Illustrative Math Alignment: Grade 7 Unit 1

Scale Drawings

Lesson 10: Changing Scales in Scale Drawings

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 24	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 24 Topic Ratios, Proportions, and Percents Description This example illustrates solving a complex proportion problem using similar equilateral triangles with algebraic expressions. Two equilateral triangles are shown, with the smaller one having a side length of 3x, and the larger one having side lengths labeled as (4x + 1) and (x + 1). The problem requires setting up a proportion: 3x / (4x + 1) = 3x / (3x + (x + 1)). Solving this equation leads to a quadratic equation, which when solved gives x ≈ 7/1.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 25	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 25 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar rectangles. Two rectangles are shown, with the smaller one having sides of 2 and 3, and the larger one having sides of x and 15. The problem requires finding the length of side x by setting up a proportion: 2 / 3 = x / 15. Solving this equation leads to x = 10.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 26	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 26 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar rectangles with algebraic expressions. Two rectangles are shown, with the smaller one having sides of 5 and 12, and the larger one having sides of x + 5 and 3x + 6. The problem requires setting up a proportion: 5 / 12 = (x + 5) / (3x + 6). Solving this equation leads to x = 10, which then allows us to find the side lengths of the larger rectangle as 15 and 36.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 27	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 27 Topic Ratios, Proportions, and Percents Description This example demonstrates solving a proportion problem using similar parallelograms. Two parallelograms are shown, with the smaller one having sides of 8 and 18, and the larger one having sides of 20 and x. The problem requires finding the length of side x by setting up a proportion: 8 / 18 = 20 / x. Solving this equation leads to x = 45.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 28	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 28 Topic Ratios, Proportions, and Percents Description This example illustrates solving a proportion problem using similar parallelograms with algebraic expressions. Two parallelograms are shown, with the smaller one having sides of 9 and 21, and the larger one having sides of x + 12 and 4x + 3. The problem requires setting up a proportion: 9 / 21 = (x + 12) / (4x + 3). Solving this equation leads to x = 15, which then allows us to find the side lengths of the larger parallelogram as 27 and 63.	Proportions
Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29	Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29 Topic Ratios, Proportions, and Percents Description This example demonstrates how to determine if two triangles are similar using proportions. Two triangles are shown, both with a 70° angle. The first triangle has sides of 12 and 10, while the second has sides of 18 and 15. The problem requires setting up a proportion to check for similarity: 12 / 10 = 18 / 15. After simplifying, both ratios are equal (6 / 5 = 6 / 5), confirming that the triangles are indeed similar.	Proportions
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 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 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
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 02, Level 1	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 02, Level 1 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 02, Level 2	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 02, 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 02, Level 3	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 02, 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
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 03, Level 1	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 03, Level 1 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 03, Level 2	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 03, 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 03, Level 3	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 03, 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
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 04, Level 1	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 04, Level 1 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 04, Level 2	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 04, 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 04, Level 3	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 04, 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
Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 05, Level 1	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 05, Level 1 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 05, Level 2	Paper-and-Pencil Quiz: Solving Proportions for a, Quiz 05, 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

Illustrative Math Alignment: Grade 7 Unit 1

Scale Drawings

Lesson 10: Changing Scales in Scale Drawings

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