id stringlengths 77 537 | text stringlengths 101 1.47M | source stringclasses 1
value | added stringdate 2025-03-17 19:52:06 2025-03-17 22:27:57 | created timestamp[s]date 2013-05-16 21:27:22 2025-03-14 14:40:33 | metadata dict |
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.1%3A_Relationships_between_Quantities | 6.1.1: Relationships between Quantities
Lesson
Let's try to solve some new kinds of problems.
Exercise \(\PageIndex{1}\): Pricing Theater Popcorn
A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag.
Complete one column of the table with prices where p... | libretexts | 2025-03-17T19:52:14.795536 | 2020-04-29T02:40:13 | {
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"book_url": "https://com... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.2%3A_Reasoning_about_Contexts_with_Tape_Diagrams | 6.1.2: Reasoning about Contexts with Tape Diagrams
Lesson
Let's use tape diagrams to make sense of different kinds of stories.
Exercise \(\PageIndex{1}\): Notice and Wonder: Remembering Tape Diagrams
- What do you notice? What do you wonder?
- What are some possible values for \(a\), \(b\), and \(c\) in the first diagr... | libretexts | 2025-03-17T19:52:14.866818 | 2020-04-29T02:39:39 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.3%3A_Reasoning_about_Equations_with_Tape_Diagrams | 6.1.3: Reasoning about Equations with Tape Diagrams
Lesson
Let's see how equations can describe tape diagrams.
Exercise \(\PageIndex{1}\): Find Equivalent Expressions
Select all the expressions that are equivalent to \(7(2-3n)\). Explain how you know each expression you select is equivalent.
- \(9-10n\)
- \(14-3n\)
- \... | libretexts | 2025-03-17T19:52:14.940699 | 2020-04-29T02:39:06 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.4%3A_Reasoning_about_Equations_and_Tape_Diagrams_(Part_1) | 6.1.4: Reasoning about Equations and Tape Diagrams (Part 1)
Lesson
Let's see how tape diagrams can help us answer questions about unknown amounts in stories.
Exercise \(\PageIndex{1}\): Algebra Talk: Seeing Structure
Find a solution to each equation without writing anything down.
\(x+1=5\)
\(2(x+1)=10\)
\(3(x+1)=15\)
\... | libretexts | 2025-03-17T19:52:15.010039 | 2020-04-29T02:38:37 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.5%3A_Reasoning_about_Equations_and_Tape_Diagrams_(Part_2) | 6.1.5: Reasoning about Equations and Tape Diagrams (Part 2)
Lesson
Let's use tape diagrams to help answer questions about situations where the equation has parentheses.
Exercise \(\PageIndex{1}\): Algebra Talk: Seeing Structure
Solve each equation mentally.
\(x-1=5\)
\(2(x-1)=10\)
\(3(x-1)=15\)
\(500=100(x-1)\)
Exercis... | libretexts | 2025-03-17T19:52:15.081917 | 2020-04-29T02:37:53 | {
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"boo... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page/6.1.6%3A_Distinguishing_between_Two_Types_of_Situations | 6.1.6: Distinguishing between Two Types of Situations
Lesson
Let's think about equations with and without parentheses and the kinds of situations they describe.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Seeing Structure
Which equation doesn't belong?
\(4(x+3)=9\)
\(4\cdot x+12=9\)
\(4+3x=9\)
\(9=12+4x\)
Exe... | libretexts | 2025-03-17T19:52:15.151470 | 2020-04-29T02:37:16 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page | 6.2: Solving Equations of the Form px+q=r and p(x+q)=r and Problems That Lead to Those Equations Last updated Save as PDF Page ID 35013 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:15.223187 | 2020-01-25T01:41:38 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.1%3A_Reasoning_about_Solving_Equations_(Part_1) | 6.2.1: Reasoning about Solving Equations (Part 1)
Lesson
Let's see how a balanced hanger is like an equation and moving its weight is like solving the equation.
Exercise \(\PageIndex{1}\): Hanger Diagrams
In the two diagrams, all the triangles weigh the same and all the squares weigh the same.
For each diagram, come up... | libretexts | 2025-03-17T19:52:15.290025 | 2020-04-29T02:43:37 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.1%3A_Reasoning_about_Solving_Equations_(Part_1)",
"book_url": "h... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.2%3A_Reasoning_about_Solving_Equations_(Part_2) | 6.2.2: Reasoning about Solving Equations (Part 2)
Lesson
Let's use hangers to understand two different ways of solving equations with parentheses.
Exercise \(\PageIndex{1}\): Equivalent to \(2(x+3)\)
Select all the expressions equivalent to \(2(x+3)\).
- \(2\cdot (x+3)\)
- \((x+3)2\)
- \(2\cdot x+2\cdot 3\)
- \(2\cdot ... | libretexts | 2025-03-17T19:52:15.360746 | 2020-04-29T02:43:08 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.2%3A_Reasoning_about_Solving_Equations_(Part_2)",
"book_url": "h... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.3%3A_Dealing_with_Negative_Numbers | 6.2.3: Dealing with Negative Numbers
Lesson
Let's show that doing the same to each side works for negative numbers too.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Rational Number Arithmetic
Which equation doesn't belong?
\(\begin{array}{llll}{15=-5\cdot -3}&{\qquad}&{\qquad}&{4--2=6}\\{2+-5=-3}&{\qquad}&{\qq... | libretexts | 2025-03-17T19:52:15.427776 | 2020-04-29T02:42:40 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.3%3A_Dealing_with_Negative_Numbers",
"book_url": "https://common... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.4%3A_Different_Options_for_Solving_One_Equation | 6.2.4: Different Options for Solving One Equation
Lesson
Let's think about which way is easier when we solve equations with parentheses.
Exercise \(\PageIndex{1}\): Algebra Talk: Solve Each Equation
\(100(x-3)=1,000\)
\(500(x-3)=5,000\)
\(0.03(x-3)=0.3\)
\(0.72(x+2)=7.2\)
Exercise \(\PageIndex{2}\): Analyzing Solution ... | libretexts | 2025-03-17T19:52:15.495708 | 2020-04-29T02:42:13 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.4%3A_Different_Options_for_Solving_One_Equation",
"book_url": "h... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.5%3A_Using_Equations_to_Solve_Problems | 6.2.5: Using Equations to Solve Problems
Lesson
Let's use tape diagrams, equations, and reasoning to solve problems.
Exercise \(\PageIndex{1}\): Remember Tape Diagrams
- Write a story that could be represented by this tape diagram.
- Write an equation that could be represented by this tape diagram.
Exercise \(\PageInde... | libretexts | 2025-03-17T19:52:15.641679 | 2020-04-29T02:41:41 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.5%3A_Using_Equations_to_Solve_Problems",
"book_url": "https://co... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.6%3A_Solving_Problems_about_Percent_Increase_or_Decrease | 6.2.6: Solving Problems about Percent Increase or Decrease
Lesson
Let's use tape diagrams, equations, and reasoning to solve problems with negatives and percents.
Exercise \(\PageIndex{1}\): 20% Off
An item costs \(x\) dollars and then a 20% discount is applied. Select all the expressions that could represent the price... | libretexts | 2025-03-17T19:52:15.710740 | 2020-04-29T02:41:09 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.02%3A_New_Page/6.2.6%3A_Solving_Problems_about_Percent_Increase_or_Decrease",
"book... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page | Skip to main content
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Text Col... | libretexts | 2025-03-17T19:52:15.784197 | 2020-01-25T01:41:39 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.1%3A_Reintroducing_Inequalities | 6.3.1: Reintroducing Inequalities
Lesson
Let's work with inequalities.
Exercise \(\PageIndex{1}\): Greater Than One
The number line shows values of \(x\) that make the inequality \(x>1\) true.
-
Select
all
the values of \(x\) from this list that make the inequality \(x>1\) true.
- \(3\)
- \(-3\)
- \(1\)
- \(700\)
- \(1... | libretexts | 2025-03-17T19:52:15.858974 | 2020-04-29T02:46:19 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.1%3A_Reintroducing_Inequalities",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.2%3A_Finding_Solutions_to_Inequalities_in_Context | 6.3.2: Finding Solutions to Inequalities in Context
Lesson
Let's solve more complicated inequalities.
Exercise \(\PageIndex{1}\): Solutions to Equations and Solutions to Inequalities
- Solve \(-x=10\)
- Find 2 solutions to \(-x>10\)
- Solve \(2x=-20\)
- Find 2 solutions to \(2x>-20\)
Exercise \(\PageIndex{2}\): Earning... | libretexts | 2025-03-17T19:52:15.933234 | 2020-04-29T02:45:48 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.2%3A_Finding_Solutions_to_Inequalities_in_Context",
"book_url": ... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.3%3A_Efficiently_Solving_Inequalities | 6.3.3: Efficiently Solving Inequalities
Lesson
Let's solve more complicated inequalities.
Exercise \(\PageIndex{1}\): Lots of Negatives
Here is an inequality: \(-x\geq -4\).
- Predict what you think the solutions on the number line will look like.
-
Select
all
the values that are solutions to \(-x\geq -4\):
- \(3\)
- \... | libretexts | 2025-03-17T19:52:16.025545 | 2020-04-29T02:45:15 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.3%3A_Efficiently_Solving_Inequalities",
"book_url": "https://com... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.4%3A_Interpreting_Inequalities | 6.3.4: Interpreting Inequalities
Lesson
Let's write inequalities.
Exercise \(\PageIndex{1}\): Solve Some Inequalities!
For each inequality, find the value or values of \(x\) that make it true.
- \(8x+21\leq 56\)
- \(56<7(7-x)\)
Exercise \(\PageIndex{2}\): Club Activities Matching
Choose the inequality that best matches... | libretexts | 2025-03-17T19:52:16.099918 | 2020-04-29T02:44:48 | {
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"book_url": "https://commons.li... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.5%3A_Modeling_with_Inequalities | 6.3.5: Modeling with Inequalities
Lesson
Let's look at solutions to inequalities.
Exercise \(\PageIndex{1}\): Possible Values
The stage manager of the school musical is trying to figure out how many sandwiches he can order with the $83 he collected from the cast and crew. Sandwiches cost $5.99 each, so he lets \(x\) re... | libretexts | 2025-03-17T19:52:16.172425 | 2020-04-29T02:44:22 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.03%3A_New_Page/6.3.5%3A_Modeling_with_Inequalities",
"book_url": "https://commons.l... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page | 6.4: Writing Equivalent Expressions Last updated Save as PDF Page ID 35015 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:16.244771 | 2020-01-25T01:41:40 | {
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"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.1%3A_Subtraction_in_Equivalent_Expressions | 6.4.1: Subtraction in Equivalent Expressions
Lesson
Let's find ways to work with subtraction in expressions.
Exercise \(\PageIndex{1}\): Number Talk: Additive Inverses
Find each sum or difference mentally.
\(-30+-10\)
\(-10+-30\)
\(-30-10\)
\(10--30\)
Exercise \(\PageIndex{2}\): A Helpful Observation
Lin and Kiran are ... | libretexts | 2025-03-17T19:52:16.319581 | 2020-04-29T02:49:02 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.2%3A_Expanding_and_Factoring | 6.4.2: Expanding and Factoring
Lesson
Let's use the distributive property to write expressions in different ways.
Exercise \(\PageIndex{1}\): Number Talk: Parentheses
Find the value of each expression mentally.
\(2+3\cdot 4\)
\((2+3)(4)\)
\(2-3\cdot 4\)
\(2-(3+4)\)
Exercise \(\PageIndex{2}\): Factoring and Expanding wi... | libretexts | 2025-03-17T19:52:16.394569 | 2020-04-29T02:48:32 | {
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"book_url": "https://commons.libr... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.3%3A_Combining_Like_Terms_(Part_1) | 6.4.3: Combining Like Terms (Part 1)
Lesson
Let's see how we can tell that expressions are equivalent.
Exercise \(\PageIndex{1}\): Why is it True?
Explain why each statement is true.
- \(5+2+3=5+(2+3)\)
- \(9a\) is equivalent to \(11a-2a\).
- \(7a+4-2a\) is equivalent to \(7a+-2a+4\).
- \(8a-(8a-8)\) is equivalent to \... | libretexts | 2025-03-17T19:52:16.468918 | 2020-04-29T02:48:05 | {
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Lesson
Let's see how to use properties correctly to write equivalent expressions.
Exercise \(\PageIndex{1}\): True or False?
Select all the statements that are true. Be prepared to explain your reasoning.
- \(4-2(3+7)=4-2\cdot 3-2\cdot 7\)
- \(4-2(3+7)=4-2\cdot 3+-2\cdot 7\)
- \(4-2... | libretexts | 2025-03-17T19:52:16.543466 | 2020-04-29T02:47:38 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.04%3A_New_Page/6.4.5%3A_Combining_Like_Terms_(Part_3) | 6.4.5: Combining Like Terms (Part 3)
Lesson
Let's see how we can combine terms in an expression to write it with less terms.
Exercise \(\PageIndex{1}\): Are They Equal?
Select all expressions that are equal to \(8-12-(6+4)\).
- \(8-6-12+4\)
- \(8-12-6-4\)
- \(8-12+(6+4)\)
- \(8-12-6+4\)
- \(8-4-12-6\)
Exercise \(\PageI... | libretexts | 2025-03-17T19:52:16.618717 | 2020-04-29T02:47:11 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.05%3A_New_Page | 6.5: Let's Put it to Work Last updated Save as PDF Page ID 35016 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:16.689371 | 2020-01-25T01:41:40 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.05%3A_New_Page/6.5.1%3A_Applications_of_Expressions | 6.5.1: Applications of Expressions
Lesson
Let's use expressions to solve problems.
Exercise \(\PageIndex{1}\): Algebra Talk: Equivalent to \(0.75t-21\)
Decide whether each expression is equivalent to \(0.75t-21\). Be prepared to explain how you know.
\(\frac{3}{4}t-21\)
\(\frac{3}{4}(t-21)\)
\(0.75(t-28)\)
\(t-0.25t-21... | libretexts | 2025-03-17T19:52:16.748912 | 2020-04-29T02:49:40 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7 | 7: Angles, Triangles, and Prisms Last updated Save as PDF Page ID 35018 Illustrative Mathematics OpenUp Resources 7.1: Angle Relationships 7.1.1: Relationships of Angles 7.1.2: Adjacent Angles 7.1.3: Nonadjacent Angles 7.1.4: Solving for Unknown Angles 7.1.5: Using Equations to Solve for Unknown Angles 7.2: Drawing Pol... | libretexts | 2025-03-17T19:52:16.833725 | 2020-01-25T01:41:42 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.01%3A_New_Page | 7.1: Angle Relationships Last updated Save as PDF Page ID 35019 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:16.979633 | 2020-01-25T01:41:43 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.01%3A_New_Page/7.1.1%3A_Relationships_of_Angles | 7.1.1: Relationships of Angles
Lesson
Let's examine some special angles.
Exercise \(\PageIndex{1}\): Visualizing Angles
Use the applet to answer the questions.
- Which angle is bigger, \(a\) or \(b\)?
- Identify an obtuse angle in the diagram.
Exercise \(\PageIndex{2}\): Pattern Block Angles
1. Look at the different pa... | libretexts | 2025-03-17T19:52:17.051863 | 2020-05-04T00:18:49 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.01%3A_New_Page/7.1.2%3A_Adjacent_Angles | 7.1.2: Adjacent Angles
Lesson
Let's look at some special pairs of angles.
Exercise \(\PageIndex{1}\): Estimating Angle Measures
Estimate the degree measure of each indicated angle.
Exercise \(\PageIndex{2}\): Cutting Rectangles
Your teacher will give you two small, rectangular papers.
1. On one of the papers, draw a sm... | libretexts | 2025-03-17T19:52:17.133056 | 2020-05-04T00:18:24 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.01%3A_New_Page/7.1.3%3A_Nonadjacent_Angles | 7.1.3: Nonadjacent Angles
Lesson
Let's look at angles that are not right next to one another.
Exercise \(\PageIndex{1}\): Finding Related Statements
Given \(a\) and \(b\) are numbers, and \(a+b=180\), which statements also must be true?
\(a=180-b\qquad a-180=b\qquad 360=2a+2b\qquad a=90\text{ and }b=90\)
Exercise \(\Pa... | libretexts | 2025-03-17T19:52:17.215655 | 2020-05-04T00:18:01 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.01%3A_New_Page/7.1.4%3A_Solving_for_Unknown_Angles | 7.1.4: Solving for Unknown Angles
Lesson
Let's figure out some missing angles.
Exercise \(\PageIndex{1}\): True or False: Length Relationships
Here are some line segments.
Decide if each of these equations is true or false. Be prepared to explain your reasoning.
\(CD+BC=BD\)
\(AB+BD=CD+AD\)
\(AC-AB=AB\)
\(BD-CD=AC-AB\)... | libretexts | 2025-03-17T19:52:17.301003 | 2020-05-04T00:17:36 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.01%3A_New_Page/7.1.5%3A_Using_Equations_to_Solve_for_Unknown_Angles | 7.1.5: Using Equations to Solve for Unknown Angles
Lesson
Let's figure out missing angles using equations.
Exercise \(\PageIndex{1}\): Is this Enough?
Tyler thinks that this figure has enough information to figure out the values of \(a\) and \(b\).
Do you agree? Explain your reasoning.
Exercise \(\PageIndex{2}\): What ... | libretexts | 2025-03-17T19:52:17.378987 | 2020-05-04T00:17:11 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page | 7.2: Drawing Polygons with Given Conditions Last updated Save as PDF Page ID 35020 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:17.454240 | 2020-01-25T01:41:44 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.1%3A_Building_Polygons_(Part_1) | 7.2.1: Building Polygons (Part 1)
Lesson
Let's build shapes.
Exercise \(\PageIndex{1}\): True or False: Signed Numbers
Decide whether each equation is true or false. Be prepared to explain your reasoning.
\(4\cdot (-6)=(-6)+(-6)+(-6)+(-6)\)
\(-8\cdot 4=(-8\cdot 3)+4\)
\(6\cdot (-7)=7\cdot (-7)+7\)
\(-10-6=-10-(-6)\)
Ex... | libretexts | 2025-03-17T19:52:17.521881 | 2020-05-04T00:22:05 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.1%3A_Building_Polygons_(Part_1)",
"book_url": "https://commons.l... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.2%3A_Building_Polygons_(Part_2) | 7.2.2: Building Polygons (Part 2)
Lesson
Let's build more triangles.
Exercise \(\PageIndex{1}\): Where is Lin?
At a park, the slide is 5 meters east of the swings. Lin is standing 3 meters away from the slide.
- Draw a diagram of the situation including a place where Lin could be.
- How far away from the swings is Lin ... | libretexts | 2025-03-17T19:52:17.593594 | 2020-05-04T00:21:35 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.2%3A_Building_Polygons_(Part_2)",
"book_url": "https://commons.l... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.3%3A_Triangles_with_3_Common_Measures | 7.2.3: Triangles with 3 Common Measures
Lesson
Let's contrast triangles.
Exercise \(\PageIndex{1}\): 3 Sides; 3 Angles
Examine each set of triangles. What do you notice? What is the same about the triangles in the set? What is different?
Set 1:
Set 2:
Exercise \(\PageIndex{2}\): 2 Sides and 1 Angle
Examine this set of ... | libretexts | 2025-03-17T19:52:17.659345 | 2020-05-04T00:21:07 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.3%3A_Triangles_with_3_Common_Measures",
"book_url": "https://com... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.4%3A_Drawing_Triangles_(Part_1) | 7.2.4: Drawing Triangles (Part 1)
Lesson
Let's see how many different triangles we can draw with certain measurements.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Triangles
Which one doesn't belong?
Exercise \(\PageIndex{2}\): Does Your Triangle Match Theirs?
Three students have each drawn a triangle. For eac... | libretexts | 2025-03-17T19:52:17.730819 | 2020-05-04T00:20:30 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.4%3A_Drawing_Triangles_(Part_1)",
"book_url": "https://commons.l... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.5%3A_Drawing_Triangles_(Part_2) | 7.2.5: Drawing Triangles (Part 2)
Lesson
Let's draw some more triangles.
Exercise \(\PageIndex{1}\): Using a Compass to Estimate Length
- Draw a \(40^{\circ}\) angle.
- Use a compass to make sure both sides of your angle have a length of 5 centimeters.
- If you connect the ends of the sides you drew to make a triangle,... | libretexts | 2025-03-17T19:52:17.799654 | 2020-05-04T00:20:04 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.02%3A_New_Page/7.2.5%3A_Drawing_Triangles_(Part_2)",
"book_url": "https://commons.l... |
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Text Col... | libretexts | 2025-03-17T19:52:17.873179 | 2020-01-25T01:41:45 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.1%3A_Slicing_Solids | 7.3.1: Slicing Solids
Lesson
Let's see what shapes you get when you slice a three-dimensional object.
Exercise \(\PageIndex{1}\): Prisms, Pyramids, and Polyhedra
Describe each shape as precisely as you can. Click on the applet and drag the mouse to show the object turning in 3D.
Exercise \(\PageIndex{2}\): What's the C... | libretexts | 2025-03-17T19:52:17.948405 | 2020-05-04T00:25:36 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.1%3A_Slicing_Solids",
"book_url": "https://commons.libretexts.or... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.2%3A_Volume_of_Right_Prisms | 7.3.2: Volume of Right Prisms
Lesson
Let's look at volumes of prisms.
Exercise \(\PageIndex{1}\): Three Prisms with the Same Volume
Rectangles A, B, and C represent bases of three prisms.
- If each prism has the same height, which one will have the greatest volume , and which will have the least? Explain your reasoning... | libretexts | 2025-03-17T19:52:18.032103 | 2020-05-04T00:25:09 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.2%3A_Volume_of_Right_Prisms",
"book_url": "https://commons.libre... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.3%3A_Decomposing_Bases_for_Area | 7.3.3: Decomposing Bases for Area
Lesson
Let's look at how some people use volume.
Exercise \(\PageIndex{1}\): Are These Prisms?
1. Which of these solids are prisms? Explain how you know.
2. For each of the prisms, what does the base look like?
- Shade one base in the picture.
- Draw a cross section of the prism parall... | libretexts | 2025-03-17T19:52:18.107594 | 2020-05-04T00:24:38 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.3%3A_Decomposing_Bases_for_Area",
"book_url": "https://commons.l... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.4%3A_Surface_Area_of_Right_Prisms | 7.3.4: Surface Area of Right Prisms
Lesson
Let's look at the surface area of prisms.
Exercise \(\PageIndex{1}\): Multifaceted
Your teacher will show you a prism.
- What are some things you could measure about the object?
- What units would you use for these measurements?
Exercise \(\PageIndex{2}\): So Many Faces
Here i... | libretexts | 2025-03-17T19:52:18.273357 | 2020-05-04T00:24:09 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.5%3A_Distinguishing_Volume_and_Surface_Area | 7.3.5: Distinguishing Volume and Surface Area
Lesson
Let's work with surface area and volume in context.
Exercise \(\PageIndex{1}\): THe Science Fair
Mai’s science teacher told her that when there is more ice touching the water in a glass, the ice melts faster. She wants to test this statement so she designs her scienc... | libretexts | 2025-03-17T19:52:18.349914 | 2020-05-04T00:23:38 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.03%3A_New_Page/7.3.6%3A_Applying_Volume_and_Surface_Area | 7.3.6: Applying Volume and Surface Area
Lesson
Let's explore things that are proportional to volume or surface area.
Exercise \(\PageIndex{1}\): You Decide
For each situation, decide if it requires Noah to calculate surface area or volume. Explain your reasoning.
- Noah is planning to paint the bird house he built. He ... | libretexts | 2025-03-17T19:52:18.429928 | 2020-05-04T00:22:59 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.04%3A_New_Page | 7.4: Let's Put It to work Last updated Save as PDF Page ID 35022 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:18.500472 | 2020-01-25T01:41:46 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/07%3A_Untitled_Chapter_7/7.04%3A_New_Page/7.4.1%3A_Building_Prisms | 7.4.1: Building Prisms
Lesson
Let's build a triangular prism from scratch.
Exercise \(\PageIndex{1}\): Nets
Here are some nets for various prisms.
- What would each net look like when folded?
- What do you notice about the nets?
Exercise \(\PageIndex{2}\): Making the Base
The base of a triangular prism has one side tha... | libretexts | 2025-03-17T19:52:18.561740 | 2020-05-04T00:26:50 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8 | 8: Probability and Sampling Last updated Save as PDF Page ID 35025 Illustrative Mathematics OpenUp Resources 8.1: Probabilities of Single Step Events 8.1.1: Mystery Bags 8.1.2: Chance Experiments 8.1.3: What are Probabilities? 8.1.4: Estimating Probabilities Through Repeated Experiments 8.1.5: More Estimating Probabili... | libretexts | 2025-03-17T19:52:18.650459 | 2020-01-25T01:41:48 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.01%3A_New_Page | 8.1: Probabilities of Single Step Events Last updated Save as PDF Page ID 35026 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:18.721872 | 2020-01-25T01:41:49 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
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"book_url": "https://commons.libretexts.org/book/math-34975",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.01%3A_New_Page/8.1.1%3A_Mystery_Bags | 8.1.1: Mystery Bags
Lesson
Let's make predictions based on what we know.
Exercise \(\PageIndex{1}\): Going Fishing
Andre and his dad have been fishing for 2 hours. In that time, they have caught 9 bluegills and 1 yellow perch.
The next time Andre gets a bite, what kind of fish do you think it will be? Explain your reas... | libretexts | 2025-03-17T19:52:18.791985 | 2020-05-11T07:53:34 | {
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"book_url": "https://commons.libretexts.org/... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.01%3A_New_Page/8.1.2%3A_Chance_Experiments | 8.1.2: Chance Experiments
Lesson
Let's investigate chance.
Exercise \(\PageIndex{1}\): Which is More Likely?
Which is more likely to happen?
- When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes, you pull out a left shoe.
- When listening to a playlist—which has 5 songs on it—in s... | libretexts | 2025-03-17T19:52:18.870421 | 2020-05-11T07:53:12 | {
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"book_url": "https://commons.libretext... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.01%3A_New_Page/8.1.3%3A_What_are_Probabilities | 8.1.3: What are Probabilities?
Lesson
Let's find out what's possible.
Exercise \(\PageIndex{1}\): Which Game Would You CHoose?
Which game would you choose to play? Explain your reasoning.
Game 1: You flip a coin and win if it lands showing heads.
Game 2: You roll a standard number cube and win if it lands showing a num... | libretexts | 2025-03-17T19:52:18.951003 | 2020-05-11T07:52:43 | {
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Lesson
Let's do some experimenting.
Exercise \(\PageIndex{1}\): Decimals on the Number Line
-
Locate and label these numbers on the number line.
- \(0.5\)
- \(0.75\)
- \(0.33\)
- \(0.67\)
- \(0.25\)
- Choose one of the numbers from the previous question. Desc... | libretexts | 2025-03-17T19:52:19.027395 | 2020-05-11T07:52:13 | {
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Lesson
Let's estimate some probabilities.
Exercise \(\PageIndex{1}\): Is it Likely?
- If the weather forecast calls for a 20% chance of light rain tomorrow, would you say that it is likely to rain tomorrow?
- If the probability of a tornado today is \(\frac{1}{10}\), would you say t... | libretexts | 2025-03-17T19:52:19.104925 | 2020-05-11T07:51:39 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.01%3A_New_Page/8.1.6%3A_Estimating_Probabilities_Using_Simulation | 8.1.6: Estimating Probabilities Using Simulation
Lesson
Let's simulate real-world situations.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Spinners
Which spinner doesn't belong?
Exercise \(\PageIndex{2}\): Deigo's Walk
Your teacher will give your group the supplies for one of the three different simulations. F... | libretexts | 2025-03-17T19:52:19.200526 | 2020-05-11T07:50:29 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page | 8.2: Probabilites of Multi-step Events Last updated Save as PDF Page ID 35027 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:19.272228 | 2020-01-25T01:41:50 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.1%3A_Simulating_Multi-step_Experiments | 8.2.1: Simulating Multi-step Experiments
Lesson
Let's simulate more complicated events.
Exercise \(\PageIndex{1}\): Notice and Wonder: Ski Business
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): Alpine Zoom
Alpine Zoom is a ski business. To make money over spring break, they need it to snow at leas... | libretexts | 2025-03-17T19:52:19.352171 | 2020-05-11T07:57:02 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.1%3A_Simulating_Multi-step_Experiments",
"book_url": "https://co... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.2%3A_Keeping_Track_of_All_Possible_Outcomes | 8.2.2: Keeping Track of All Possible Outcomes
Lesson
Lets explore sample spaces for experiments with multiple parts.
Exercise \(\PageIndex{1}\): How Many Different Meals?
How many different meals are possible if each meal includes one main course, one side dish, and one drink?
| main courses | side dishes | drinks |
|-... | libretexts | 2025-03-17T19:52:19.508289 | 2020-05-11T07:56:29 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.2%3A_Keeping_Track_of_All_Possible_Outcomes",
"book_url": "https... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.3%3A_Multi-step_Experiments | 8.2.3: Multi-step Experiments
Lesson
Let's look at probabilities of experiments that have multiple steps.
Exercise \(\PageIndex{1}\): True or False?
Is each equation true or false? Explain your reasoning.
\(8=(8+8+8+8)\div 3\)
\((10+10+10+10+10)\div 5=10\)
\(6+4+6+4+6+4)\div 6=5\)
Exercise \(\PageIndex{2}\): Spinning a... | libretexts | 2025-03-17T19:52:19.577809 | 2020-05-11T07:55:52 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.3%3A_Multi-step_Experiments",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.02%3A_New_Page/8.2.4%3A_Designing_Simulations | 8.2.4: Designing Simulations
Lesson
Let's simulate some real-life scenarios.
Exercise \(\PageIndex{1}\): Number Talk: Division
Find the value of each expression mentally.
\((4.2+3)\div 2\)
\((4.2+2.6+4)\div 3\)
\((4.2+2.6+4+3.6)\div 4\)
\((4.2+2.6+4+3.6+3.6)\div 5\)
Exercise \(\PageIndex{2}\): Breeding Mice
A scientist... | libretexts | 2025-03-17T19:52:19.650541 | 2020-05-11T07:54:47 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.03%3A_New_Page",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.03%3A_New_Page/8.3.1%3A_Comparing_Groups | 8.3.1: Comparing Groups
Lesson
Let's compare two groups.
Exercise \(\PageIndex{1}\): Notice and Wonder: Comparing Heights
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): More Team Heights
-
How much taller is the volleyball team than the gymnastics team?
- Gymnastics team’s heights (in inches) : 56,... | libretexts | 2025-03-17T19:52:19.795887 | 2020-05-11T07:59:27 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
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"book_url": "https://commons.libretexts.... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.03%3A_New_Page/8.3.2%3A_Larger_Populations | 8.3.2: Larger Populations
Lesson
Let's compare larger groups.
Exercise \(\PageIndex{1}\): First Name versus Last Name
Consider the question: In general, do the students at this school have more letters in their first name or last name? How many more letters?
- What are some ways you might get some data to answer the qu... | libretexts | 2025-03-17T19:52:19.876357 | 2020-05-11T07:58:55 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.03%3A_New_Page/8.3.3%3A_What_Makes_a_Good_Sample | 8.3.3: What Makes a Good Sample?
Lesson
Let's see what makes a good sample.
Exercise \(\PageIndex{1}\): Number Talk: Division by Powers of 10
Find the value of each quotient mentally.
\(34,000\div 10\)
\(340\div 100\)
\(34\div 10\)
\(3.4\div 100\)
Exercise \(\PageIndex{2}\): Selling Paintings
Your teacher will assign y... | libretexts | 2025-03-17T19:52:19.954162 | 2020-05-11T07:58:24 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.03%3A_New_Page/8.3.3%3A_What_Makes_a_Good_Sample",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.03%3A_New_Page/8.3.4%3A_Sampling_in_a_Fair_Way | 8.3.4: Sampling in a Fair Way
Lesson
Let's explore ways to get representative samples.
Exercise \(\PageIndex{1}\): Ages of Moviegoers
A survey was taken at a movie theater to estimate the average age of moviegoers.
Here is a dot plot showing the ages of the first 20 people surveyed.
- What questions do you have about t... | libretexts | 2025-03-17T19:52:20.038586 | 2020-05-11T07:57:55 | {
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Lesson
Let's use samples to estimate measures of center for the population.
Exercise \(\PageIndex{1}\): Describing the Center
Would you use the median or mean to describe the center of each data set? Explain your reasoning.
Heights of 50 basketball players
Ages of 30 peop... | libretexts | 2025-03-17T19:52:20.197472 | 2020-05-11T08:02:50 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.04%3A_New_Page/8.4.1%3A_Estimating_Population_Measures_of_Center",
"book_url": "htt... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.04%3A_New_Page/8.4.2%3A_Estimating_Population_Proportions | 8.4.2: Estimating Population Proportions
Lesson
Let's estimate population proportions using samples.
Exercise \(\PageIndex{1}\): Getting to School
A teacher asked all the students in one class how many minutes it takes them to get to school. Here is a list of their responses:
\(20\quad 10\quad 15\quad 8\quad 5\quad 15\... | libretexts | 2025-03-17T19:52:20.289174 | 2020-05-11T08:02:20 | {
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Lesson
Let's compare samples from the same population.
Exercise \(\PageIndex{1}\): Average Reactions
The other day, you worked with the reaction times of twelfth graders to see if they were fast enough to help out at the track meet. Look back at the sample you collected.
- Calcula... | libretexts | 2025-03-17T19:52:20.365751 | 2020-05-11T08:01:53 | {
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Lesson
Let's compare different populations using samples.
Exercise \(\PageIndex{1}\): Same Mean? Same MAD?
Without calculating, tell whether each pair of data sets have the same mean and whether they have the same mean absolute deviation.
-
set A 1 3 3 5 6 8 10 14 set B 21 23 ... | libretexts | 2025-03-17T19:52:20.456481 | 2020-05-11T08:01:23 | {
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Lesson
Let's ask important questions to compare groups.
Exercise \(\PageIndex{1}\): Features of Graphic Representations
Dot plots, histograms, and box plots are different ways to represent a data set graphically.
Which of those displays would be the easiest to use to find each ... | libretexts | 2025-03-17T19:52:20.531084 | 2020-05-11T08:00:48 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/08%3A_Untitled_Chapter_8/8.05%3A_New_Page | 8.5: Let's Put it to Work Last updated Save as PDF Page ID 35030 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:20.601725 | 2020-01-25T01:41:53 | {
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Lesson
Let's put it all together.
Exercise \(\PageIndex{1}\): Collecting a Sample
You teacher will give you a paper that lists a data set with 100 numbers in it. Explain whether each method of obtaining a sample of size 20 would produce a random sample.
Option 1: A spinner has 10 equal sections on it... | libretexts | 2025-03-17T19:52:20.735072 | 2020-05-11T08:03:40 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9 | 9: Putting it All Together Last updated Save as PDF Page ID 35032 Illustrative Mathematics OpenUp Resources 9.1: Running a Restaurant 9.1.1: Planning Recipes 9.1.2: Costs of Running a Restaurant 9.1.3: More Costs of Running a Restaurant 9.1.4: Restaurant Floor Plan 9.2: Making Connections 9.2.1: How Crowded Is this Nei... | libretexts | 2025-03-17T19:52:20.816658 | 2020-01-25T01:41:54 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.01%3A_New_Page/9.1.1%3A_Planning_Recipes | 9.1.1: Planning Recipes
Lesson
Let's choose some recipes for a restaurant.
Exercise \(\PageIndex{1}\): A Recipe for Your Restaurant
Imagine you could open a restaurant.
- Select a recipe for a main dish you would like to serve at your restaurant.
-
Record the amount of each ingredient from your recipe in the first two ... | libretexts | 2025-03-17T19:52:21.323995 | 2020-01-25T01:41:58 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.01%3A_New_Page/9.1.2%3A_Costs_of_Running_a_Restaurant | 9.1.2: Costs of Running a Restaurant
Lesson
Let's explore how much the food will cost.
Exercise \(\PageIndex{1}\): Introducing Spreadsheets
-
Type each formula into the cells of a spreadsheet program and press enter. Record what the cell displays. Make sure to type each formula exactly as it is written here.
A B C D 1 ... | libretexts | 2025-03-17T19:52:21.396708 | 2020-01-25T01:41:59 | {
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Lesson
Let's explore how much it costs to run a restaurant.
Exercise \(\PageIndex{1}\): Are We Making Money?
-
Restaurants have many more expenses than just the cost of the food.
- Make a list of other items you would have to spend money on if you were running a restaurant.
- I... | libretexts | 2025-03-17T19:52:21.457678 | 2020-01-25T01:41:59 | {
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Lesson
Let's design the floor plan for a restaurant.
Exercise \(\PageIndex{1}\): Dining Area
- Restaurant owners say it is good for each customer to have about 300 in 2 of space at their table. How many customers would you seat at each table?
-
It is good to have about 15 ft
2
of floor spac... | libretexts | 2025-03-17T19:52:21.515911 | 2020-05-20T18:27:56 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.02%3A_New_Page | 9.2: Making Connections Last updated Save as PDF Page ID 35034 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:21.586414 | 2020-01-25T01:41:56 | {
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Lesson
Let's see how proportional relationships apply to where people live.
Exercise \(\PageIndex{1}\): Dot Density
The figure shows four squares. Each square encloses an array of dots. Squares A and B have side length 2 inches. Squares C and D have side length 1 inch.
-
Complet... | libretexts | 2025-03-17T19:52:21.657323 | 2020-05-20T18:31:07 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.02%3A_New_Page/9.2.2%3A_Fermi_Problems | 9.2.2: Fermi Problems
Lesson
Let's estimate some quantities.
Exercise \(\PageIndex{1}\): How Old Are You?
What is your exact age at this moment?
Exercise \(\PageIndex{2}\): A Heart Stoppingly Large Number
How many times has your heart beat in your lifetime?
Exercise \(\PageIndex{3}\): All the Hairs on Your Head
How man... | libretexts | 2025-03-17T19:52:21.712760 | 2020-05-20T18:30:32 | {
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Lesson
Let's solve harder problems by writing equivalent expressions.
Exercise \(\PageIndex{1}\): Tickets for the School Play
Student tickets for the school play cost $2 less than adult tickets.
- If \(a\) represents the price of one adult ticket, write an expression for the price ... | libretexts | 2025-03-17T19:52:21.771312 | 2020-05-20T18:30:06 | {
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Lesson
Let's check how accurate our measurements are.
Exercise \(\PageIndex{1}\): How Long Are These Pencils?
- Estimate the length of each pencil.
- How accurate are your estimates?
- For each estimate, what is the largest possible percent error?
Exercise \(\PageIndex{2}\): How Long A... | libretexts | 2025-03-17T19:52:21.899499 | 2020-05-20T18:29:39 | {
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Lesson
Let's check how accurate our calculations are.
Exercise \(\PageIndex{1}\): Measurement Error for Area
Imagine that you measure the length and width of a rectangle and you know the measurements are accurate within 5% of the actual measurements. If you use your measurements to fin... | libretexts | 2025-03-17T19:52:21.954544 | 2020-05-20T18:29:00 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.03%3A_New_Page | 9.3: Designing a Course Last updated Save as PDF Page ID 35035 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:22.026722 | 2020-01-25T01:41:57 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.03%3A_New_Page/9.3.1%3A_Measuring_Long_Distances_Over_Uneven_Terrain | 9.3.1: Measuring Long Distances Over Uneven Terrain
Lesson
Let's measure long distances over uneven terrain.
Exercise \(\PageIndex{1}\): How Far Is It?
How do people measure distances in different situations? What tools do they use? Come up with at least three different methods and situations where those methods are us... | libretexts | 2025-03-17T19:52:22.087847 | 2020-05-20T18:33:19 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.03%3A_New_Page/9.3.2%3A_Building_a_Trundle_Wheel | 9.3.2: Building a Trundle Wheel
Lesson
Let's build a trundle wheel.
Exercise \(\PageIndex{1}\): What Is a Trundle Wheel?
A tool that surveyors use to measure distances is called a trundle wheel.
- How does a trundle wheel measure distance?
- Why is this method of measuring distances better than the methods we used in t... | libretexts | 2025-03-17T19:52:22.144331 | 2020-05-20T18:32:48 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.03%3A_New_Page/9.3.3%3A_Using_a_Trundle_Wheel_to_Measure_Distances | 9.3.3: Using a Trundle Wheel to Measure Distances
Lesson
Let's use our trundle wheels.
Exercise \(\PageIndex{1}\): Measuring Distances with the Trundle Wheel
Earlier you made trundle wheels so that you can measure long distances.
If you do not have a trundle wheel, you can use an applet to simulate measuring. Your teac... | libretexts | 2025-03-17T19:52:22.203839 | 2020-05-20T18:32:19 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/09%3A_Untitled_Chapter_9/9.03%3A_New_Page/9.3.4%3A_Designing_a_5K_Course | 9.3.4: Designing a 5K Course
Lesson
Let's map out the 5K course.
Exercise \(\PageIndex{1}\): Make a Proposal
Your teacher will give you a map of the school grounds.
- On the map, draw in the path you measured earlier with your trundle wheel and label its length.
- Invent another route for a walking course and draw it o... | libretexts | 2025-03-17T19:52:22.259535 | 2020-05-20T18:31:51 | {
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https://human.libretexts.org/Courses/American_River_College/HUM_301%3A_Introduction_to_Humanities_Textbook_(Collom)/02%3A_The_Self/2.05%3A_Art_and_Identity-_Introduction | 2.5: Art and Identity- Introduction
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One of the more important themes emerging from the last century has been the individual’s search for identity. For example, genealogical websites have proliferated and special television programs are devoted to the subject. Since it first aired on PBS i... | libretexts | 2025-03-17T19:52:22.625207 | 2021-06-15T23:26:21 | {
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"book_url": "https://comm... |
https://human.libretexts.org/Courses/American_River_College/HUM_301%3A_Introduction_to_Humanities_Textbook_(Collom)/03%3A_Morality/3.04%3A_Art_and_Ethics-_Introduction | 3.4: Art and Ethics- Introduction
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This chapter is concerned with the perception, susceptibility, and ethics of art. It will explore and analyze the moral responsibility of artists and their rights to represent and create without censorship.
Morality and art are connected usually in art th... | libretexts | 2025-03-17T19:52:23.042976 | 2021-06-15T23:26:33 | {
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"book_url": "https://common... |
https://human.libretexts.org/Courses/American_River_College/HUM_301%3A_Introduction_to_Humanities_Textbook_(Collom)/04%3A_Happiness/4.01%3A_The_Pursuit_of_Happiness | 4.1: The Pursuit of Happiness
Learning Objectives
- Define and discuss happiness, including its determinants
- Describe the field of positive psychology and identify the kinds of problems it addresses
- Explain the meaning of positive affect and discuss its importance in health outcomes
- Describe the concept of flow a... | libretexts | 2025-03-17T19:52:23.343777 | 2021-06-15T23:26:42 | {
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https://human.libretexts.org/Courses/American_River_College/HUM_301%3A_Introduction_to_Humanities_Textbook_(Collom)/08%3A_Freedom/8.01%3A_Freedom_of_the_Will | 8.1: Freedom of the Will
Free will is the ability to choose between different possible courses of action. It is closely linked to the concepts of responsibility, praise, guilt, sin, and other judgments which apply only to actions that are freely chosen. It is also connected with the concepts of advice, persuasion, deli... | libretexts | 2025-03-17T19:52:24.433205 | 2021-06-15T23:27:14 | {
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“ Alan Turing ” 29
Alan Mathison Turing OBE FRS (/ˈtjʊərɪŋ/; 23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst and theoretical biologist. He was highly influential in the development of theoretical computer science,... | libretexts | 2025-03-17T19:52:24.512935 | 2021-06-15T23:27:17 | {
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“Physical Determinism” 33
Physical determinism generally refers to the assertion of a deterministic physical universe (greater physical system). This holds that a complete description of the physical state of the world at any given time and a complete statement of the p... | libretexts | 2025-03-17T19:52:24.596566 | 2021-06-15T23:27:17 | {
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https://human.libretexts.org/Courses/American_River_College/HUM_301%3A_Introduction_to_Humanities_Textbook_(Collom)/08%3A_Freedom/8.01%3A_Freedom_of_the_Will/8.1.03%3A_The_Illusion_of_Free_Will | 8.1.3: The Illusion of Free Will
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The Illusion of Free Will 35
80. Theologians repeatedly tell us, that man is free, while all their principles conspire to destroy his liberty. By endeavouring to justify the Divinity, they in reality accuse him of the blackest injustice. They suppose, that... | libretexts | 2025-03-17T19:52:24.658346 | 2021-06-15T23:27:18 | {
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Compatibilism 36
Frankfurt Cases - The Principle of Alternate Possibilities
Alternative Possibilities are one of the key requirements for the freedom component of free will, critically needed for libertarian free will.
Alternative Possibilities have been part of the p... | libretexts | 2025-03-17T19:52:24.724350 | 2021-06-15T23:27:19 | {
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