PEC 2015 Algebra tiles by Chizuko Matsumoto Sweeny

PEC 2015 Algebra tiles by Chizuko Matsumoto & Sweeny Term What topics can we use it for? How can we use it?

algebra tiles in “Algebra 1” Chapter-Lesson Topic 2 -1 Model One-Step Equations 2 -4 Model Equations with Variables on Both Sides 6 -2 Model Systems of Linear Equations (by Substitution) 6 -3 Model Systems of Linear Equations (by Elimination) 7 -6 Model Polynomial Addition and Subtraction 7 -7 Model Polynomial Multiplication 8 -2 Model Factoring (by GCF) 8 -3 Model Factorization of Trinomials 9 -8 Model Completing the Square 12 -6 Model Polynomial Division

Let’s check the prior knowledge! Step 1. I know the name of Algebra tile. Step 2. I have used the Algebra tile. Step 3. I have delivered the class lesson using the Algebra tile. Step 4. I did workshop focusing on the way how to use the Algebra tile. If you can help this workshop, I welcome your support anytime and in anyway. Thank you.

Positive tiles x 2 x 1 -x -1 Negative tiles - x 2

Zero pairs x x 2 1 x 2 = 0 - x 2 -x x = 0 -1 1 = 0

Topic 1. Model One-Step Equations

Use algebra tiles to model and solve x+6=2 MODEL ALGEBRA X + 6 = 2 X + 6 + (-6) = 2 + (-6) X + 0 = 0 + (-4) X = -4 Zero pairs

Topic 2. 　 Model Equations with Variables on Both Sides

Use algebra tiles to model and solve 5 x – 2 = 2 x + 10 MODEL ALGEBRA 5 X - 2 = 2 x + 10 5 X – 2 x - 2 = 2 x – 2 x + 10 3 X - 2 = 10 3 X - 2 + 2= 10 + 2 3 X = 12 3 3 Zero pairs X = 4

Try This Topic 1&2. Use algebra tiles to model and solve each equation. 1. X – 5 = 3 X = 8 2. X = -2 X + 9 X = 3

Topic 3. Model Polynomial Addition and Subtraction

Activity 1 Use algebra tiles to find (2 x 2 – x) + (x 2 + 3 x -1) MODEL ALGEBRA 2 x 2 – x + x 2 + 3 x -1 2 X -1 2 3 X Zero pairs 3 x 2 + 2 x -1

Activity 2 Use algebra tiles to find (2 x 2 + 6) +(- 3 x 2) MODEL ALGEBRA 2 x 2 + 6 - 3 x 2 . -x 2 + 6 Zero pairs

Try This Topic 3. Use algebra tiles to find the sum. 2 2 (3 x + 2 x + 5) + (x – 4)

Topic 4. Model Polynomial Multiplication

Activity 1 Use algebra tiles to find 2(x+1) MODEL ALGEBRA X＋1 × 2 2（x + 1) = x + 1 + 1 = 2 x + 2

Activity 2 Use algebra tiles to find 2 x(x-3) MODEL ALGEBRA X-3 × 2 x（x - 3) = x 2 + x 2 - x - x - x 2 x = 2 x 2 - 6 x

Activity 3 Use algebra tiles to find (x+1)(x-2) MODEL ALGEBRA X-2 × (x +1)（x -2) = x 2 + x - x – 1 -1 X+1

Activity 3 Use algebra tiles to find (x+1)(x-2) MODEL ALGEBRA X-2 × (x +1)（x -2) = x 2 + x - x – 1 -1 0 X+1 = x 2 – x - 2 Zero pairs

Try This Topic 4. Use algebra tiles to find each product. 1. 3(x + 2) 2. x (2 x-1) 3. (x – 1)(x + 3)

Topic 5. Model Polynomial Division

Activity 1 Use algebra tiles to find the quotient (x 2 + 5 x + 6) ÷(x + 2). MODEL X＋2 × X+3 ALGEBRA (x 2 + 5 x + 6) ÷(x + 2) Try to form a rectangle with a length of x + 2. = x + 3

Try This Topic 8. Use algebra tiles to find each quotient. 1. (x 2 + 5 x + 4) ÷(x + 1) 2. (x 2 + 4 x – 5)÷(x – 1) 3. (x 2 - 6 x + 8)÷(x - 2) 4. (2 x 2 + 5 x + 2) ÷(x + 2)

Topic 6. Model Factoring (by GCF)

Activity 1 Use algebra tiles to factor 4 x+8 MODEL ALGEBRA X＋2 × 4 x + 8 = 4(x + 2) 4

Activity 2 Use algebra tiles to factor x 2 – 2 x MODEL ALGEBRA X - 2 × x 2 – 2 x = x (x – 2) x

Try This Topic 5. Use algebra tiles to factor each polynomial. 1. 3 x – 12 2. 3 x 2 – 3 x

Topic 7. Model Factorization of Trinomials

Activity 1 Use algebra tiles to factor x 2 + 7 x + 6 MODEL × ALGEBRA x 2 + 7 x + 6 Try to arrange all of the tiles into a rectangle! This arrange doesn’t work because two xtiles are left over.

Activity 1 Use algebra tiles to factor x 2 + 7 x + 6 MODEL ALGEBRA X＋6 × x 2 + 7 x + 6 Try again ! X+1 This is the correct arrangement. = (x + 6)(x + 1)

Try This Topic 6. Activity 1. Use algebra tiles to factor the trinomial. x 2 + 6 x + 8

Activity 2 Use algebra tiles to factor x 2 + x - 2 MODEL X＋2 × X-1 ALGEBRA x 2 + x - 2 Try to arrange all of the tiles in a rectangle! Add a zero pair. Arrange the x-tiles to complete the rectangle. (x + 2)(x – 1)

Try This Topic 6. Use algebra tiles to factor each polynomial. 1. x 2 - 2 x - 3 2 2. x - 5 x + 4 2 3. x - 2 x + 1 2 4. x + 3 x – 4 2 5. x + 3 x - 10

Topic 8. Model Completing the Square

Activity Use algebra tiles to model x 2 + 6 x. Add unit tiles to complete a perfectsquare trinomial. Then write the new expression in factored form. MODEL X＋3 × ALGEBRA 9 x 2 + 6 x + ____ Part of the square is missing. X+3 How many one-tiles do you need to complete it? . = (x + 3)2

Try This Topic 7. Use algebra tiles to model the expression. Add unit tiles to complete a perfect-square trinomial. Then write the new expression in factored form. x 2 + 8 x

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Marshall Island High School Open Class

Grade 10

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For printing

Equation(Topic 1&2) MODEL ALGEBRA

Polynomial addition/subtraction (Topic 3) MODEL Answer _______________

Polynomial Multiplication/Division or factorization (Topic 4~8) MODEL × ALGEBRA

Try This Topic 1&2 Topic 6 1. X – 5 = 3 2. X = -2 X + 9 1. 3 x – 12 2. 3 x 2 – 3 x Topic 3 (3 x 2 + 2 x + 5) + (x 2 – x – 4) Topic 4 Topic 7 1. 3(x + 2) x 2 + 6 x + 8 2. x (2 x-1) 3. (x – 1)(x + 3) Topic 5 Topic 8 x 2 + 8 x 1. (x 2 + 5 x + 4) ÷(x + 1) 2. (x 2 + 4 x – 5)÷(x – 1) 3. (x 2 - 6 x + 8)÷(x - 2) 4. (2 x 2 + 5 x + 2) ÷(x + 2)