Illustrative Math Alignment: Grade 7 Unit 5

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Topic

Equations

Topic

Equations

Topic

Equations

Topic

Equations

Topic

Equations

Topic

Equations

This Teacher's Guide provides an overview of the 28 worked-out examples that show how to graph Rational Functions.

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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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12/19/11. In this issue we look at the steep drop in the price of NetFlix’s stock. We examine why it happened and make a prediction about the stock’s future.

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January 2012. In this issue of Math in the News we look at the Facebook IPO.

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February 2014. In this issue of Math in the News we look at the investment strategy known as Dollar Cost Averaging. We explore several simulated scenarios and look at the pros and cons of this strategy.

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All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms. Note: The download for this resources is the Promethean Flipchart.

To view the full video [Algebra Applications: Rational Functions, Segment 2: Biology]: https://www.media4math.com/library/algebra-applications-rational-functions-segment-2-biology

The Hubble Telescope, like all telescopes, relies on the lens formula to focus an image. The lens formula results in a rational equation that can be solved for determining the settings on the lens. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Applications: Rational Functions, Segment 3: Hubble Telescope]: https://www.media4math.com/library/algebra-applications-rational-functions-segment-3-hubble-telescope

In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Applications: Rational Functions, Segment 1: Submarines]: https://www.media4math.com/library/algebra-applications-rational-functions-segment-1-submarines

After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Nspirations: Rational Functions and Expressions]: https://media4math.com/library/algebra-nspirations-rational-functions-and-expressions

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.

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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.

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

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.