Illustrative Math Alignment: Grade 6 Unit 9
Putting it All Together
Lesson 4: How Do We Choose?
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 8 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 9 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 10 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 1 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 2 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 3 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 4 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 5 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 6 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 7 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 8 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 9 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 10 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 01 | Math Clip Art--Number Systems--Rational Numbers 01
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 02 | Math Clip Art--Number Systems--Rational Numbers 02
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 03 | Math Clip Art--Number Systems--Rational Numbers 03
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 04 | Math Clip Art--Number Systems--Rational Numbers 04
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 05 | Math Clip Art--Number Systems--Rational Numbers 05
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 06 | Math Clip Art--Number Systems--Rational Numbers 06
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 07 | Math Clip Art--Number Systems--Rational Numbers 07
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 08 | Math Clip Art--Number Systems--Rational Numbers 08
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 09 | Math Clip Art--Number Systems--Rational Numbers 09
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 10 | Math Clip Art--Number Systems--Rational Numbers 10
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Number Systems--Rational Numbers 11 | Math Clip Art--Number Systems--Rational Numbers 11
This is part of a collection of math clip art images about different number systems. Included are integers, rational numbers, and real numbers. |
Numerical Expressions |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 01 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 01TopicRatios, Proportions, and Percents DescriptionThe image introduces the concept of percent change with the formula: Percent Change = (New - Original) / Original * 100%. It establishes the formula as the foundation for understanding percent change throughout the sequence. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 02 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 02TopicRatios, Proportions, and Percents DescriptionThis image explains that percent increase measures the change from one number to a greater number. It provides context for when to apply the concept of percent increase in real-life scenarios. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 03 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 03TopicRatios, Proportions, and Percents DescriptionThis image highlights that the numerical increase is the difference between the new and original values. It adds clarity by breaking down the calculation into a numerical difference. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 04 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 04TopicRatios, Proportions, and Percents DescriptionThis image demonstrates how numerical increase is represented as fractional change using the formula: (b - a) / a. It bridges numerical increase to fractional change, setting up for conversion to percent increase. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 05 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 05TopicRatios, Proportions, and Percents DescriptionThis image shows the formula for percent change as a fractional change expressed as a percentage: (b - a) / a * 100%. It reinforces the connection between fractional change and percent increase as part of the calculation process. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 06 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 06TopicRatios, Proportions, and Percents DescriptionThis image provides an example of a percent increase calculation from 8 to 10, resulting in 25%. It offers a practical example to illustrate how the formula is applied to real numbers. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 07 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 07TopicRatios, Proportions, and Percents DescriptionThis image reiterates the example calculation, emphasizing that the change from 8 to 10 is a 25% increase. It reinforces understanding by repeating the example with emphasis on the interpretation of the result. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 08 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 08TopicRatios, Proportions, and Percents DescriptionThis image defines percent decrease as the change from one number to a lesser number. It introduces the complementary concept of percent decrease to show both directions of percent change. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 09 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 09TopicRatios, Proportions, and Percents DescriptionThis image explains that numerical decrease is the difference between the new and original values. It mirrors the earlier explanation of numerical increase, ensuring consistency in presenting both cases. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 10 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 10TopicRatios, Proportions, and Percents DescriptionThis image demonstrates fractional change for a decrease using the formula: (b - a) / a. It completes the explanation of percent change by connecting numerical decrease to fractional representation. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 11 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 11TopicRatios, Proportions, and Percents DescriptionThis image explains that percent decrease represents fractional change expressed as a percentage: (b - a) / a * 100%. It extends the explanation to show how fractional change can be converted to percent decrease. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 12 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 12TopicRatios, Proportions, and Percents DescriptionThis image provides an example of a percent decrease calculation from 10 to 8, resulting in -20%. It offers a practical example illustrating the application of the formula to calculate percent decrease. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percent Change 13 | Math Clip Art--Ratios, Proportions, Percents--Percent Change 13TopicRatios, Proportions, and Percents DescriptionThis image reiterates the example, emphasizing that the change from 10 to 8 represents a 20% decrease. It reinforces understanding by summarizing the example with focus on the final interpretation of the result. Math clip art provides a visual and engaging way to explore complex mathematical concepts such as percent change. These examples illustrate how numbers, fractions, and percentages are interconnected, helping to build students' numerical reasoning skills. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01 | Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01
This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents. |
Proportions |
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Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02 | Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02
This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents. |
Proportions |
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Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03 | Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03
This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents. |
Proportions |
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Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04 | Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04
This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents. |
Proportions |
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Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05 | Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05
This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents. |
Proportions |
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Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06 | Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06
This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents. |
Proportions |
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Math Clip Art--Ratios, Proportions, Percents--Percents 01 | Math Clip Art--Ratios, Proportions, Percents--Percents 01TopicRatios, Proportions, and Percents DescriptionThe image illustrates the concept of an introductory image that visually connects percents with proportions, showcasing a grid and a formula (a / b = c / d) next to a hurdler and a large percent sign. The golden ratio a / b = 1.618 is also present, symbolizing relationships, and expands on this idea by showing that serves as a thematic and conceptual introduction to percents by emphasizing proportional relationships and the idea of ratios. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percents 02 | Math Clip Art--Ratios, Proportions, Percents--Percents 02TopicRatios, Proportions, and Percents DescriptionThe image illustrates the concept of fractions with different denominators: 1/4, 2/5, 5/6, and 5/8, each depicted as shaded portions of circles. and expands on this idea by showing that highlights the challenge of comparing fractions with different denominators, setting up the need for a common framework such as percents. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percents 03 | Math Clip Art--Ratios, Proportions, Percents--Percents 03TopicRatios, Proportions, and Percents DescriptionThe image illustrates the concept of and expands on the previous image by comparing and ordering the fractions using inequality symbols: 1/4 < 2/5 < 5/8 < 5/6. This image expands on this idea by emphasizing the difficulty of comparing fractions and transitions to the rationale for using percents as a standard for comparison. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percents 04 | Math Clip Art--Ratios, Proportions, Percents--Percents 04TopicRatios, Proportions, and Percents DescriptionThe image illustrates the concept of converting the fractions 1/4, 2/5, 5/6, and 5/8 into percents (25%, 40%, 83.33%, 62.5%) with their corresponding pie diagrams. It expands on this idea by showing that introduces percents as an easier method for comparing fractions by representing them with a common denominator of 100. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percents 05 | Math Clip Art--Ratios, Proportions, Percents--Percents 05TopicRatios, Proportions, and Percents DescriptionThe image illustrates the concept of how fractions such as 3/4 and 3/5 convert to percents (75% and 60%) using shaded 10 x 10 grids. It expands on this idea by showing the concept of percents using a visual and tangible representation, reinforcing the idea of 100 as the base for comparison. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percents 06 | Math Clip Art--Ratios, Proportions, Percents--Percents 06TopicRatios, Proportions, and Percents DescriptionThe image illustrates the concept of connecting coins (1¢, 5¢, 10¢, 25¢) to their percent values of a dollar (1%, 5%, 10%, 25%). It expands on this idea by establishing a real-world application of percents, showing their utility in everyday contexts like money. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students. |
Percents |
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Math Clip Art--Ratios, Proportions, Percents--Percents 07 | Math Clip Art--Ratios, Proportions, Percents--Percents 07TopicRatios, Proportions, and Percents DescriptionThe image illustrates percentages as fractions with a denominator of 100, such as 10% = 10 / 100, 15% = 15 / 100, and so on. It expands on this idea by showing how percents relate to fractions, reinforcing their equivalency and further grounding the concept. The topic of Ratios, Proportions, and Percents explores fundamental math concepts by using practical examples. This collection aids in visualizing the connection between different mathematical forms such as ratios, percents, and fractions, making abstract concepts more accessible to students. |
Percents |
