Illustrative Math Alignment: Grade 7 Unit 8

Probability and Sampling

Lesson 20: Memory Test

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3 Topic Ratios, Proportions, and Percents Description This example demonstrates solving for b in a proportion where a = 8, c = 4, and d = 3. We set up the proportion 8 / b = 4 / 3 and solve for b, resulting in b = 6. This problem shows how to find an unknown value in the denominator of a proportion.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30 Topic Ratios, Proportions, and Percents Description This example illustrates how to determine if two triangles are not similar using proportions. Two triangles are shown, both with a 75° angle. The first triangle has sides of 15 and 9, while the second has sides of 28 and 18. The problem requires setting up a proportion to check for similarity: 15 / 9 = 28 / 18. After simplifying, the ratios are not equal (5 / 3 ≠ 14 / 9), concluding that the triangles are not similar.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31 Topic Ratios, Proportions, and Percents Description This example demonstrates how to determine if two right triangles are similar using proportions. Two right triangles are shown, one with legs of length 4 and 3, and the other with legs of length 10 and 7.5. The problem requires setting up a proportion to check for similarity: 4 / 3 = 10 / 7.5. After simplifying, both ratios are equal (4 / 3 = 4 / 3), confirming that the triangles are indeed similar.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32 Topic Ratios, Proportions, and Percents Description This example illustrates how to determine if two right triangles are not similar using proportions. Two right triangles are shown, one with legs of length 12 and 5, and the other with legs of length 35 and 15. The problem requires setting up a proportion to check for similarity: 12 / 5 = 35 / 15. After simplifying, the ratios are not equal (12 / 5 ≠ 7 / 3), concluding that the triangles are not similar.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33 Topic Ratios, Proportions, and Percents Description This example demonstrates how to determine if two rectangles are similar using proportions. Two rectangles are shown, with the first having dimensions 3 and 8, and the second having dimensions 9 and 24. The problem requires setting up a proportion to check for similarity: 3 / 8 = 9 / 24. After simplifying, the ratios are equal, confirming that the rectangles are indeed similar.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34 Topic Ratios, Proportions, and Percents Description This example illustrates how to determine if two rectangles are similar using proportions with algebraic expressions. Two rectangles are shown, with the first having dimensions 11.5 and 23, and the second having dimensions 23x and 46x. The problem requires setting up a proportion to check for similarity: 11.5 / 23 = 23x / 46x. After simplifying, the ratios are equal, confirming that the rectangles are indeed similar for any value of x.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 35	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 35 Topic Ratios, Proportions, and Percents Description This example demonstrates how to determine if two parallelograms are similar using proportions. Two parallelograms are shown, with the first having dimensions 6 and 9, and the second having dimensions 15 and 22.5. The problem requires setting up a proportion to check for similarity: 6 / 9 = 15 / 22.5. After simplifying, the ratios are equal, confirming that the parallelograms are indeed similar.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 36	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 36 Topic Ratios, Proportions, and Percents Description This example demonstrates how to determine if two parallelograms are not similar using proportions. Two parallelograms are shown, with the first having dimensions 9 and 28, and the second having dimensions 18 and 54. The problem requires setting up a proportion to check for similarity: 9 / 18 ≠ 28 / 54. After simplifying, the ratios are not equal, concluding that the parallelograms are not similar.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 37	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 37 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar triangles with algebraic expressions. Two triangles are shown, one with side lengths 9 and 18, and the other with expressions 6x and 10x + 6. The problem requires setting up a proportion to determine the value of x for which the triangles are similar: 9 / 18 = 6x / (10x + 6). Solving this equation leads to x = 3.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 38	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 38 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar right triangles with algebraic expressions. Two right triangles are shown, one with side lengths 4 and 3, and the other with expressions 3x and 2x + 1. The problem requires setting up a proportion to determine the value of x for which the triangles are similar: 4 / 3 = 3x / (2x + 1). Solving this equation leads to x = 4.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 39	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 39 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar rectangles with an unknown side length. Two rectangles are shown, one with side lengths of 4 and x, and the other with side lengths of 15 and 4. The problem requires setting up a proportion to determine the value of x for which the rectangles are similar: 4 / 15 = x / 4. Solving this equation leads to x = 16/15.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 4	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 4 Topic Ratios, Proportions, and Percents Description This example illustrates solving for b in a proportion where a is expressed as x + 2, and c and d are given constants (c = 5, d = 2). We set up the equation (x + 2) / b = 5 / 2 and solve for b, resulting in the expression b = (2(x + 2)) / 5. This problem demonstrates how to handle algebraic expressions in proportions.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 40	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 40 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar parallelograms with algebraic expressions. Two parallelograms are shown, one with side lengths of 6 and x, and the other with expressions of 3x + 2 and 22. The problem requires setting up a proportion to determine the value of x for which the parallelograms are similar: 6 / 22 = x / (3x + 2). Solving this equation leads to x = 3.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5 Topic Ratios, Proportions, and Percents Description This example demonstrates solving for c in a proportion where a = 9, b = 4, and d = 12. We set up the proportion 9 / 4 = c / 12 and solve for c, resulting in c = 27. This problem shows how to find an unknown value in the numerator of a proportion.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6 Topic Ratios, Proportions, and Percents Description This example illustrates solving for c in a proportion where a = 8, b = 3, and d is expressed as x + 3. We set up the equation 8 / 3 = c / (x + 3) and solve for c, resulting in the expression c = (8(x + 3)) / 3. This problem demonstrates how to handle algebraic expressions in the denominator of a proportion.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7 Topic Ratios, Proportions, and Percents Description This example demonstrates solving for d in a proportion where a = 12, b = 5, and c = 48. We set up the proportion 12 / 5 = 48 / d and solve for d, resulting in d = 20. This problem shows how to find an unknown value in the denominator of a proportion when all other values are known.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8 Topic Ratios, Proportions, and Percents Description This example illustrates solving for d in a proportion where a = 11, b = 5, and c is expressed as x - 4. We set up the equation 11 / 5 = (x - 4) / d and solve for d, resulting in the expression d = (5(x - 4)) / 11. This problem demonstrates how to handle algebraic expressions in the numerator of a proportion.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar triangles. Two triangles are shown, with one having sides of 3 and 4, and the other having sides of 6 and x. The problem requires finding the length of side x by setting up a proportion based on the similar triangles: 3 / 4 = 6 / x. Solving this equation leads to x = 8.	Proportions
Math in the News: Issue 100--Late Night TV Ratings	Math in the News: Issue 100--Late Night TV Ratings July 2014. In this issue of Math in the News we look at the mathematics of the Nielsen Ratings. This provides an excellent application of ratios, proportions, and percents. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 110--Summer Travel	Math in the News: Issue 110--Summer Travel August 2016. In this issue of Math in the News calculate average speed to various vacation destinations when traveling by car. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 113--Olympic Power	Math in the News: Issue 113--Olympic Power November 2016. In this issue of Math in the News, we look at the history of the Olympics. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 12--Doppler to the Rescue	Math in the News: Issue 12--Doppler to the Rescue 6/6/11. In this issue we look at the technology of Doppler Radar and explore its underlying mathematical structure. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Radical Functions and Equations and Ratios and Rates
Math in the News: Issue 30--An Improbable Collapse!	Math in the News: Issue 30--An Improbable Collapse! 10/10/11. In this issue we look at the Boston Red Sox and their improbable collapse in September. They were one out away from making the playoffs, but they ended their game and season in dramatic fashion. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 46--The Unemployment Rate	Math in the News: Issue 46--The Unemployment Rate February 2012. In this issue we look at unemployment statistics from the Bureau of Labor Statistics. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 48--How Good Is Jeremy Lin?	Math in the News: Issue 48--How Good Is Jeremy Lin? February 2012. In this issue of Math in the News, we look at basketball statistics, in particular the stats for Jeremy Lin. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 51--Peyton Manning	Math in the News: Issue 51--Is Peyton Manning a Good Investment? March 2012. In this issue of Math in the News we look at Peyton Manning's new contract with the Denver Broncos. Was this a good deal or not? This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 6--The BP Oil Spill, a Year Later	Math in the News: Issue 6--The BP Oil Spill, a Year Later 4/25/11. In this issue we discuss the BP oil spill one year after the spill. In particular we look at how damaging oil spills are to marine life and to oxygen levels in the water. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 62--The Washington Nationals	Math in the News: Issue 62--The Washington Nationals September 2012. In this issue of Math in the News we look at the remarkable success of the Washington Nationals baseball team. In the process we look at the success of new baseball franchises and why this happens. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 67--Election Results	Math in the News: Issue 67--Election Results November 2012. In this issue of Math in the News, we look at statistics for the recent Presidential election. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 68--Flu Season	Math in the News: Issue 68--Flu Season February 2013. In this issue of Math in the News, we look at statistics for the flu season. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 80--A Season for the Ages	Math in the News: Issue 80--A Season for the Ages October 2013. In this issue we follow Peyton Manning's extraordinary season with the Denver Broncos. This is a follow-up from Issue 51. This is an excellent opportunity to look at different data graphs, including box-and-whisker plots, bar graphs, and tabular data. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 81--The Growth of America	Math in the News: Issue 81--The Growth of America October 2013. In this issue we look at how America has grown from its formation as a country. We look at the increase in the number of states, the increase in the population, and the demographic factors that have become prominent in recent years. We look at data in tables and graphs. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 82--Halloween Stats	Math in the News: Issue 82--Halloween Stats October 2013. In this issue we look at statistics related to Halloween 2013. We explore how the economy is affecting holiday spending. We also investigate why Halloween has grown in popularity over the years. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 85--2013 Movies: A Year in Review	Math in the News: Issue 85--2013 Movies: A Year in Review January 2014. In this issue of Math in the News we look at box office data from 2013. We look for patterns in the data and analyze the data using different data displays, including bar graphs, line graphs, scatterplot, and tables. This provides an excellent opportunity for data analysis. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 86--The Rise of the Chinese Yuan	Math in the News: Issue 86--The Rise of the Chinese Yuan January 2014. In this issue of Math in the News we look at the foreign exchange market and the rise of the Chinese Yuan. The Yuan has become a significant player in the foreign exchange market and we look at currency exchange, and how to convert from one currency to another by solving a proportion. This issue provides an excellent opportunity to introduce the mathematics of money on the international market. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 95--The Iditarod Race	Math in the News: Issue 95--The Iditarod Race March 2014. In this issue of Math in the News we look at the Iditarod Race in Alaska. This gives us an opportunity to analyze data on average speed. We look at data in tables and line graphs and analyze the winning speeds over the history of the race. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Math in the News: Issue 99--What Is Bitcoin?	Math in the News: Issue 99--What Is Bitcoin? May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Ratios, Proportions, and Percents and Proportions
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 01, Level 1	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 01, Level 1 This is part of a collection of math quizzes on the topic of solving one-step equations. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Proportions
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 01, Level 2	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 01, Level 2 This is part of a collection of math quizzes on the topic of solving proportions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Proportions
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 01, Level 3	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 01, Level 3 This is part of a collection of math quizzes on the topic of solving proportions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Proportions

Illustrative Math Alignment: Grade 7 Unit 8

Probability and Sampling

Lesson 20: Memory Test

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