Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 8

Pythagorean Theorem and Irrational Numbers

Lesson 15: Infinite Decimal Expansions

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Numerical Expressions--Dividing Integers: Example 23 Math Example--Numerical Expressions--Dividing Integers: Example 23 Math Example--Numerical Expressions--Dividing Integers: Example 23

Topic

Numerical Expressions

Description

This example demonstrates the division of three integers: (-150) / (-5) / 4. The solution shows that dividing a negative integer by a negative integer and then by a positive integer results in a positive mixed number quotient. The calculation is presented step-by-step: 

(-150) / (-5) / 4 = -150 / -5 / 4 = 30 / 4 = 7 1/2.

 Numerical Expressions
Math Example--Numerical Expressions----Dividing Integers: Example 24 Math Example--Numerical Expressions--Dividing Integers: Example 24 Math Example--Numerical Expressions--Dividing Integers: Example 24

Topic

Numerical Expressions

Description

This example illustrates the division of three negative integers: (-108) ÷ (-2) ÷ (-7). The solution demonstrates that dividing three negative integers results in a negative mixed number quotient. The calculation is presented step-by-step: 

(-108) ÷ (-2) ÷ (-7) = -108 / -2 ÷ (-7) = 54 / -7 = -7 5/7.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 3 Math Example--Numerical Expressions--Dividing Integers: Example 3 Math Example--Numerical Expressions--Dividing Integers: Example 3

Topic

Numerical Expressions

Description

This example demonstrates the division of a negative integer by a positive integer: -18 divided by 6. The solution shows that when dividing one integer by another, the result is a rational number. In this case, when dividing a negative integer by a positive integer, the quotient is negative. The calculation is presented as (-18) ÷ 6 = -18 / 6 = -3.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 4 Math Example--Numerical Expressions--Dividing Integers: Example 4 Math Example--Numerical Expressions--Dividing Integers: Example 4

Topic

Numerical Expressions

Description

This example illustrates the division of two negative integers: -9 divided by -3. The solution demonstrates that when dividing one integer by another, the result is a rational number. In this case, when dividing two negative integers, the quotient is positive. The calculation is presented as (-9) ÷ (-3) = -9 / -3 = 3.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 5 Math Example--Numerical Expressions--Dividing Integers: Example 5 Math Example--Numerical Expressions--Dividing Integers: Example 5

Topic

Numerical Expressions

Description

This example demonstrates the division of three positive integers: 20 ÷ 2 ÷ 5. The solution shows that dividing three positive integers results in a positive quotient. The calculation is presented step-by-step: 20 ÷ 2 ÷ 5 = 20 / 2 ÷ 5 = 10 / 5 = 2.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 6 Math Example--Numerical Expressions--Dividing Integers: Example 6 Math Example--Numerical Expressions--Dividing Integers: Example 6

Topic

Numerical Expressions

Description

This example demonstrates the division of three integers: 48 ÷ 6 ÷ (-4). The solution shows that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: 48 ÷ 6 ÷ (-4) = 48 / 6 ÷ (-4) = 8 / -4 = -2.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 7 Math Example--Numerical Expressions--Dividing Integers: Example 7 Math Example--Numerical Expressions--Dividing Integers: Example 7

Topic

Numerical Expressions

Description

This example illustrates the division of three integers: 24 ÷ (-6) ÷ 2. The solution demonstrates that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: 24 ÷ (-6) ÷ 2 = -4 / 2 = -2.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 8 Math Example--Numerical Expressions--Dividing Integers: Example 8 Math Example--Numerical Expressions--Dividing Integers: Example 8

Topic

Numerical Expressions

Description

This example demonstrates the division of three integers: (-72) ÷ 2 ÷ 6. The solution shows that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: (-72) ÷ 2 ÷ 6 = -72 / 2 ÷ 6 = -36 / 6 = -6.

 Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 9 Math Example--Numerical Expressions--Dividing Integers: Example 9 Math Example--Numerical Expressions--Dividing Integers: Example 9

Topic

Numerical Expressions

Description

This example illustrates the division of three integers: 125 ÷ (-25) ÷ (-5). The solution demonstrates that dividing three integers, two negative and one positive, results in a positive quotient. The calculation is presented step-by-step: 125 ÷ (-25) ÷ (-5) = -5 / -5 = 1.

 Numerical Expressions
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 1 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 1 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 10 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 10 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 2 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 2 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 3 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 3 Math Example--Rational Concepts--Comparing and Ordering 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
ComparingOrderingIntegersRationals--Example04.png Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 4 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 5 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 5 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 6 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 6 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 7 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 7 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 8 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 8 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 9 Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 9 Math Example--Rational Concepts--Comparing and Ordering 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 1 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 1 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
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 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 2 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 2 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 3 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 3 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 4 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 4 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 5 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 5 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 6 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 6 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 7 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 7 Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--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
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 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
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 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 1 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 10 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 2 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 3 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 4 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 5 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 6 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 7 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 8 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
Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 9 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
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 1 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 1 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 10 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 10 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 2 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 2 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 3 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 3 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 4 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 4 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 5 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 5 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 6 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 6 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 7 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 7 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 8 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 8 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 9 Math Example--Rational Concepts--Rational Approximations of Irrational Numbers--Example 9 Math Example--Rational Concepts--Rational Approximations of Irrational 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.

 Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 1 Math Example--Rational Concepts--Rational vs Irrational--Example 1 Math Example--Rational Concepts--Rational vs Irrational--Example 1

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

 Rational Expressions