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7.G.A.1 | Activity
In this introductory lesson students get a chance to recall what they have previously learned about ratios and proportional relationships. They will build on these ideas in the next few lessons where they will work with ratios and rates involving fractions. In this activity, students can leverage their recent ... |
6.G.A.3 | Warm-up
The purpose of this warm-up is to ensure students understand that
they can infer the coordinates of a point based on knowing the coordinates of points on the same horizontal and vertical lines;
the length of a horizontal or vertical line segment can be determined based on the coordinates of its endpoints. Each ... |
G-SRT.D.10 | Problem 1
The Law of Cosines states that:
Given
$${\triangle ABC}$$
,
###IMAGE0###
What measurements of a triangle make the most sense to use the Law of Cosines?
Problem 2
For each of the triangles below, would you use the Law of Sines, Law of Cosines, or Pythagorean theorem to find the value of
$$x$$
? Explain your re... |
4.OA.B.4 | Narrative
The purpose of this activity is for students to solve problems about a locker game by using the ideas of factors and multiples and by observing patterns in the numbers. The situation offers many possible explorations, but the questions around which lockers are touched and by how many people are designed to el... |
7.G.A.2 | Optional activity
This activity reviews the work students did previously drawing shapes with given conditions. Students draw as many different triangles as they can that could be the base of the triangular prism, given two side lengths and one angle measure for the triangle.
In preparation for calculating surface area ... |
7.RP.A.3 | Optional activity
The purpose of this activity is for students to encounter a situation where the quantity given is not the whole amount, but rather is the amount after a decrease. In this case, they are given the amount after a 10% decrease. They should make the connection from previous lessons that the amount given i... |
3.OA.A.1 | Narrative
The purpose of this activity is for students to apply their knowledge from previous activities to draw arrays to match multiplication expressions. Have connecting cubes or counters available for students who need them. In the launch, students use their bodies to make an array for the expression
\(4\times6\)
.... |
8.EE.C.7a | Activity
In this activity, students examine equations with one variable to determine the number of solutions. In the associated Algebra lesson, students will find the number of solutions for a system of equations. In the discussion after this activity, students are asked to look for ways they can connect the number of ... |
5.NF.B.7b | Narrative
The purpose of this activity is for students to solve problems about dividing a whole number by a unit fraction in a way that makes sense to them. The context of quilt making is used so students can visualize a strip of paper that is a whole number length being cut into fractional sized pieces. As students de... |
7.EE.B.3 | Activity
This activity is parallel to one in the previous lesson, except that students are creating a tape diagram after interpreting an equation rather than interpreting a story. The intention is for students to reason in any way that makes sense to them about the equations and diagrams to figure out the solution to e... |
4.NBT.A.1 | Task
Maned wolves are a threatened species that live in South America. People estimate that there are about 24,000 of them living in the wild.
###IMAGE0###
The dhole is an endangered species that lives in Asia. People estimate there are ten times as many maned wolves as dholes living in the wild.
###IMAGE1###
About how... |
4.MD.C.7 | Narrative
In this Info Gap activity, students solve abstract multi-step problems involving an arrangement of angles with several unknown measurements. By now students have the knowledge and skills to find each unknown value, but the complexity of the diagram and the Info Gap structure demand that students carefully mak... |
7.RP.A.2 | Activity
This activity provides the first example in this unit of a relationship that is not proportional. The second question focuses students’ attention on the unit rates. If the relationship were proportional then regardless of the number of people in a vehicle, the cost per person would be the same. The question ab... |
6.EE.A.2c | Optional activity
This activity allows students to practice identifying the base and height of triangles and using them to find areas.
Because there are no directions on which base or height to use, and because not all sides would enable them to calculate area easily, students need to think structurally and choose stra... |
F-IF.A.2 | Activity
The purpose of this activity is to strengthen connections between zeros of a function (input(s) when the output is 0), the output when the input is 0, and the coordinates of the intercept(s) of a graph of the function.
Launch
To ensure that students understand the task before beginning, display one of the func... |
6.SP.B.4 | Warm-up
In a previous lesson, students were exposed to the ideas of center and spread. Here, they begin connecting that idea informally to the word “typical” and a value that could be considered typical or characteristic of a data set by thinking about two good options and reasonings. They continue to interpret a dot p... |
7.SP.A | Task
Members of the seventh grade math group have nominated a member of their group to be class president. Every student in seventh grade will cast a vote. There are 2 candidates in the race and a candidate needs at least 50% of the votes to be elected. The math group wants to conduct a survey to assess their candidat... |
K.G.B.4 | Narrative
The purpose of this activity is for students to begin to distinguish triangles from other shapes. By working with variants and non-examples of triangles, students begin to develop their understanding of what makes a shape a triangle. Students may more easily identify equilateral triangles as triangles but may... |
1.OA.C.6 | Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting. The expressions are explicitly chosen to encourage students to use their understanding of the 10 + n structure of teen numbers to subtract (MP7). This method will be discussed in more depth is this lesson... |
5.NBT.B.7 | Solve. Show or explain your work.
a. 4.62 ÷ 0.07
b. 51.2 ÷ 0.08
c. 2.91 ÷ 0.6
|
6.SP.A.1 | Activity
In the previous activity, students commented on distributions on a dot plot and had opportunities to hear different ways to describe distributions. In this activity, they begin to think about how to characterize a distribution as a whole, in terms of its
center
and
spread
. Students learn that we can give a ge... |
8.F.A.1 | Warm-up
The purpose of this warm-up is for students to jump back into recognizing functions and determining if two quantities are a function of each other. Students are asked questions similar to these throughout this lesson, and the discussion of this warm-up is meant to get students using the language of functions, w... |
7.G.B.4 | Optional activity
In the previous lesson, students built trundle wheels using three different wheel sizes, and they tested the functionality of their wheels in the classroom. In this activity, they use their trundle wheels to measure a longer path of about 50–100 meters. This is the same path that they measured during ... |
4.NF.B.3d | Narrative
The purpose of this activity is to represent and solve a measurement problem with fractions. Students may approach this activity in multiple ways and are invited to apply what they know about operations with fractions, comparing fractions, and fraction equivalence to make sense of and solve the problems (MP2)... |
5.NBT.A.2 | Narrative
The purpose of this Number Talk is for students to reason about place value relationships and the properties of multiplication. The elicited understandings and strategies will be helpful in later lessons and units when they multiply large numbers. In this unit, students produce and interpret multiplication ex... |
K.CC | Narrative
The purpose of this warm-up is for students to practice the verbal count sequence to 10 and show quantities on their fingers.
Launch
“Count to 10 with your fingers. Each time you say a number, put up 1 finger.”
Count to 10 as a class using fingers.
Activity
“As you count and put up your fingers, I will write ... |
6.G.A.2 | A tank that measures
$$1\frac{1}{2}$$
feet across,
$$2\frac{1}{3}$$
feet wide, and
$$1\frac{1}{2}$$
feet tall, is filled halfway with water, as shown below. To fill the tank to the very top with water, how many cubic feet of water need to be added?
###IMAGE0###
|
K.CC.B.5 | Stage 1: Draw 1–10
Required Preparation
Materials to Gather
Connecting cubes
Materials to Copy
Blackline Masters
Number Mat 1-10
Math Libs Scenes
Narrative
Students roll a cube onto a number mat and write the number in the space provided next to one of the images. They draw a scene with the appropriate number of that ... |
F-LE.A.3 | Activity
This activity prompts students to again compare a linear function with an exponential one, but this time without a context, and the exponential function grows much more slowly over a long period of time. Even if students predict that the exponential function will grow more quickly because it is exponential, th... |
K.CC.B.4 | Narrative
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. The images used introduce students to the context that will be used throughout the lesson.
When students use the placement of objects in a 10-frame, they look for and make use of str... |
F-BF.B.4 | Task
The table below shows some input-output pairs of two functions $f$ and $g$ that agree for the values that are given but some of their output values are missing.
###TABLE0###
Complete the table in a way so that $f$ could be invertible and so that $g$ is definitely not invertible.
Graph both functions and explain fr... |
3.OA.C.7 | Stage 7: Multiply with 6–9
Required Preparation
Materials to Gather
Colored pencils or crayons
Number cubes
Paper clips
Materials to Copy
Blackline Masters
Capture Squares Stage 7 Gameboard
Capture Squares Stage 7 Spinner
Narrative
Students roll a number cube and spin a spinner and find the product of the two numbers ... |
3.OA.B.5 | Warm-up
Students perform mental calculations by applying strategies involving the distributive property.
Launch
Display one problem at a time. Give students 30 seconds of quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the t... |
G-SRT.C.8 | Problem 1
Find the value of the side length marked
$$x$$
.
###IMAGE0###
Problem 2
Given the following right triangle, find all of the angle measures to the nearest degree.
###IMAGE1###
|
1.MD.B.3 | Narrative
The purpose of this activity is to connect the time shown on a digital clock with an analog clock with only the hour hand displayed. Students use the cards created in the first activity to write times in the digital format to represent each clock.
Required Materials
Materials to Gather
Materials from a previo... |
4.G.A.1 | Narrative
This warm-up prompts students to carefully analyze and compare quadrilaterals and their sides. When students make comparisons, they have a reason to use geometric language precisely (MP6). The activity also enables the teacher to hear the terminology students know and how they talk about characteristics of tw... |
S-ID.B.6 | Warm-up
The mathematical purpose of this activity is for students to describe the relationship between variables using mathematical terminology, such as strong or weak relationship and positive or negative relationship. These terms were defined in the previous lesson. Students must reason abstractly and quantitatively ... |
5.NBT.B.7 | Problem 1
Elena and Zack want some change to buy penny candy. Their mom keeps rolls of 10 pennies to give to them for just this purpose. Their mom gives them 5 rolls and 4 loose pennies. How can Zack and Elena split the change they got from their mom evenly?
Problem 2
Elena used base-ten diagrams to find 3.72 ÷ 3. She ... |
4.NF.A.2 | Complete the following comparison between two fractions.
(1 / 8) _ (4 / 1). |
4.NF.A.2 | Using the same approach we used before, now think about the comparison between (6 / 8) and (4 / 1). Complete the comparison using the same symbols (<, >, =).
(6 / 8) _ (4 / 1).
This is similar to the previous problem but now you are comparing a different fraction with the same whole number. |
4.NF.A.2 | Determine which symbol appropriately fills in the blank (either '<', '=', or '>') to accurately compare these two fractions:
(7 / 2) _ (10 / 6) |
4.NF.A.2 | Let's modify our previous problem slightly and continue the exercise. Fill in the blank with one of the following symbols: <, >, or =, to properly compare the two fractions.
(6 / 2) _ (10 / 6) |
4.NF.A.2 | Complete the following comparison by filling in the blank (<, >, or =):
(6 / 8) _ (8 / 7) |
4.NF.A.2 | Complete the following comparison by filling in the blank (<, >, or =). Consider what will happen if we are comparing the fraction 6/8 to the fraction 6/7 instead:
(6 / 8) _ (6 / 7) |
4.NF.A.2 | Compare the values of the two fractions below by filling in the blank with <, >, or =.
(9 / 3) _ (7 / 1) |
4.NF.A.2 | Consider the original problem where we compared the fractions (9 / 3) and (7 / 1). Now, instead of comparing it with (7 / 1), let's compare it with the fraction (1 / 1).
Fill in the blank in the new problem:
(9 / 3) _ (1 / 1)
Use the symbols <, >, or = to make the correct comparison. |
4.NF.A.2 | Fill in the blank with one of the following signs: <, >, or =
(5 / 3) _ (10 / 5) |
4.NF.A.2 | Consider the following situation:
Previously, you compared the values of the fractions (5 / 3) and (10 / 5). Now, imagine if the second fraction was changed to (7 / 5) instead. Based on this new situation, fill in the blank with one of the following signs: <, >, or =
(5 / 3) _ (7 / 5) |
4.NF.A.2 | Compare the values of the two fractions by filling in the blank with <, >, or =. Here are the fractions:
(3 / 2) _ (9 / 10) |
4.NF.A.2 | Let's consider a slight change to our previous fractions problem. This time, fill in the blank to compare these two fractions:
(3 / 7) _ (9 / 10)
Is the comparison the same or different than the comparison between 3 / 2 and 9 / 10? Think about the impact of decreasing the numerator of our first fraction on the compa... |
4.NF.A.2 | Compare the values of these fractions by filling in the blank with <, >, or =.
(10 / 9) _ (5 / 6) |
4.NF.A.2 | Now, consider the following fractions and fill in the blank with <, >, or =, to compare their values.
(10 / 9) _ (5 / 5) |
4.NF.A.2 | Compare the values of the two fractions and fill in the blank with <, >, or =.
(10 / 9) _ (5 / 10) |
4.NF.A.2 | Using the same logic as the previous problem, fill in the blank with <, >, or =. However, now consider the case where the second fraction is changed to 5/3. So the question is:
(10 / 9) _ (5 / 3) |
4.NF.A.2 | Compare the two fractions by completing the following statement with <, >, or =.
(9 / 8) _ (6 / 4) |
4.NF.A.2 | Let's consider a modification to the previous problem. Now, compare the fractions in the following statement:
(9 / 9) _ (6 / 4)
What happens to the relational comparison when the numerator of first fraction changes from 9 to 9 (effectively making it 1), while the second fraction remains same? Fill in the blank with <... |
4.NF.A.2 | Compare the two fractions below by filling in the gap with the appropriate symbol (<,>,=).
(10 / 3) _ (10 / 2) |
4.NF.A.2 | Let's revisit the previous comparison of fractions, but this time consider the change:
(10 / 3) _ (10 / 10)
Complete the comparison by filling in the blank with the appropriate symbol (<, >, or =). What happens to the comparison when the denominator of the second fraction is increased to 10? |
4.NF.A.2 | Compare the two fractions by filling in the blank with <, >, or =.
(2 / 1) _ (6 / 5) |
4.NF.A.2 | Compare the two fractions by filling in the blank with <, >, or =.
In the last example, you were comparing the fractions 2 / 1 and 6 / 5.
Now consider how the result might change when you compare these fractions:
(2 / 2) _ (6 / 5) |
4.NF.A.2 | Compare the fractions 5 / 4 and 10 / 3 by filling in the blank with one of the following symbols: <, >, or =. |
4.NF.A.2 | Consider now the fractions 5 / 4 and 8 / 3. Compare these two fractions by filling in the blank with one of the following symbols: <, >, or =. |
4.NF.A.2 | Compare the values of these two fractions by filling in the blank with <, > or =:
(7 / 5) _ (9 / 9) |
4.NF.A.2 | Now consider this situation:
Instead of dividing 7 by 5, you divided 7 by 10 to form a new fraction. How would this new fraction compare to the fraction 9 / 10? Fill in the blank using <, >, or =:
(7 / 5) _ (9 / 10) |
4.NF.A.2 | Compare the following two fractions by filling in the blank with <, >, or =:
(3 / 7) _ (5 / 8) |
4.NF.A.2 | Following up on the previous comparison, let's consider a similar one:
Compare the value of the fractions (3 / 7) and (6 / 8) by filling in the blank with <, >, or =:
(3 / 7) _ (6 / 8)
This comparison would tell you how the situation would change if we considered 6 parts out of 8 instead of 5 parts out of 8 as on th... |
4.NF.A.2 | Question:
Compare these two fractions:
(3 / 1) _ (5 / 9)
Hint: Fill the blank with one of the following: <, >, or =. |
4.NF.A.2 | Question:
In the previous question where we compared two fractions, we had (3 / 1) _ (5 / 9). Now, consider a change in the second number we are comparing. Instead of (5 / 9), we now have (5 / 5).
Compare these two fractions:
(3 / 1) _ (5 / 5)
Hint: Fill the blank with one of the following: <, >, or =. |
4.NF.A.2 | Compare the values of the following fractions:
(2 / 2) _ (6 / 6)
Fill in the blank with <, >, or = . |
4.NF.A.2 | Consider the change to the previous problem: instead of comparing (2 / 2) with (6 / 6), we now have (2 / 2) and (6 / 5).
Now, fill in the blank with <, >, or = to compare these two fractions:
(2 / 2) _ (6 / 5) |
4.NF.A.2 | Compare the following fractions by inserting "<", ">" or "=" between them.
(7 / 6) _ (9 / 6) |
4.NF.A.2 | Now let's consider a slight change to the fractions. Please fill in the blank with <, >, or =:
(7 / 9) _ (9 / 6)
This is just like in our previous problem, but this time we're looking at 7/9 instead of 7/6. |
4.NF.A.2 | Fill in the blank in the following question with <, >, or = :
(2 / 7) _ (2 / 9)
to express whether the first fraction is greater than, less than, or equal to the second fraction. |
4.NF.A.2 | Now let's consider a slight alteration to our previous question.
Using the same comparison methods, compare the following fractions:
(2 / 7) _ (2 / 4)
As you did previously, fill in the blank with <, >, or = signs to correctly compare the two fractions. Does the outcome change if we adjust the denominator in our se... |
4.NF.A.2 | Determine the relation between the two following fractions by filling in the blank with <, >, or =:
(9 / 4) _ (7 / 1) |
4.NF.A.2 | Consider now a different set of fractions:
(9 / 10) _ (7 / 1)
Fill in the blank with <, >, or = to correctly compare these two fractions. How do these fractions compare to the previous fractions we worked with? Has our answer changed? |
4.NF.A.2 | Fill in the blank with one of the symbols <, >, or = to complete the comparison between the two fractions.
(4 / 8) _ (2 / 1) |
4.NF.A.2 | Consider the previous problem where we compared (4 / 8) with (2 / 1). Now, imagine we change the second fraction to (2 / 6) instead of (2 / 1).
Fill in the blank with one of the symbols <, >, or = to complete this new comparison:
(4 / 8) _ (2 / 6) |
4.NF.A.2 | Fill in the blank with either <, >, or = in the following expression:
(9 / 9) _ (8 / 9),
to properly compare the two fractions. |
4.NF.A.2 | Continuing from the previous question, let's adjust the fractions slightly.
Now consider:
(9 / 2) _ (8 / 9)
What symbol (<, >, =) would you use in the blank to accurately compare these two fractions? |
4.NF.A.2 | Compare the following fractions by filling in the blank with <, >, or =.
(9 / 10) _ (3 / 10) |
4.NF.A.2 | Consider the values of two different fractions instead of the ones in the previous problem. Fill in the blank with <, >, or = to compare the fractions:
(9 / 4) _ (3 / 10) |
4.NF.A.2 | Determine if the first fraction is less than, equal to, or greater than the second. Fill in the blank with one of the following: <, >, or =.
(3 / 7) _ (5 / 3) |
4.NF.A.2 | Consider the same fractions as in the previous problem, but with a change in the latter fraction. Determine if the first fraction is less than, equal to, or greater than the second. Fill in the blank with one of the following: <, >, or =.
(3 / 7) _ (5 / 5) |
4.NF.A.2 | Compare the values of the following fractions by filling in the blank with <, >, or =.
(6 / 5) _ (7 / 10) |
4.NF.A.2 | Consider a change in the fractions previously compared. Now, compare the values of the following fractions by filling in the blank <, >, or =.
(1 / 5) _ (7 / 10) |
4.NF.A.2 | Fill in the blank in the following equation with one of these symbols: <, >, or =.
(1 / 9) _ (1 / 4) |
4.NF.A.2 | Considering the previous comparison between 1/9 and 1/4, let's now change the first fraction to 1/2 instead. This means modifying the comparison as per the following instruction.
Fill in the blank in the following equation with one of these symbols: <, >, or =.
(1 / 2) _ (1 / 4) |
4.NF.A.2 | Compare the following fractions and fill in the blank with <, >, or =:
(7 / 1) _ (6 / 1) |
4.NF.A.2 | Continue from the previous problem and now consider the fractions (9 / 1) and (6 / 1). Fill in the blank with <, >, or =:
(9 / 1) _ (6 / 1) |
4.NF.A.2 | Please fill in the blank with <, >, or = to compare the following fractions.
(5 / 4) _ (9 / 8) |
4.NF.A.2 | Please consider the following change to the previous problem and fill in the blank with <, >, or = to compare the fractions:
If the value of the second fraction's denominator was 1 instead of 8, contrast the following fractions:
(5 / 4) _ (9 / 1) |
4.NF.A.2 | Determine the correct symbol to place between the two fractions in the following expression. Fill in the blank with <, >, or =.
(8 / 9) _ (3 / 4) |
4.NF.A.2 | Consider the following comparison:
(8 / 2) _ (3 / 4)
Compared to the previous scenario where the fractions were (8 / 9) and (3 / 4), we've now changed the denominator of the first fraction from 9 to 2.
Fill in the blank with <, >, or = to show how this change affects the comparison of these two fractions. |
4.NF.A.2 | Compare the following fractions by choosing the correct symbol (<, >, or =) to fill in the blank:
(2 / 1) _ (4 / 9) |
4.NF.A.2 | Now, let's consider a change in the fractions. Use the correct symbol (<, >, or =) to complete the following comparison:
(2 / 1) _ (8 / 9) |
4.NF.A.2 | Compare the following fractions by inserting either <, >, or = in the space provided:
(9 / 9) _ (2 / 2) |
4.NF.A.2 | Now consider the following fractions:
(9 / 3) _ (2 / 2)
Perform the same comparison operation as in the previous problem. Recall in the previous problem we compared the fractions (9 / 9) and (2 / 2). Consider what happens if we change the denominator of the first fraction from 9 to 3. Would this make the first fracti... |
4.NF.A.2 | Determine the relationship between the following two fractions by filling the blank with <, >, or =:
(6 / 1) _ (4 / 4) |
4.NF.A.2 | Now consider this scenario:
Determine the relationship between the following two fractions by filling the blank with <, >, or =:
(6 / 1) _ (4 / 3)
How does this result compare to the previous one? |
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