause they weigh more they have to, they are growing faster\". The interviewer\u2019s attempt to urge the pupil to read the graph as a whole failed again since the pupil was focusing only on the two points  and not on the relative steepness of the two curves"
    },
    {
        "Misconception":"when students struggle to grasp the concept that a linear function represents a consistent rate of change",
        "Misconception ID":"MaE38",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"Crystal placed a bucket under a faucet and collected 6 ounces of water in 20 minutes. Joanne placed a bucket under a second faucet and collected 3 ounces of water in 10 minutes. Were the faucets dripping equally fast or was one dropping faster than the other?",
        "Incorrect Answer":"Crystal's faucet is dripping more slowly than Joanne's because it took its time. \nNo, Crystal's faucet is dripping faster because both amounts, time and water, for Crystal's faucet are greater than the corresponding amounts for Joanne's faucet.",
        "Correct Answer":"The faucets were dripping equally fast, because 6\/20=3\/10 and both proportions are linear relationships",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Lobato, J. (2010)\n\np. 19",
        "Explanation":"This response indicates that she did not form a ratio between the amount of water and the amount of time"
    },
    {
        "Misconception":"when students confuse linear and exponential functions' properties and representations.",
        "Misconception ID":"MaE39",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"Determine whether a situation of 3^(x-1) repeated 6 times would produce a greater yield than 2^(x-1) repeated 64 times. Do you predict this situation will be linear or exponential? How do you know? What did you think about to help you make this prediction?",
        "Incorrect Answer":"The second situation will produce a greater yield, because it is repeated more thimes. I predict this situation would be linear, because x-1 is a linear relationship. To help me make this prediction, I thought about an example from previous classes, where x-1 was a linear situation.",
        "Correct Answer":"The situation will be exponential in both cases because each term is raised to a power that includes a variable x.",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"LA Kasmer, OK Kim  (2012)\np. 12",
        "Explanation":"The learner gets confused between a linear and an exponential function, because the exponent includes a linear expression."
    },
    {
        "Misconception":"when students confuse linear and exponential functions' properties and representations.",
        "Misconception ID":"MaE39",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"Consider a coin collection with an initial value of $2,500 that increased in value by 6% each year. Generate a table showing the value of the collection each year for 10 years and determine the growth factor of this situation. Do you predict the increase in coin value would be linear, exponential, or something else? Explain why.",
        "Incorrect Answer":"The increase in coin value would be something else. The reason it's not linear is it doesn't always increase the same amount. The reason it's not exponential is the #'s don't double or triple. In this case every year goes by and the value increases, but 6% comes out of the higher value every year to add on.",
        "Correct Answer":"Exponential because it's not going at a constant rate and its growth factor is 1 .06 from 2500 to 2650 and also 2650 to 2809 has a growth factor of 1.06. So if it keeps multiplying by 1.06 then its exponential growth",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"LA Kasmer, OK Kim  (2012)\np. 7",
        "Explanation":"This vignette demonstrates the prediction question afforded the student an opportunity to make an explicit connection to attributes of linear (\"doesn't always increase the same amount\") and exponential (\"the #s don't double or triple\") relationships. Although the response is not mathematically accurate, as this in fact is considered an exponential relationship, the prediction response was coded as logical because it revealed an initial understanding of compound growth. The student seemed to regard exponential growth only as whole number growth factors and perhaps those that only double and triple, but recognized the addition of 6% value each year from the previous year."
    },
    {
        "Misconception":"when students confuse linear and exponential functions' properties and representations.",
        "Misconception ID":"MaE39",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"Determine whether a situation that doubles x amount of times would yield more rubas than adding 5x amount of times and beginning with 20 rubas.\nPredict whether this situation will be a better offer for the peasant or the king. How do you know?",
        "Incorrect Answer":"Adding 5x will make more, because 5 is bigger than 2 (doubles)",
        "Correct Answer":"Doubling x will yield more rubas than adding 5x amount, because doubling is exponential and adding 5x is a linear relationship",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"LA Kasmer, OK Kim  (2012)\np. 12",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse linear and exponential functions' properties and representations.",
        "Misconception ID":"MaE39",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"Explore growth of paper ballots as they are repeatedly cut in half. If Alejandro makes ten cuts, can you predict how many ballots Alejandro might have? What is your reasoning?",
        "Incorrect Answer":"Yes. If you set up an equation like 2x then you put 10 in for x and 2 times 10 equals 20 and find the answer 20. All you have to do is set up the equation",
        "Correct Answer":"2^n=2^10=1024",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"LA Kasmer, OK Kim (2012)\np. 14",
        "Explanation":"As is apparent from this example, the student relied solely on a mathematical calculation [multiplying 2 by 10] to arrive at the response to the prediction question\n"
    },
    {
        "Misconception":"when students misinterpret slope signs in equations versus their upward or downward trends in graphs.",
        "Misconception ID":"MaE40",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"Make a table of values that would produce the function seen on the graph",
        "Incorrect Answer":"m=(3-0)\/(0-25)=3\/-2.5\ny=(-3\/2.5)x-3\nx    |   y\n0   | -3\n1   | -2\n2   | -1\n2.5 |   0",
        "Correct Answer":"One example of a possible correct answer is:\nx    |   y\n0   | -6\n1   | -5\n2   | -4\n 3   |  -3\n 6   |   0\n 10   |  4",
        "Question image":"MaE40-Ex1Q",
        "Learner Answer image":"MaE40-Ex1LA",
        "Correct Answer image":"",
        "Source":"Kalchman, M., & Koedinger, K. R.  2005\n\np. 3-8",
        "Explanation":"The student mislabeled the coordinate for the y-intercept (0, 3) rather than (0, \u20133). This led him to make an error in calculating \u2206y by subtracting 0 from 3 rather than from \u20133. In so doing, he arrived at a value for the slope of the function that was negative\u2014an impossible solution given that the graph is of an increasing  linear function. The student did not recognize the inconsistency between the positive slope of the line and the negative slope in the equation.\nThe table of values does not represent a linear function. That is, there is not a constant change in y for every unit change in x. The first three coordinates in the student\u2019s table were linear, but he then recorded (2.5, 0) as the fourth coordinate pair rather than (3, 0), which would have made the function linear. He appears to have estimated and recorded coordinate points by visually reading them off the graph without regard for whether the final table embodied linearity. The student did not realize that the equation he produced, y=(-3\/2.5)x-3, translates not only into a decreasing line, but also into a table of numbers that decreases by -3\/2.5 for every positive unit change in x."
    },
    {
        "Misconception":"when students misinterpret slope signs in equations versus their upward or downward trends in graphs.",
        "Misconception ID":"MaE40",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"This line [pointing to a graph of y=x that goes from (0,0) to (10,10); the x- and y- axes are labeled as 0, 2, 4, 6, 8, 10] has a certain steepness to it... If you had to give a number to this steepness, what would you give it? Look at these numbers (pointing to the corresponding table of values).\nTable of values\nx   |   y\n-4  |  -4\n-2  |  -2\n0  |  0\n2  |  2\n4  |  4",
        "Incorrect Answer":"I would give it a steepness of -2",
        "Correct Answer":"The steepness is +1",
        "Question image":"MaE40-Ex2Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kalchman, M., & Koedinger, K. R.  2005 \np. 30",
        "Explanation":""
    },
    {
        "Misconception":"when students misinterpret slope signs in equations versus their upward or downward trends in graphs.",
        "Misconception ID":"MaE40",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"Pairs of students use prepared spreadsheet files to work with a computer screen such as that seen in the figure [the figure is a screenshot  of a spreadsheet showing a quadratic function represented with a graph on the left side of the window, and its parameters in columns on the right side of the window, so that students are able to change the equation parameters by editing the cells of the right side of the spreadsheet].\nStudents are asked to change specific parameters in the function y = x^2 to make it curve down and go through a colored point that is in the lower right quadrant.\nHow would you change the parameters to make the curve go through the colored point?",
        "Incorrect Answer":"Using minus in the exponent",
        "Correct Answer":"Making the coefficient of the independent variable a negative number",
        "Question image":"MaE40-Ex3Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kalchman, M., & Koedinger, K. R.  2005\np. 36",
        "Explanation":"The learners' first intuition is often to make the exponent rather than the coefficient negative. When they make that change, they are surprised to find that the graph changes its shape entirely and that a negative exponent will not satisfy their needs. By trying a number of other possible  alterations (persevering), some students discover that they need to change the coefficient of x^2 rather than the exponent to a negative number to make the function curve down"
    },
    {
        "Misconception":"when students misinterpret slope signs in equations versus their upward or downward trends in graphs.",
        "Misconception ID":"MaE40",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"How did you make a straight line come down or change direction?",
        "Incorrect Answer":"Using minus in the number that is alone in the equation, the one that is not multiplied by x",
        "Correct Answer":"Changing the sign of the slope, the coefficient of the independent variable.",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kalchman, M., & Koedinger, K. R.  2005\np. 37",
        "Explanation":"The learner left the positive sign to the slope, not relating that the line comes down by the effect of a negative slope"
    },
    {
        "Misconception":"when students struggle to connect different representations of the same function (graph, equation, table).",
        "Misconception ID":"MaE41",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"What shape would the graph of the function y=x^2+1 have? Elaborate a data table and sketch the graph.",
        "Incorrect Answer":"[Image]",
        "Correct Answer":"Table\nx | -1.2 | -1 | -0.8 | -0.6 | -0.4 | -0.2 | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 | 1.2\ny  2.44 | 2 | 1.64 | 1.36 | 1.16 | 1.04 | 1 | 1.04 | 1.16 | 1.36 | 1.64 | 2 | 2.44\n[Graph in the Image]",
        "Question image":"",
        "Learner Answer image":"MaE41-Ex1LA",
        "Correct Answer image":"MaE41-Ex1CA",
        "Source":"Kalchman, M., & Koedinger, K. R.  2005\np. 358",
        "Explanation":"The learner seemed to read incorrectly the numbers from the x- and y- axes, rounding the numbers, and did not see the connection between the graph and the data table"
    },
    {
        "Misconception":"when students struggle to connect different representations of the same function (graph, equation, table).",
        "Misconception ID":"MaE41",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"For the function f(x)=2x^2+3x-1, (i) make a table of data points and (ii) sketch a graph of the data",
        "Incorrect Answer":"x   |    y\n0   |    1\n1  |   8\n1.5    | 11.5  \n5   |  36\n-1  |  -6 \n[No graph provided]",
        "Correct Answer":"An example of possible correct answer is:\nx   |   y\n-4  | 19\n-2  | 1  \n  0  |  -1 \n2  | 13\n4  | 43\n[The graph is a curved line that represents the parabolla given by the equation f(x)=2x^2+3x-1]",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"MaE41-Ex2CA",
        "Source":"Kalchman, M., & Koedinger, K. R.  2005\np. 3-8",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to connect different representations of the same function (graph, equation, table).",
        "Misconception ID":"MaE41",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"For the function f(x)=2x^2+3x-1, (a) make a sketch of the graph of the function's inverse (b) make a table of data points that represents the inverse function, and (c) find the explicit equation for the inverse function",
        "Incorrect Answer":"(a) \ny  |  x\n0  |   \n(b)\n??\n(c)\n2x^2+3x-1=0\n x=[-3+-[9-4(2)(-1)]^(1\/2)]\u00f7[(2)(2)]=[-3+-(17^(1\/2))]\u00f74",
        "Correct Answer":"(a) The sketch of the graph of the function's inverse is a curve representing a square root.\n(b) Same data table for the original function, with the variables inverted.\n  y  |  x\n 19  |  -4\n   1  |  -2\n  -1  | 0  \n 13 | 2 \n43 | 4\nThese points can be used to sketch the graph\nThe inverse function for a quadratic is a square root function:\nf(x)=y=2x^2+3x+1\nx=[(1\/2)y+(1\/16)]^(1\/2)-(3\/4)\nf^-1(x)=[(1\/2)y+(1\/16)]^(1\/2)-(3\/4)",
        "Question image":"",
        "Learner Answer image":"MaE41-Ex3LA",
        "Correct Answer image":"MaE41-Ex3CA",
        "Source":"Bair, S. L., & Rich, B. S.  2011\np. 14",
        "Explanation":"The learner confused the data table with the graph, and did not have any idea on how to make the sketch of the graph of the function's inverse. Instead of finding the equation of the inverse function of f(x), the learner used the general equation trying to solve the quadratic function, which shows a lack of understanding of the formula representation of a function and its inverse"
    },
    {
        "Misconception":"when students struggle to connect different representations of the same function (graph, equation, table).",
        "Misconception ID":"MaE41",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"Graph the function 4x+1.",
        "Incorrect Answer":"The slope, which is 4, the y-intercept, which is 1, ...and... the x-intercept, which is 1\/4, so we've found everything. [The learner did not make the graph]",
        "Correct Answer":"f(x)=4x+1 and the correct graph shown in the image",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"MaE41-Ex4CA",
        "Source":"Kalchman, M., & Koedinger, K. R. (2005)\np. 20",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse linear relationships with direct proportions, believing that because a linear function increases or decreases at a constant rate, it must be a direct proportion.",
        "Misconception ID":"MaE42",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":1,
        "Question":"Sue and Julie were running equally fast around a track. Sue started first. When she had run 9 laps, Julie had run 3 laps. When Julie completed 15 laps, how many laps had Sue run?",
        "Incorrect Answer":"9\/3=x\/15, so x=45",
        "Correct Answer":"Sue had run 21 laps when Julie completed 15 laps",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"W Van Dooren, D De Bock, A Hessels, D Janssens (2004)",
        "Explanation":"The learner answered by means of a proportion, while the problem is a linear relationship, because both Sue and Julie had run a distance before observing them."
    },
    {
        "Misconception":"when students confuse linear relationships with direct proportions, believing that because a linear function increases or decreases at a constant rate, it must be a direct proportion.",
        "Misconception ID":"MaE42",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":2,
        "Question":"Sara has made several purchases from a mail-order company.  She has found that the company charges $12.90 to ship an 8-kg package, $6.40 to ship a 3-kg package, and $9.00 to ship a 5-kg package.  Sara decides that the company must be using a  simple rule to determine how much to charge for shipping.  Help her figure out how much it would most likely cost to ship a 1-kg package and how much each additional kilogram would cost.",
        "Incorrect Answer":"I will calculate the cost per kilogram for each package:\n12.9\/8=1.6125\u00a0dollars\u00a0per\u00a0kg, for the 8-kg package\n6.40\/3=2.1333\u00a0dollars\u00a0per\u00a0kg, for the 3-kg package\n9.00\/5=1.80\u00a0dollars\u00a0per\u00a0kg, for the 5-kg package\nThe average is: (1.6125+2.1333+1.80)\/3=1.8486\u00a0dollars\u00a0per\u00a0kg\nThe cost to ship 1-kg package is: (1.8486\u00a0dollars\/kg)*(1\u00a0kg)=1.8486\u00a0dollars\nIt will cost $1.85 to ship a 1-kg package, and each additional kilogram will cost $1.85",
        "Correct Answer":"A linear function (y = 1.30x + 2.50) fits the three given values, the cost to ship a 1-kg package would be $3.80, and the cost for each additional kilogram is $1.30 (the slope).",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kilpatrick, J., Swafford, J. O., & Findell, B. (2001)\np. 415",
        "Explanation":"The learner tried to find a simple, constant rate per kilogram by averaging the costs and weights given, considering the problem as a direct proportion while it is a linear relationship."
    },
    {
        "Misconception":"when students confuse linear relationships with direct proportions, believing that because a linear function increases or decreases at a constant rate, it must be a direct proportion.",
        "Misconception ID":"MaE42",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":3,
        "Question":"Two carnivals are coming to town. You and your friend decide to go to different carnivals. The carnival that you attend charges $10 to get in and an additional $2 for each ride. The carnival your friend attends charges $6 to get in, but each additional ride costs $3. If the two of you spent the same amount of money, how many rides could each of you have ridden?",
        "Incorrect Answer":"If we spent the same amount of money, then I can calculate the money spent by each one, until it is equal and so I get the rides.\nRides | Money I spent | Money spent by my friend\n1       |             2          |                      3                 \n  2       |             4          |                      6                   \n  3       |             6          |                      9                   \nI would have ridden 3 rides, and my friend would have ridden 2 rides",
        "Correct Answer":"For my carnival, the total cost is: 10+2x\nFor my friend's carnival, the total cost is: 6+3y\nAs we spent the same money: 10+2x=6+3y\nThere are two possible solutions: If I took 1 ride, my friend took 2 rides. If I took 4 rides, my friend took 4 rides.",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kilpatrick, J., Swafford, J. O., & Findell, B. (2001)\np. 291",
        "Explanation":""
    },
    {
        "Misconception":"when students confuse linear relationships with direct proportions, believing that because a linear function increases or decreases at a constant rate, it must be a direct proportion.",
        "Misconception ID":"MaE42",
        "Topic":"Patterns, relationships, and functions",
        "Example Number":4,
        "Question":"You have two gears on your table. Gear A has 8 teeth, and gear B has 12 teeth. Answer the following questions. \nDevise  a way to keep track of gear B's revolutions",
        "Incorrect Answer":"x  |  y\n0  |  5\n1   | 12\n2   | 19\n3   | 26\n5   | 40\n6   | 47\nOn the x side, it's going up by ones, and on the other side, it's going up by ... sevens. It's a pattern, but this isn't linear. It has to\n be a pattern that doesn't change. You know? It has to be like 3, 6, 9, like that.",
        "Correct Answer":"Each time gear A makes one revolution, gear B moves 5 spaces. This is a linear function that can be modeled with the equation:\ny=7x+5",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ellis, A. B. (2009)",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle with plotting points, reversing the x- and y-coordinates",
        "Misconception ID":"MaE43",
        "Topic":"Algebraic representations",
        "Example Number":1,
        "Question":"Use your ruler to solve this problem.\nOn the grid below [An empty cartesian plane is provided, that goes from -6 to 6 on each of the axes, increasing by one], graph the points (-2,4), (3,4), (2,2) and (-3,2)\nNow connect the points in the order listed above to make a polygon. On the line below, write the name of the polygon you drew.",
        "Incorrect Answer":"[The learner plotted: (4,-2), (4,3), (2,2), and (2,-3)] \nIt's a rhombus",
        "Correct Answer":"A quadrilateral or parallelogram [the correct graph contains the dots of the ordered pairs plotted and lines connecting the dots in the correct order that the ordered pairs are provided, making the shape of a quadrilateral which base goes from x = -3 to x = 2 (5 units long), and its height goes from y = 2 to y = 4 (2 units high)]",
        "Question image":"MaE43-Ex1 Q",
        "Learner Answer image":"MaE43-Ex1LA",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 243",
        "Explanation":"Although the leaner correctly identified the paralellogram, the shape the student obtained has different dimensions from the correct one, given that the student reversed the x- and y-coordinates. The student's quadrilateral gas a base of  units (from x = 4, to x = 4) and it's 5 units high (from y = -3, to y = 2)"
    },
    {
        "Misconception":"when students struggle with plotting points, reversing the x- and y-coordinates",
        "Misconception ID":"MaE43",
        "Topic":"Algebraic representations",
        "Example Number":2,
        "Question":"On a Coordinate plane, plot the ordered pairs (5,8), ( 2,2), (3,4), (4,6), and (7,8)",
        "Incorrect Answer":"[The learners elaborated a graph plotting the coordinate pairs: (8,5), (2,2), (4,3), (6,4), and (8,7)]",
        "Correct Answer":"[A graph where the correct ordered pairs are plotted as required]",
        "Question image":"MaE43-Ex2Q",
        "Learner Answer image":"MaE43-Ex2LA",
        "Correct Answer image":"MaE43-Ex2CA",
        "Source":"Bush, 2011\np. 205",
        "Explanation":"The learners reversed the x- and y- coordinates, plotting the inverted values on the coordinate plane"
    },
    {
        "Misconception":"when students struggle with plotting points, reversing the x- and y-coordinates",
        "Misconception ID":"MaE43",
        "Topic":"Algebraic representations",
        "Example Number":3,
        "Question":"Use your ruler as a straightedge\nOn the coordinate plane below, graph the line with the slope of 2\/3 that passes through the point (-3,-4)\n[Coordinate plane from -6 to 6 both for x- and y- axes is provided to the learner]",
        "Incorrect Answer":"[Learner's response is a linear graph that represents the function: f(x)=(2\/3)x-1\/3, from x=-4 to x=4]",
        "Correct Answer":"[The plot of f(x)=(2\/3)x-2 from x=-6 to 6 from y=-6 to 6]",
        "Question image":"MaE43-Ex3Q",
        "Learner Answer image":"MaE43-Ex3LA",
        "Correct Answer image":"MaE43-Ex3CA",
        "Source":"Bush, 2011\np. 187",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle with plotting points, reversing the x- and y-coordinates",
        "Misconception ID":"MaE43",
        "Topic":"Algebraic representations",
        "Example Number":4,
        "Question":"Write down an example of a function. Represent that same function in four different ways",
        "Incorrect Answer":"The learner represented the function with the equation: x=1(y)+5\nWith the statement: \"Every hour you earn $5 more\"\nAnd with a data-table and a graph\nData table:\nx | 1 |  2  |  3  |  4  | 5  \ny | 5 | 10 | 15 | 20 | 25\nOn the graph, the learner plotted the y-data on the horizontal axis and the x-data on the vertical one",
        "Correct Answer":"For the example provided by the student, the equation should be: y=5x\nData table:\nx | 1 |  2  |  3  |  4  | 5  \ny | 5 | 10 | 15 | 20 | 25\nGraph: a straight line or a scatter plot with the x-data on the horizontal axis and the y-data on the vertical axis",
        "Question image":"",
        "Learner Answer image":"MaE43-Ex4LA",
        "Correct Answer image":"MaE43-Ex4CA",
        "Source":"",
        "Explanation":"The learner understands the concept of a function and the different ways it can be represented, however, reversed the variables both in the equation and on the graph."
    },
    {
        "Misconception":"when students struggle to grasp the concept of independent and dependent variables",
        "Misconception ID":"MaE44",
        "Topic":"Algebraic representations",
        "Example Number":1,
        "Question":"Ellie is planting different numbers of seeds in flower pots. The graph below shows the size, in inches, of each pot, y, Ellie uses to plant x seeds\n[The graph is a straight line with a positive slope. It starts at (0,0). There are 5 points plotted that make the straight line: (1,3), (2,5), (3,7), (4,9), and (5,11)]\nAccording to the graph, what is the size, in inches, of the flower pot Ellie uses to plant 4 seeds?\nWhat is the difference, in inches, of the size of the flower pot Ellie uses to plant 4 seeds compared to the flower pot that Ellie uses to plant 2 seeds?",
        "Incorrect Answer":"1.5 inches\nThe graph doesn't show a data for 2 seeds",
        "Correct Answer":"9 inches when she plants 4 seeds. The difference is 4 inches",
        "Question image":"MaE44-Ex1Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\n\np. 191-192",
        "Explanation":"The graph shows the required data, but learners reversed x- and y- coordinates"
    },
    {
        "Misconception":"when students struggle to grasp the concept of independent and dependent variables",
        "Misconception ID":"MaE44",
        "Topic":"Algebraic representations",
        "Example Number":2,
        "Question":"In some states, a deposit is charged on aluminum pop cans and is refunded when the cans are returned. In New York, the deposit is 5 cents a can.\nWhat would be the refund for returning 6 (10 or 12) cans?\nDescribe how the store owner would figure the amount of refund for any number of returned cans.",
        "Incorrect Answer":"For 6 cans, the refund would be 30 cents, 50 cents for 10 and 60 cents for 12.\nThe store owner would have to add as plenty of times the 5 cents per can, according to the total amount of cans. For example, for 6 cans I added: 5 + 5 + 5 + 5 + 5 + 5 = 30 cents\nIt depends on the refund he wants to obtain, the amount of cans he has to return.",
        "Correct Answer":"refund = 5x, (being x the amount of cans)\n6 cans: 30 cents, 10 cans: 50 cents, 12 cans: 60 cents\nThe owner has to multiply the amount of cans times the 5 cents for each one, as in the equation provided, for the refund obtained depends on the amount of returned cans",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford & Langrall (2000)",
        "Explanation":"The learner is thinking additively, because of a confusion among the variables: the students lacks understanding the concepts of the independent and dependent variables in this problem, not relating the dependency of the refunded money to the amount of returned cans"
    },
    {
        "Misconception":"when students struggle to grasp the concept of independent and dependent variables",
        "Misconception ID":"MaE44",
        "Topic":"Algebraic representations",
        "Example Number":3,
        "Question":"Mary's basic wage is $20 per week. She is also paid another $2 for each hour of over-time she works.\nCould you use a formula to find out how much over time Mary would have to work to earn a total wage of $50",
        "Incorrect Answer":"I don't think so. It is guess and check....  You could do it in your head. It would be $30 the overtime, because 20 plus 30 equals 50. So  she would have to work 15 overtime hours, because 30 divided by 2 is 15.",
        "Correct Answer":"Yes, it is possible to use a formula to find out how much over time Mary would have to work, the equation is: 50 = 20 + 2H",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford & Langrall (2000)",
        "Explanation":"Instead of using their equations, most of the students used mental mathematics strategies or extended tables to solve problems that could have been solved by using an equation, because they did not identify the variables involved in the problem\n"
    },
    {
        "Misconception":"when students struggle to grasp the concept of independent and dependent variables",
        "Misconception ID":"MaE44",
        "Topic":"Algebraic representations",
        "Example Number":4,
        "Question":"Let N represent the number of squares along one edge of a grid and let B represent the number of squares in the border. Write an equation for finding the number of squares in the border. Can you use your equation to find the size of a grid with a border that contains 76 squares?",
        "Incorrect Answer":"n*4 - 4 = b\nWell, I thought just to divide 76 by 4 would be too complicated, so I subtracted the 4 from that... No, wait, I added the 4 because that would be the reverse of the formula. and then I got 80. And then I divided that by 4 and got 20",
        "Correct Answer":"B=4(N-1)\nB=4(76-1)=4(75)=300",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford & Langrall (2000)\np. 6, 17",
        "Explanation":"Some students used the same reversing process but did not associate it with their equation because they did not identify the variables involved in the problem"
    },
    {
        "Misconception":"when students mistakenly switch variables when transposing expressions involving subtraction",
        "Misconception ID":"MaE45",
        "Topic":"Variables, expressions, and operations",
        "Example Number":1,
        "Question":"Write an algebraic expression to represent: Three less than a number.",
        "Incorrect Answer":"3-x",
        "Correct Answer":"x-3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Capraro, M. M., & Joffrion, H. (2006)\np. 7",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly switch variables when transposing expressions involving subtraction",
        "Misconception ID":"MaE45",
        "Topic":"Variables, expressions, and operations",
        "Example Number":2,
        "Question":"Write the expression that represents: \u201cTachi is exactly one year older than Bill\u201d if T represented Tachi\u2019s age and B, Bill\u2019s age.",
        "Incorrect Answer":"B-T=1",
        "Correct Answer":"T=B+1",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Capraro, M. M., & Joffrion, H. 2006\np.18",
        "Explanation":"The learner transposed the variables"
    },
    {
        "Misconception":"when students mistakenly switch variables when transposing expressions involving subtraction",
        "Misconception ID":"MaE45",
        "Topic":"Variables, expressions, and operations",
        "Example Number":3,
        "Question":"At a meeting there are five more women than men. There are 25 women.\nHow many men are there?",
        "Incorrect Answer":"M=W+5=25+5=30",
        "Correct Answer":"M=W-5=25-5=20",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stacey, K & MacGregor M (2014)\n\np. 5",
        "Explanation":"The learner transposed the variables"
    },
    {
        "Misconception":"when students mistakenly switch variables when transposing expressions involving subtraction",
        "Misconception ID":"MaE45",
        "Topic":"Variables, expressions, and operations",
        "Example Number":4,
        "Question":"\"z is equal to the sum of 3 and y.\" Write this information in mathematical symbols",
        "Incorrect Answer":"z=3y",
        "Correct Answer":"z=3+y",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stacey, K & MacGregor M (2014)\n\np. 5",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly perceive variables as labels or units, or associate their value with their alphabetical position",
        "Misconception ID":"MaE46",
        "Topic":"Variables, expressions, and operations",
        "Example Number":1,
        "Question":"The following question is about this expression:\n   2n + 3\n\u2191\nThe arrow above points to a symbol.\nWhat does the symbol stand for?",
        "Incorrect Answer":"The symbol stands for something which name starts with letter n.",
        "Correct Answer":"The symbol can stand for any number.",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Asquith et al.  2007p. 11",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly perceive variables as labels or units, or associate their value with their alphabetical position",
        "Misconception ID":"MaE46",
        "Topic":"Variables, expressions, and operations",
        "Example Number":2,
        "Question":"David is 10 cm taller than Con. Con is h cm tall. What can you write for David's height?",
        "Incorrect Answer":"Dh\nD stands for David's and h for height. Dh is David's height",
        "Correct Answer":"h+10",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stacey and MacGregor, 1997b\np. 2",
        "Explanation":"This abbreviation stands for the words \"David's height\""
    },
    {
        "Misconception":"when students mistakenly perceive variables as labels or units, or associate their value with their alphabetical position",
        "Misconception ID":"MaE46",
        "Topic":"Variables, expressions, and operations",
        "Example Number":3,
        "Question":"Given the equation: a=28+b\nWhich of the following would be true?\n(i) a is greater than b\n(ii) b is greater than a\n(iii) a=28\n(iv) you cannot tell which number is greater",
        "Incorrect Answer":"b is greater because it has 28 added to it, whereas a has nothing added to it",
        "Correct Answer":"(iv) you cannot tell which number is greater",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stacey and MacGregor, 1997b\np. 2",
        "Explanation":""
    },
    {
        "Misconception":"when students mistakenly perceive variables as labels or units, or associate their value with their alphabetical position",
        "Misconception ID":"MaE46",
        "Topic":"Variables, expressions, and operations",
        "Example Number":4,
        "Question":"Sue weighs 1 kg less than Chris. Chris weighs y kg. What can you write for Sue's weight?",
        "Incorrect Answer":"x",
        "Correct Answer":"y-1",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"MacGregor and Stacey  1997\np. 6",
        "Explanation":"Assumed reasoning: \"Although 10 can be 'joined' to h, as 10h, 1 cannot be 'removed' from y. To denote 1 less than y, write x\""
    },
    {
        "Misconception":"when students incorrectly assume two variables in an equation must represent distinct numerical values, rather than potentially representing the same expression",
        "Misconception ID":"MaE47",
        "Topic":"Variables, expressions, and operations",
        "Example Number":1,
        "Question":"h+m+n=h+p+n always, sometimes, or never true?",
        "Incorrect Answer":"never true",
        "Correct Answer":"Sometimes true",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stephens (2005)\np. 1",
        "Explanation":"Learners consider that each variable represents a different number, thence m and n should have a different value and so the equation is never true"
    },
    {
        "Misconception":"when students incorrectly assume two variables in an equation must represent distinct numerical values, rather than potentially representing the same expression",
        "Misconception ID":"MaE47",
        "Topic":"Variables, expressions, and operations",
        "Example Number":2,
        "Question":"Ricardo has 8 pet mice. He keeps them in two cages that are connected so that the mice can go back and forth between the cages. One of the cages is blue, and the other is green. Show all the ways that 8 mice can be in two cages.\nThe situation can be represented by the equation  b + g = 8, where b represents the blue cage and g the green cage.\nCan b=g be true?",
        "Incorrect Answer":"b can't be the same as g, because the letters represent different things",
        "Correct Answer":"b=g is true when there are 4 mice in each box, so b = g is true for number 4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stephens (2005)\np. 2-4",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly assume two variables in an equation must represent distinct numerical values, rather than potentially representing the same expression",
        "Misconception ID":"MaE47",
        "Topic":"Variables, expressions, and operations",
        "Example Number":3,
        "Question":"Are these number sentences true or false?\na = a\nc = r",
        "Incorrect Answer":"The first sentence is true, the variable a has to be the same in the same problem. The second one must be false, because when a letter represents a number, usually each letter represents a different number, not the same ones.",
        "Correct Answer":"c=r could be true or false, depending on the values of these variables",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stephens (2005)\np. 1",
        "Explanation":""
    },
    {
        "Misconception":"when students incorrectly assume two variables in an equation must represent distinct numerical values, rather than potentially representing the same expression",
        "Misconception ID":"MaE47",
        "Topic":"Variables, expressions, and operations",
        "Example Number":4,
        "Question":"Will different solutions be obtained from the following equations?\n7w+22=109\nand\n7n+22=109",
        "Incorrect Answer":"Can't tell until both equations are solved.",
        "Correct Answer":"Of course, the solution is the same",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Herscovics, N., & Kieran, C.  (1980)\np. 2",
        "Explanation":"The learner's answer implies that w and n can't represent the same number"
    },
    {
        "Misconception":"when students struggle to grasp that variables can represent changing or varying quantities",
        "Misconception ID":"MaE48",
        "Topic":"Variables, expressions, and operations",
        "Example Number":1,
        "Question":"A store is having a sale. They have advertised 10% off everything in the store. They also have just purchased a new shipment of computer games. These games cost the store $32.11 each. They want to price the game so that they will make at least a 40% profit, even at the sale price. What is the lowest regular selling price  for the game that will allow this profit? \nUse x to represent the regular selling price of the game and state an equation to solve this problem. \nIf the store changed the % off in the store, would x continue representing the selling price? What would change in your equation?",
        "Incorrect Answer":"[32.11 + .4(32.11)] = x - .1x\n32.11 + 12.844 = x(1 - .1)\n44.954 = x(.9)\n49.94888.. = x\nx = $49.90\nThe regular selling price should be at least $49.90 \nIf the offer changes, x cannot represent the selling price anymore, two different letters will be needed to solve the new problem.",
        "Correct Answer":"x = $49.95\nIf the offer changes, x will continue representing the selling price, the only thing that changes is the decimal number that multiplies x",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bair, S. L., & Rich, B. S.  2011\np. 12",
        "Explanation":"The learner fails to understand that variables can represent varying quantities, so can be used to solve the same problem with different values for the selling price, the discount or any other quantity"
    },
    {
        "Misconception":"when students struggle to grasp that variables can represent changing or varying quantities",
        "Misconception ID":"MaE48",
        "Topic":"Variables, expressions, and operations",
        "Example Number":2,
        "Question":"What can you say about r if r=s+t and r+s+t=30",
        "Incorrect Answer":"r < 30",
        "Correct Answer":"r=15",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kuchemann (1978)\np. 5",
        "Explanation":"The learner fails to understand that s + t in the second equation can be replaced with r to solve it, because lacks understanding that variables represent varying quantities"
    },
    {
        "Misconception":"when students struggle to grasp that variables can represent changing or varying quantities",
        "Misconception ID":"MaE48",
        "Topic":"Variables, expressions, and operations",
        "Example Number":3,
        "Question":"Can you tell which is larger, 2n or n+2? Please explain your answer",
        "Incorrect Answer":"2n, because it is a multiplication",
        "Correct Answer":"Can't tell, because for some n, 2n may equal or be less than n+2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kuchemann 1978\np. 5",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to grasp that variables can represent changing or varying quantities",
        "Misconception ID":"MaE48",
        "Topic":"Variables, expressions, and operations",
        "Example Number":4,
        "Question":"What can you say about c if c+d=10 and c is less than d?",
        "Incorrect Answer":"c=4",
        "Correct Answer":"c can be equal to any number between 0 and 4, depending on the value of d",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Kuchemann (1978)\np.3",
        "Explanation":"The learner fails to understand that the variable c can take different values to make the equation true"
    },
    {
        "Misconception":"when students find it challenging to comprehend the various meanings and applications of variables",
        "Misconception ID":"MaE49",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"The perimeter of a triangle is 44 cm. One side of the triangle equals 14 cm, the second side is 2x cm long and the third side equals x cm.\nWrite an algebraic equation and work out x",
        "Incorrect Answer":"44-14=30, 30\/3=10, x=5 [the learners did not write any equation, but they used the \"backward operations'' to calculate the missing value]",
        "Correct Answer":"Equation: 44=14+2x+x, 44=14+3x, 30=3x, x=10",
        "Question image":"MaE51-Ex1Q",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Stacey, K., & MacGregor, M. 2000\np. 5",
        "Explanation":"They could see from a logical analysis of the situation how to get directly from the measure of the perimeter to the measure of the unknown side. They implicitly know what \"forward operations'' are (that 14 has been added to get 44) and they know that there are three of the unknown lengths contributing to the perimeter, but they use the \"backward operations'' (in this case subtracting and dividing) to move directly to the solution, calculating from known numbers at every stage, avoiding to use algebraic language and equations."
    },
    {
        "Misconception":"when students find it challenging to comprehend the various meanings and applications of variables",
        "Misconception ID":"MaE49",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Mary's basic wage is $20 per week. She is also paid another $2 for each hour of over-time she works. \nIf H stands for the number of hours of overtime Mary works and if W stands for her total wage, write an equation for finding Mary's total wage.",
        "Incorrect Answer":"n=20n+2n",
        "Correct Answer":"W=20+2H",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford & Langrall  2000\np. 6",
        "Explanation":"The learner struggles with the meaning of a variable and uses letter n to represent all the varying quantities in the problem"
    },
    {
        "Misconception":"when students find it challenging to comprehend the various meanings and applications of variables",
        "Misconception ID":"MaE49",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"x+4=2",
        "Incorrect Answer":"x=2\nVariables can't take negative numbers, so the answer has to be 2",
        "Correct Answer":"x=-2",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Vlassis, J (2008)\np. 5",
        "Explanation":"The learners show struggle in finding the negative value of x. Students also attempt to avoid negative solutions to equations, involving for example, changing the structure of an equation or a problem definition in order to obtain a positive solution, because they think that variables can't take negative values, or they are no longer sure if the minus sign is a subtraction sign or if it is part of a negative number"
    },
    {
        "Misconception":"when students find it challenging to comprehend the various meanings and applications of variables",
        "Misconception ID":"MaE49",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"Mary's basic wage is $20 per week. She is also paid another $2 for each hour of over-time she works.\nIf H stands for the number of hours of overtime Mary works and if W stands for her total wage, write an equation for finding Mary's total wage.",
        "Incorrect Answer":"W=x+yH\nUsing one letter for each unknown is easier",
        "Correct Answer":"W=20+2H",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford & Langrall  2000\np. 6",
        "Explanation":"The learner just uses a different letter to represent each number, not identifying the constant values"
    },
    {
        "Misconception":"when students struggle with forming and understanding algebraic expressions and equations.",
        "Misconception ID":"MaE50",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"There were three kinds of candy bars being sold at the concession stand during the Friday dance. There were 22 more Snickers bars sold than Kit Kat bars and there were 32 more Reese\u2019s Peanut Butter Cups sold than Kit Kat bars. There were 306 candy bars sold in all. How many  of each kind of candy bar was sold?",
        "Incorrect Answer":"I'll use K for the Kit Kat bars, S for Snickers and P for Peanut Butter Cups.\nK=S+22\nP=K+32\nP+k+S=306\nIf I divide 306 by 3, I get 102, there would be 102 bars of each if all were equal. Since there are more Kit Kats, I'll guess K=80.\nP=80+32=112\n80=S+22\n80=58+22, S=58\nP=112, K=80 and S=58\nChecking: 112+80+58=250\nThen, there are more Kit Kats...  My initial guess is wrong...",
        "Correct Answer":"K+(K+32)+(K+22)=306\nK=84\nS=106\nP=116",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Baroudi (2006)\np. 4\n",
        "Explanation":"The Learner wrote incorrectly the syntax of the algebraic equation for snickers and, instead of writing one single equation, the learner wrote 3, from which one was not correctly stated, showing a difficulty with the syntax of algebraic notation\n"
    },
    {
        "Misconception":"when students struggle with forming and understanding algebraic expressions and equations.",
        "Misconception ID":"MaE50",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Solve:\n(x+3)^2<=6x+18",
        "Incorrect Answer":"(x+3)^2+6(x+3)=0",
        "Correct Answer":"-3<=x<=3",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Novotna, J., & Hoch, M. (2008) \np. 8",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle with forming and understanding algebraic expressions and equations.",
        "Misconception ID":"MaE50",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"Two students have the same amount of candies. Briana has one box, two tubes, and 7 loose candies. Susan has one box, one tube, and 20 loose candies. If each box has the same amount and each tube has the same amount, can you figure out how much each tube holds? Each box? Write algebraic expressions to represent the problem.",
        "Incorrect Answer":"Box=B\nTube=T\nBriana: 1B+2T+7\nSusan: 1B+1T+20\nB+2T+B+T=20+7\n2B+3T=27\nI need more information to solve the problem, or I have to guess the amount of candies in the box...",
        "Correct Answer":"Tube:13 candies\nThe box could contain any amount of candies",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Baroudi (2006)\np. 5",
        "Explanation":"The learner shows difficulty with the syntax of algebraic notation, given that the two initial expressions were correctly stated, but failed to put them together in one single equation to find a possible solution"
    },
    {
        "Misconception":"when students struggle with forming and understanding algebraic expressions and equations.",
        "Misconception ID":"MaE50",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"The first row of a concert hall has 10 seats. Each row thereafter has 2 more seats than the row in the front of it.\nLet R represent the number of the row and let S represent the number of seats in that row. Can you give an equation for finding the number of seats?",
        "Incorrect Answer":"You could do guess and check. For example if the last row has 50 seats, you do 50-8=42 and you would have to figure out what times 2 equals 42. That would be 21. It's easy, so you don't need an equation for finding the number of seats.",
        "Correct Answer":"S=10+2(R-1)",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Brown, G., & Quinn, R. J.  2006, \np. 7",
        "Explanation":"The learner did not write the equation and rather, solved the problem by iteration and using inverse operations"
    },
    {
        "Misconception":"when students misunderstand the equal sign as indicating \"the answer is\" rather than representing a relationship between quantities",
        "Misconception ID":"MaE51",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"3 + 4 = 7\n      \u2191\nThe arrow above points to a symbol.\nWhat does the symbol mean?",
        "Incorrect Answer":"The symbol means \"add the numbers\"",
        "Correct Answer":"The symbol is the equal sign and it means that the statement on the left side is equivalent to the statement on the right side",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Asquith et al.  2007\np. 9",
        "Explanation":""
    },
    {
        "Misconception":"when students misunderstand the equal sign as indicating \"the answer is\" rather than representing a relationship between quantities",
        "Misconception ID":"MaE51",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Is the number that goes in the [_] the same number in the following two equations?\n2*[_]+15=31\n2*[_]+15-9=31-9",
        "Incorrect Answer":"Yes, the answer is 31 in both equations",
        "Correct Answer":"The number that goes in the squares is the same for both equations and it equals 8",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Asquith et al.  2007\np. 9",
        "Explanation":""
    },
    {
        "Misconception":"when students misunderstand the equal sign as indicating \"the answer is\" rather than representing a relationship between quantities",
        "Misconception ID":"MaE51",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"For the following expressions, answer:\nWhat do the equal signs tell us?\nWhich is more, one third or four twelfths?\n1\/3 = 4\/12 \n+\n1\/4 = 3\/12 \n1\/3 + 1\/4 = 7\/12",
        "Incorrect Answer":"The equal signs tell us ... that you just do the answer.\nIs one third more than four twelfths? .... no ...",
        "Correct Answer":"The equal signs tell us that both expressions at each side are equivalent to each other. One third is equal to four twelfths.",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock (2006)",
        "Explanation":""
    },
    {
        "Misconception":"when students misunderstand the equal sign as indicating \"the answer is\" rather than representing a relationship between quantities",
        "Misconception ID":"MaE51",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"Students were shown the following equation on a balance: 5n+3n+11=5n+11+39 and asked if they noticed any equal terms on both sides and if they thought those terms could be removed. Next, students were asked to solve the remaining equation, 3n=39. Once the equation was solved, n=13, students were asked if this solution was also true for the original equation, 5n+3n+11=5n+11+39",
        "Incorrect Answer":"I'm not sure that the solution is true for the original equation",
        "Correct Answer":"\"yes, it's true for the original equation\"",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"L Linchevski, N Herscovics (1996)\np. 15",
        "Explanation":""
    },
    {
        "Misconception":"when students neglect to check their solutions or make errors during the checking process",
        "Misconception ID":"MaE52",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"Solve for n, check your answer\n7-1\/2n=18",
        "Incorrect Answer":"7-1\/2n=18\n-1\/2n=11\nn=22\nChecking:\n7-1\/2\u00b722=18\n7+11=18\n18=18",
        "Correct Answer":"n=-22\nChecking:\n7-1\/2(-22)=18\n7+11=18",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Perrenet & Wolters, 1994\np. 5",
        "Explanation":""
    },
    {
        "Misconception":"when students neglect to check their solutions or make errors during the checking process",
        "Misconception ID":"MaE52",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Solve for t:\nt-24=23t\nCheck your answer",
        "Incorrect Answer":"t-24=23t\n-24=24t\n-1=t\nt=-1\nCheck:\n-1-24=23*-1\n-23=23*-1\nOK",
        "Correct Answer":"t=-12\/11\nCheck:\n-12\/11-24=23(-12\/11)\n-25 1\/11=-25 1\/11",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Perrenet & Wolters, 1994\np. 5",
        "Explanation":""
    },
    {
        "Misconception":"when students neglect to check their solutions or make errors during the checking process",
        "Misconception ID":"MaE52",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"Solve m-3=4m\nAnd check your answer",
        "Incorrect Answer":"Solving: m=3m\nm=3\nChecking\n[nothing]",
        "Correct Answer":"m=-1\nCheck:\n-3-3=4(-1)\n-4=-4",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Perrenet, J. C., & Wolters, M. A. \n(1994)\np.5",
        "Explanation":""
    },
    {
        "Misconception":"when students neglect to check their solutions or make errors during the checking process",
        "Misconception ID":"MaE52",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"Solve 4p+40=60 and check your answer",
        "Incorrect Answer":"Solving: 4p=20\np=5\nChecking: 5+5+5+5=20\n60-40=20",
        "Correct Answer":"p=5\nCheck:\n4(5)+40=60\n20+40=60\n60=60",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Perrenet, J. C., & Wolters, M. A. \n(1994)\np.5",
        "Explanation":""
    },
    {
        "Misconception":"when students get confusion over operation symbols and their meanings in algebra",
        "Misconception ID":"MaE53",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"Mary's basic wage is $20 per week. She is also paid another $2 for each hour of over-time she works.\nIf H stands for the number of hours of overtime Mary works and if W stands for her total wage, write an equation for finding Mary's total wage.",
        "Incorrect Answer":"I don't need to write an equation, I just have to analyze that\n1 week and 1 hour=20+2=22\n2 weeks and 2 hours=40+4=44 and so on...",
        "Correct Answer":"W=20+2H",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Swafford & Langrall  2000\np. 6",
        "Explanation":"The learner uses iteration rather than writing an equation to represent the problem symbolically"
    },
    {
        "Misconception":"when students get confusion over operation symbols and their meanings in algebra",
        "Misconception ID":"MaE53",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Kate sold 12 tickets to a school play. Katie's total sales, t, for the tickets is given by the formula \n12c=t\nwhere c is the cost per ticket.\nWhat were Katie's total sales if the cost of each ticket is $5?",
        "Incorrect Answer":"All I have to do is to replace the first letter in the equation, with the first number given in the statement:\n12(12)=144",
        "Correct Answer":"12c=t\n12*($5)=$60\nKatie's total sales were $60",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 183",
        "Explanation":"The learner did not understand the meaning of the symbols representing the variables, so they substituted the amount of tickets in the variable on the left side of the equation"
    },
    {
        "Misconception":"when students get confusion over operation symbols and their meanings in algebra",
        "Misconception ID":"MaE53",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"The amount of money Hank earns after working h hours is given by the equation below. Let m equal the amount of money Hank earns.\nm=$7h\nHow much money would Hank earn after working 35 hours?",
        "Incorrect Answer":"m=7+35=42\n$42",
        "Correct Answer":"m=$7h\nm=7*35=245\nHank would earn $245 after working 35 hours",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np, 184",
        "Explanation":"The learner has issues interpreting the symbolic notation in the equation, and adds instead of multiplying"
    },
    {
        "Misconception":"when students get confusion over operation symbols and their meanings in algebra",
        "Misconception ID":"MaE53",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"Solve mn=\nWhere m=10 and n=13",
        "Incorrect Answer":"23",
        "Correct Answer":"130",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Arcavi et. al., 2016",
        "Explanation":"The learner did not write the equation and rather, solved the problem by iteration and using inverse operations"
    },
    {
        "Misconception":"when students make reversal order errors, swapping variables in equations, such as writing 2X=Y instead of X=2Y",
        "Misconception ID":"MaE54",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"Write an equation using the variables S and P to represent the following statement: \"There are six times as many students as professors at this university\". Use S for the number of students and P for the number of professors.",
        "Incorrect Answer":"6S=P",
        "Correct Answer":"S=6P",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Clement, J. (1982)\np. 3",
        "Explanation":""
    },
    {
        "Misconception":"when students make reversal order errors, swapping variables in equations, such as writing 2X=Y instead of X=2Y",
        "Misconception ID":"MaE54",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Write an equation using the variables C and S to represent the following statement: \"At Mindy's restaurant, for every four people who ordered cheesecake, there are five people who ordered strudel\". Let C represent the number of cheesecake and S represent the number of strudels ordered.",
        "Incorrect Answer":"4C=5S",
        "Correct Answer":"4S=5C",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Clement, J. (1982)\np. 3",
        "Explanation":""
    },
    {
        "Misconception":"when students make reversal order errors, swapping variables in equations, such as writing 2X=Y instead of X=2Y",
        "Misconception ID":"MaE54",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"Write an equation to represent the following statement: \u2018At this company, there are six times as many workers as managers\u2019. Assuming that the variable W represents the number of workers and M the number of managers.",
        "Incorrect Answer":"6W=M",
        "Correct Answer":"W=6M",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Soneira, C., Bansilal, S., Govender, R. (2021)\np. 3",
        "Explanation":""
    },
    {
        "Misconception":"when students make reversal order errors, swapping variables in equations, such as writing 2X=Y instead of X=2Y",
        "Misconception ID":"MaE54",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"Write an expression that could be used to represent the number of rows, if there were n girls all together and each row had 6 girls.",
        "Incorrect Answer":"6n",
        "Correct Answer":"n\/6",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Capraro, M. M., & Joffrion, H. (2006)\np. 10",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to recognize when to combine like terms, failing to add or subtract terms with the same variable, as in 4x+2x+x=7x",
        "Misconception ID":"MaE55",
        "Topic":"Equations and inequalities",
        "Example Number":1,
        "Question":"Solve: 2x+x=24",
        "Incorrect Answer":"x=2\n22+2=24",
        "Correct Answer":"x=8",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to recognize when to combine like terms, failing to add or subtract terms with the same variable, as in 4x+2x+x=7x",
        "Misconception ID":"MaE55",
        "Topic":"Equations and inequalities",
        "Example Number":2,
        "Question":"Solve: 3x+2x=50",
        "Incorrect Answer":"x=0\n30+20=50",
        "Correct Answer":"x=10",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to recognize when to combine like terms, failing to add or subtract terms with the same variable, as in 4x+2x+x=7x",
        "Misconception ID":"MaE55",
        "Topic":"Equations and inequalities",
        "Example Number":3,
        "Question":"Solve: 5x+6x=110",
        "Incorrect Answer":"x=0\n50+60=110",
        "Correct Answer":"x=10",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Ashlock, 2006",
        "Explanation":""
    },
    {
        "Misconception":"when students struggle to recognize when to combine like terms, failing to add or subtract terms with the same variable, as in 4x+2x+x=7x",
        "Misconception ID":"MaE55",
        "Topic":"Equations and inequalities",
        "Example Number":4,
        "Question":"Simplify: 3(6x-4)+2(3x-3)\nShow your work",
        "Incorrect Answer":"3(6x-4)+2(3x-3)=18x-12+6x-6=18x-18+6x",
        "Correct Answer":"24x-18",
        "Question image":"",
        "Learner Answer image":"",
        "Correct Answer image":"",
        "Source":"Bush, 2011\np. 215-216",
        "Explanation":"The learner only added the numbers, but did not combine the like terms containing x"
    }
]