Illustrative Math Alignment: Grade 7 Unit 7

Topic

Rationals and Radicals

Description

Factoring a radical expression involves extracting whole number factors. For example, √36x2 = 6x or solving x = (-6 ± √(36 - 16)) / 4, which simplifies to -3 ± √5 / 2. Factoring radicals is a key step in simplifying expressions and solving equations with square roots.

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

Topic

Polynomials

Description

Factorial: For a positive integer n, the product of all integers in the range 1 ≤ n. Written n! and pronounced "n factorial". Examples: 3! = 3 × 2 × 1 = 6, 5! = 5 × 4 × 3 × 2 × 1 = 120. Links the concept of polynomial roots to their factors, aiding in factorization.

Topic

Polynomials

Description

Factorial: For a positive integer n, the product of all integers in the range 1 ≤ n. Written n! and pronounced 'n factorial'. Examples: 3! = 3 × 2 × 1 = 6, 5! = 5 × 4 × 3 × 2 × 1 = 120. Links the concept of polynomial roots to their factors, aiding in factorization.

This is the transcript that goes with the video segment entitled Video Tutorial: Quadratics: Solving Quadratic Equations in Standard Form by Factoring.

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What Are Rational Numbers?

This is the transcript that goes with the video segment entitled Video: Rational Numbers: Comparing and Ordering Rational Numbers.

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

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

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

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

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

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

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

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Distance Measures on a Number Line

Distance Measures on a Number Line

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

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

What Are Rational Numbers?

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Testing If One Polynomial Is a Factor of Another.

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Topic

Polynomials

Description

This segment focuses on factoring techniques for polynomials, including using patterns like the difference of squares and sum-product relationships. Applications include solving equations and finding polynomial roots. Key vocabulary includes factoring, roots, quadratic trinomial, and binomial product.

This video is essential to understand the topic of Polynomials. It provides insights into mathematical concepts and their applications, with a focus on building foundational understanding.

Topic

Polynomials

Description

This video discusses factorials and their applications in counting, permutations, and combinations. It explains the growth of factorials, illustrating how they are used for calculating arrangements and combinations. Examples cover permutations of objects, arranging items, and deriving combinations for groups. Key terms include factorials, permutations, combinations, and the fundamental counting principle. Applications extend to password generation and probability calculations. The segment bridges counting techniques with practical problem-solving.

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.

Watch this video about rational numbers. (The transcript is included.)

Video Transcript

In your study of integers you saw that dividing integers sometimes resulted in a non-integer quotient. In this video we look at a class of numbers called rational numbers, which also includes the integers.

Let’s start with an example.

Watch this video about rational numbers. (The transcript is included.)

Video Transcript

In your study of integers you saw that dividing integers sometimes resulted in a non-integer quotient. In this video we look at a class of numbers called rational numbers, which also includes the integers.

Let’s start with an example.

Watch this video about rational numbers. (The transcript is included.)

Video Transcript

In your study of integers you saw that dividing integers sometimes resulted in a non-integer quotient. In this video we look at a class of numbers called rational numbers, which also includes the integers.

Let’s start with an example.

This worksheet covers the topic of factors and multiples.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations.

Related Resources

Worksheet Library