Illustrative Math Alignment: Grade 8 Unit 3

Topic

Numerical and Algebraic Expressions

Description

This example illustrates solving the equation 3x + (-2) = x + (-5) using algebra tiles. The image shows green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually determine that x = -2/3.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates solving the equation 4x + (-4) = x + (-4) using algebra tiles. The image depicts green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually see that x = 0.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates the addition of 5 and -8 using algebra tiles. It shows 5 yellow tiles representing positive integers and 8 red tiles representing negative integers. After removing zero pairs, the result is 3 red tiles, illustrating that 5 + (-8) = -3.

Topic

Numerical and Algebraic Expressions

Description

This example shows a quadratic equation x2 + 2x - 1 = 0 being solved using algebra tiles. The image illustrates factoring by completing the square and solving for x. This visual representation helps students understand the process of solving quadratic equations.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates solving the quadratic equation x2 + 2x + 1 = 0 using algebra tiles. The image shows factoring as (x + 1)2 = 0 and solving for x, resulting in the solution x = -1. This visual representation helps students understand perfect square trinomials and their solutions.

Topic

Numerical and Algebraic Expressions

Description

This example presents solving the quadratic equation x2 - 3x + 2 = 0 using algebra tiles, showing a different approach with negative tiles. It factors as (x - 2)(x - 1) = 0, leading to solutions x = 2 and x = 1. This visual representation helps students understand factoring and solving quadratic equations with two solutions.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates solving the quadratic equation x2 - 3x + 2 = 0 using algebra tiles. It illustrates completing the square and factoring into (x - 2)(x - 1) = 0, followed by solving for x to get solutions x = 1 and x = 2. This visual representation helps students understand the process of completing the square and its relation to factoring.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates solving the equation x - 3 = 5 using algebra tiles. It shows modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand the process of solving linear equations with one variable.

Topic

Numerical and Algebraic Expressions

Description

This example illustrates solving the equation x - 2 = -3 with algebra tiles. The image shows the steps of modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand how to solve equations with negative numbers.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates solving the equation x - 2 = -2 using algebra tiles. The image shows a step-by-step solution, including modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations where the solution is zero.

Topic

Numerical and Algebraic Expressions

Description

This example illustrates solving the equation x - (-2) = 4 using algebra tiles. The image shows a step-by-step solution, including modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations involving subtraction of negative numbers.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates solving the equation x - (-4) = 2 with algebra tiles. The image shows the process of modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations involving subtraction of negative numbers and their solutions.

Topic

Numerical and Algebraic Expressions

Description

This example illustrates solving the equation x - (-3) = 3 using algebra tiles. The image shows the steps of modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations involving subtraction of negative numbers and their solutions.

Topic

Numerical and Algebraic Expressions

Description

This example illustrates the addition of 7 and -7 using algebra tiles. It shows 7 yellow tiles representing positive integers and 7 red tiles representing negative integers. When combined, these tiles form zero pairs, resulting in a sum of zero. This demonstrates that 7 + (-7) = 0, visually representing the concept of additive inverses.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates the addition of two negative numbers, -6 and -8, using algebra tiles. The image shows 6 red tiles representing -6 and 8 red tiles representing -8. When combined, these tiles result in a total of 14 red tiles, illustrating that -6 + (-8) = -14.

Topic

Numerical and Algebraic Expressions

Description

This example illustrates the subtraction of 5 from 14 using algebra tiles. The image shows 14 yellow tiles representing the initial value, and then 5 tiles are removed, leaving 9 yellow tiles. This visually demonstrates that 14 - 5 = 9.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates the subtraction of 10 from 8 using algebra tiles. The image shows 8 yellow tiles representing the initial value, and two red tiles next to them. To subtract 10, zero pairs are added as necessary, resulting in a final answer of -2, represented by two red tiles.

Topic

Numerical and Algebraic Expressions

Description

This example demonstrates the subtraction of 16 from itself using algebra tiles. The image shows 16 yellow tiles arranged in two rows of eight. Below this, the same 16 tiles are shown with a subtraction sign, illustrating the process of removing all tiles to reach zero.

Topic

Numerical and Algebraic Expressions

Description

This example illustrates the subtraction of a negative number, specifically 8 - (-3), using algebra tiles. The image shows 8 yellow tiles representing the positive 8, and three red tiles are added to represent the subtraction of -3. This visual representation demonstrates that subtracting a negative number is equivalent to adding its positive counterpart, resulting in a total of 11 yellow tiles.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve two-step equations that involve combinations of addition, subtraction, multiplication, and division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.