Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 11: Percentages and Double Number Lines

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
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 Example: Percents with Double Number Lines: Example 1	Math Example: Percents with Double Number Lines: Example 1 Topic Ratios, Proportions, Percents Description This example demonstrates how to find 50% of 250 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 250. By aligning 50% on the percentage line with its corresponding value on the numerical line, we can see that 50% of 250 is 125. This method visually represents the concept that 50% is equivalent to one-half of a quantity.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 10	Math Example: Percents with Double Number Lines: Example 10 Topic Ratios, Proportions, Percents Description This example demonstrates how to determine an unknown value using a double number line when given a part and its corresponding percentage, involving a decimal percentage. The image shows two number lines: one ranging from 0 to 100% and another from 0 to an unknown number x. The position 70 is marked on the second line, visually illustrating the process of finding x when 70 is 12.5% of x.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 11	Math Example: Percents with Double Number Lines: Example 11 Topic Ratios, Proportions, Percents Description This example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 75, with 25 marked as an intermediate point. This visual representation helps students understand the relationship between the part (25) and the whole (75) in percentage terms.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 12	Math Example: Percents with Double Number Lines: Example 12 Topic Ratios, Proportions, Percents Description This example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 220, with 55 marked as an intermediate point. This visual representation helps students understand the relationship between the part (55) and the whole (220) in percentage terms.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 13	Math Example: Percents with Double Number Lines: Example 13 Topic Ratios, Proportions, Percents Description This example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 495, with 99 marked as an intermediate point. This visual representation helps students understand the relationship between the part (99) and the whole (495) in percentage terms.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 14	Math Example: Percents with Double Number Lines: Example 14 Topic Ratios, Proportions, Percents Description This example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 396, with 198 marked at the midpoint. This visual representation helps students understand the relationship between the part (198) and the whole (396) in percentage terms.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 15	Math Example: Percents with Double Number Lines: Example 15 Topic Ratios, Proportions, Percents Description This example demonstrates how to determine what percent one number is of another using a double number line, particularly when dealing with more complex ratios. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 856, with 107 marked at an eighth of the way. This visual representation helps students understand the relationship between the part (107) and the whole (856) in percentage terms.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 2	Math Example: Percents with Double Number Lines: Example 2 Topic Ratios, Proportions, Percents Description This example illustrates how to calculate 25% of 180 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 180. By aligning 25% on the percentage line with its corresponding value on the numerical line, we can determine that 25% of 180 is 45. This method visually demonstrates that 25% is equivalent to one-quarter of a quantity.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 3	Math Example: Percents with Double Number Lines: Example 3 Topic Ratios, Proportions, Percents Description This example demonstrates how to find 33 1/3% of 240 using a double number line. The solution displays two parallel number lines: one ranging from 0 to 100% and the other from 0 to 240. By aligning 33 1/3% on the percentage line with its corresponding value on the numerical line, we can see that 33 1/3% of 240 is 80. This method visually represents the concept that 33 1/3% is equivalent to one-third of a quantity.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 4	Math Example: Percents with Double Number Lines: Example 4 Topic Ratios, Proportions, Percents Description This example illustrates how to calculate 40% of 105 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 105. By aligning 40% on the percentage line with its corresponding value on the numerical line, we can determine that 40% of 105 is 42. This method visually demonstrates that 40% is equivalent to two-fifths of a quantity.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 5	Math Example: Percents with Double Number Lines: Example 5 Topic Ratios, Proportions, Percents Description This example demonstrates how to find 12.5% of 88 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 88. By aligning 12.5% on the percentage line with its corresponding value on the numerical line, we can see that 12.5% of 88 is 11. This method visually represents the concept that 12.5% is equivalent to one-eighth of a quantity.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 6	Math Example: Percents with Double Number Lines: Example 6 Topic Ratios, Proportions, Percents Description This example demonstrates how to solve for an unknown value using a double number line when given a percentage. The image features two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 75 is 50% of x.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 7	Math Example: Percents with Double Number Lines: Example 7 Topic Ratios, Proportions, Percents Description This example illustrates how to determine an unknown value using a double number line when given a part and its corresponding percentage. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to an unknown value x. It visually demonstrates the process of finding x when 120 is 25% of x.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 8	Math Example: Percents with Double Number Lines: Example 8 Topic Ratios, Proportions, Percents Description This example demonstrates how to find an unknown value using a double number line when given a part and its corresponding percentage, involving a fractional percentage. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 125 is 33 1/3% of x.	Ratios and Rates
Math Example: Percents with Double Number Lines: Example 9	Math Example: Percents with Double Number Lines: Example 9 Topic Ratios, Proportions, Percents Description This example illustrates how to solve for an unknown value using a double number line when given a part and its corresponding percentage. The image shows two horizontal number lines: the top line ranges from 0 to 100%, and the bottom line ranges from 0 to an unknown number x. The 40% mark on the top line aligns with 220 on the bottom line, visually demonstrating the process of finding x when 220 is 40% of x.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 1	Math Example: Ratios with Double Number Lines: Example 1 Topic Ratios Description This example demonstrates the use of double number lines to solve a ratio problem involving orange and lemon juice. The juice mixture uses a ratio of 2 parts orange juice to 1 part lemon juice. Given 6 cups of orange juice, students are asked to determine the amount of lemon juice needed. The solution involves aligning the double number lines at the amount of orange juice and reading the corresponding amount of lemon juice, which is 3 cups.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 10	Math Example: Ratios with Double Number Lines: Example 10 Topic Ratios Description This example introduces a four-part ratio of 5:2:1:1 for orange, lemon, lime, and strawberry juice. Given 10 cups of orange juice, students need to determine the amounts of lemon, lime, and strawberry juice required. The solution shows that 4 cups of lemon juice and 2 cups each of lime and strawberry juice are needed to maintain the ratio.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 2	Math Example: Ratios with Double Number Lines: Example 2 Topic Ratios Description This example builds upon the previous one, using the same ratio of 2 parts orange juice to 1 part lemon juice. However, in this case, students are given 4 cups of lemon juice and asked to determine the amount of orange juice needed. The solution involves aligning the double number lines at the amount of lemon juice and reading the corresponding amount of orange juice, which is 8 cups.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 3	Math Example: Ratios with Double Number Lines: Example 3 Topic Ratios Description This example introduces a new ratio of 3 parts orange juice to 1 part lime juice. Students are given 9 cups of orange juice and asked to determine the amount of lime juice needed. The solution involves using a double number line to align at the amount of orange juice and find the corresponding amount of lime juice, which is 3 cups.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 4	Math Example: Ratios with Double Number Lines: Example 4 Topic Ratios Description This example introduces a more complex ratio of 3 parts orange juice to 2 parts lime juice. Students are given 4 cups of lime juice and asked to determine the amount of orange juice needed. The solution involves using a double number line to align at the amount of lime juice and find the corresponding amount of orange juice, which is 6 cups.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 5	Math Example: Ratios with Double Number Lines: Example 5 Topic Ratios Description This example introduces a three-part ratio of 2:1:1 for orange, lemon, and raspberry juice. Given 4 cups of orange juice, students need to determine the amounts of lemon and raspberry juice required. The solution shows that 2 cups each of lemon and raspberry juice are needed to maintain the ratio.	Ratios and Rates
Math Example: Ratios with Double Number Lines: Example 6	Math Example: Ratios with Double Number Lines: Example 6 Topic Ratios Description This example presents a three-part ratio of 3:2:2 for orange, lemon, and raspberry juice. Given 6 cups of lemon juice, students need to determine the amounts of orange and raspberry juice required. The solution shows that 9 cups of orange juice and 6 cups of raspberry juice are needed to maintain the ratio.	Ratios and Rates

Illustrative Math Alignment: Grade 6 Unit 3

Unit Rates and Percentages

Lesson 11: Percentages and Double Number Lines

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