Illustrative Math Alignment: Grade 7 Unit 5

This is part of a series of math examples that show how to solve ratio problems involving double number lines.

Note: The download is a PNG file.

Topic

Ratios

Description

This example presents a three-part ratio of 4:3:2 for orange, lemon, and lime juice. Given 4 cups of lime juice, students need to determine the amounts of orange and lemon juice required. The solution shows that 8 cups of orange juice and 6 cups of lemon juice are needed to maintain the ratio.

Topic

Ratios

Description

This example features a three-part ratio of 5:2:1 for orange, lemon, and lime juice. Given 6 cups of lemon juice, students need to determine the amounts of orange and lime juice required. The solution demonstrates that 15 cups of orange juice and 3 cups of lime juice are needed to maintain the ratio.

This Teacher's Guide provides an overview of the 28 worked-out examples that show how to simplify a variety of rational expressions.

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6/6/11. In this issue we look at the technology of Doppler Radar and explore its underlying mathematical structure.

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4/11/11. In this issue we look at the high price of gasoline and investigate whether a hybrid car makes more economic sense. We look at various statistics to make a determination.

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Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

In this set of interactive flash cards, find the ratios for a given set of shapes.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

This 45-minute SAT Math lesson focuses on solving problems involving unit rates, dimensional analysis, and unit conversions. Students will learn how to calculate speed, cost per item, and population density, as well as how to convert between units using proportion and dimensional analysis. The lesson also includes multi-step word problems that combine rate calculations with percent-based reasoning—realistic scenarios frequently tested on the SAT.

Topic

Rationals and Radicals

Description

Addition of rational expressions involves combining rational expressions to create a new rational expression, often requiring a common denominator. Examples include 1 / x + 1 / 2x = 3 / 2x and 1 / (x + 1) + 1 / (x - 1) = 2x / (x2 - 1). This term introduces the concept of combining rational expressions, which is fundamental to operations involving fractions with polynomial expressions.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

The geometric mean is the nth root of the product of n terms. Examples include the geometric mean of 3 and 12, √(3 × 12) = 6, and the geometric mean of 3, 4, and 12, ∛(3 × 4 × 12) ≈ 5.24. Geometric mean connects multiplication and roots, commonly used in statistics, geometry, and proportional reasoning.

Topic

Rationals and Radicals

Description

The geometric mean is the nth root of the product of n terms. Examples include the geometric mean of 3 and 12, √(3 × 12) = 6, and the geometric mean of 3, 4, and 12, ∛(3 × 4 × 12) ≈ 5.24. Geometric mean connects multiplication and roots, commonly used in statistics, geometry, and proportional reasoning.

This video includes Spanish audio and can be used with multilingual learners.

Topic

Rationals and Radicals

Description

Graphs of radical functions have a characteristic shape where the domain is limited to values resulting in a positive radicand. For y = √x, the domain is x >= 0, and the range is y >= 0. This highlights the inherent properties of square root functions. Introduces the concept of radical graphs and their domain/range constraints, setting a foundation for graph behavior analysis.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

Graphs of rational functions often feature asymptotes, which are lines the graph approaches but never touches. For example, f(x) = 1 / x has vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain and range exclude zero. Explains the unique characteristics of rational function graphs and the significance of asymptotes in defining their behavior.

Topic

Rationals and Radicals

Description

Graphs of rational functions often feature asymptotes, which are lines the graph approaches but never touches. For example, f(x) = 1 / x has vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain and range exclude zero. Explains the unique characteristics of rational function graphs and the significance of asymptotes in defining their behavior.

Topic

Rationals and Radicals

Description

Horizontal asymptotes describe the behavior of a graph as x approaches infinity or negative infinity. For example, the equation y = (x + 1) / (x - 2) has a horizontal asymptote at y = 1, demonstrating long-term behavior of the function. Focuses on the role of horizontal asymptotes in describing the long-term trends of rational functions.

Topic

Rationals and Radicals

Description

Horizontal asymptotes describe the behavior of a graph as x approaches infinity or negative infinity. For example, the equation y = (x + 1) / (x - 2) has a horizontal asymptote at y = 1, demonstrating long-term behavior of the function. Focuses on the role of horizontal asymptotes in describing the long-term trends of rational functions.

Topic

Rationals and Radicals

Description

The index of a radical specifies the root being taken, such as the square root (index 2) or cube root (index 3). Examples include √25 for index 2 and the cube root of 27 for index 3. Defines and applies the concept of indices in radicals, foundational for understanding roots and powers.

Topic

Rationals and Radicals

Description

The index of a radical specifies the root being taken, such as the square root (index 2) or cube root (index 3). Examples include √25 for index 2 and the 3√27 for index 3. Defines and applies the concept of indices in radicals, foundational for understanding roots and powers.

This video includes Spanish audio and can be used with multilingual learners.

Topic

Rationals and Radicals

Description

Integers are a subset of rational numbers including positive, negative, and zero values, represented by {..., -3, -2, -1, 0, 1, 2, 3, ...}. This emphasizes their role in forming the basis of discrete mathematics. Introduces integers as a key component of number systems, aiding comprehension of rational numbers.