Illustrative Math Alignment: Grade 7 Unit 5

This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers On the Cartesian Coordinate System.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Subtracting Rational Numbers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Variable Expressions with Rational Numbers.

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What Are Rational Numbers?

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Adding and Subtracting Rational Expressions.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Multiplying Rational Expressions.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Simplifying Rational Expressions.

To see the complete collection of video transcriptsy, click on this link.

Topic

Expressions and Equations

Description

This video focuses on modeling integer multiplication with algebra tiles. Examples include 6 • 3, -6 • 3, and -6 • -3. Rectangular arrays of tiles are used to visualize products. Key vocabulary includes multiplication, rectangular arrays, and integers.

Topic

Rational Numbers

Description

This video introduces rational numbers, defined as ratios of two integers where the denominator is non-zero. Key concepts include fractions, ratios, and integers as rational numbers. Applications involve classroom ratios and number line representation with positions like 5/4 and -2/4. It emphasizes rational numbers in everyday contexts, such as temperature comparisons using decimals.

Topic

Rational Numbers

Description

The video explores the interaction of rational numbers with exponents. Examples include expressing square roots as rational exponents and simplifying complex expressions. Applications in geometry and algebra highlight the versatility of these concepts for further mathematical studies.

Topic

Rational Numbers

Description

This video discusses evaluating numerical expressions with rational numbers, emphasizing the order of operations (PEMDAS). Examples include calculating areas of rectangles and finding the slope of a line using the Cartesian plane. It highlights parentheses' role in operations and real-world applications like geometry and measurements.

Topic

Rational Numbers

Description

The video explores variable expressions involving rational numbers. Examples include finding combined areas of rectangles using algebraic expressions and analyzing the trajectory of a ball using a formula with time as a variable. It demonstrates real-world applications of rational number operations in algebra and physics.

Topic

Rational Numbers

Description

This video focuses on graphing rational numbers on the Cartesian coordinate system, calculating slopes, and writing line equations. It explains conditions for positive, negative, zero, and undefined slopes using delta-y and delta-x. Applications include geometry and understanding coordinate relationships.

Topic

Rational Numbers

Description

The video explores rational and irrational numbers. Rational numbers include integers, fractions, and repeating decimals. Irrational numbers, such as the square root of non-perfect squares and pi, are non-terminating and non-repeating. Examples include Pythagorean triples and circle circumference ratios. Applications focus on distinguishing between the two.

Topic

Rational Numbers

Description

This video demonstrates how rational numbers are plotted on a number line, showing positive and negative values sequentially. Examples include ecosystem measurements and thermometers interpreted as number lines. It highlights the infinite nature and precise placement of rational numbers in real-world scenarios.

Topic

Rational Numbers

Description

The video explains absolute value as the distance between two points on a number line. Key examples include altitude changes of kites and submersibles. Techniques involve counting increments or using subtraction. It emphasizes absolute value's role in understanding distances irrespective of direction.

Topic

Rational Numbers

Description

This video presents methods for comparing and ordering rational numbers using number lines. It emphasizes arranging numbers from least to greatest and graphing positions. Real-world applications include submersible depths and relative point positioning.

Topic

Rational Numbers

Description

This video introduces techniques for adding rational numbers. Examples include altitude changes and submersible descents. It covers adding mixed numbers, decimals, and opposites, showcasing the relationship between rational numbers and their negative counterparts, with applications in various contexts.

Topic

Rational Numbers

Description

This video explores subtracting rational numbers, with examples like temperature ranges and vertical distances. Techniques highlight the relationship between subtraction and addition of negatives. Applications include interpreting distances and temperature differences.

Topic

Rational Numbers

Description

The video covers multiplying rational numbers with examples like drilling depths and financial credits. It explains how repeated addition is modeled as multiplication. The mathematical proof demonstrates that multiplying rational numbers yields another rational number.

Topic

Rational Numbers

Description

This video explains dividing rational numbers using examples like sharing pizzas and complex fraction simplifications. It emphasizes rewriting terms to align with the rational number definition and addresses why dividing rational numbers results in another rational number.

Topic

Rational Functions

Description

Explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Topic

Rational Functions

Description

Examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Topic

Rational Functions

Description

Demonstrates the optics of the Hubble telescope through rational functions, analyzing lens properties and asymptotes for image clarity.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Topic

Rational Functions

Topic

Rational Functions

Description

This segment explores rational functions, focusing on direct and inverse variation. Key terms include constant of proportionality and rational function. Boyle's Law serves as a central example, showcasing the relationship between pressure and volume of a gas. Data plotting and regression analysis with TI-Nspire help identify mathematical models. Applications highlight scientific principles from physics and chemistry.

Topic

Rational Functions

Description

In this Math Lab explore rational numbers that can be written as repeating decimals.

This video provides an in-depth exploration of the concept of rational functions and their applications. By understanding the mathematical intricacies and observing real-world examples, students can connect abstract concepts to practical scenarios.

Topic

Rational Functions

Description

This part examines graphs of rational functions like y = a/x, including their asymptotic behavior and properties. Key terms include hyperbola, vertical asymptote, and horizontal asymptote. TI-Nspire is used to analyze effects of parameter changes, transitions between quadrants, and graphical intersections. Applications include real-world scenarios and mathematical exploration of function behaviors.

Topic

Rational Functions

Description

In this Math Lab explore the graphs of rational functions.

This video provides an in-depth exploration of the concept of rational functions and their applications. By understanding the mathematical intricacies and observing real-world examples, students can connect abstract concepts to practical scenarios.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to multiply rational expressions. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad.

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

What Are Composite Functions?