Transcript Algebra Tiles

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!
Step1.I know the name of Algebra tile.
Step2.I have used the Algebra tile.
Step3.I have delivered the class lesson
using the Algebra tile.
Step4.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
x2
x
1
-x
-1
Negative tiles
- x2
Zero pairs
x
x2
1
x2
=0
- x2
-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 5x – 2 = 2x + 10
MODEL
ALGEBRA
5X - 2 = 2x + 10
5X – 2x - 2 = 2x – 2x + 10
3X - 2 = 10
3X - 2 + 2= 10 + 2
3X = 12
3X = 12
3
3
Zero pairs
X=4
Try This
Topic1&2.
Use algebra tiles to model and solve each equation.
1. X – 5 = 3
X=8
2. X = -2X + 9
X=3
Topic 3.
Model Polynomial Addition
and Subtraction
Activity 1
Use algebra tiles to find (2x2 – x) + (x2 + 3x -1)
MODEL
ALGEBRA
2x2 – x
+ x2 + 3x -1
2X
3x2 + 2x -1
-1
2
3X
Zero pairs
Activity 2
Use algebra tiles to find (2x2 + 6) +(- 3x2)
MODEL
ALGEBRA
2x2 + 6
- 3x2
-x2 + 6
Zero pairs
.
Try This
Topic 3. Use algebra tiles to find the sum.
2
(3x
+ 2x + 5) +
2
(x
– 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+x+1+1
= 2x + 2
Activity 2
Use algebra tiles to find 2x(x-3)
MODEL
ALGEBRA
X-3
×
2x（x - 3)
= x2 + x2
-x-x-x-x-x-x
2x
= 2x2 - 6x
Activity 3
Use algebra tiles to find (x+1)(x-2)
MODEL
ALGEBRA
X-2
×
(x +1)（x -2)
= x2 + x - 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)
= x2 + x - x - x – 1-1
0
X+1
= x2 – x - 2
Zero pairs
Try This
Topic 4. Use algebra tiles to find each product.
1. 3(x + 2)
2. x (2x-1)
3. (x – 1)(x + 3)
Topic 5.
Model Polynomial Division
Activity 1
Use algebra tiles to find the quotient (x2 + 5x + 6) ÷(x + 2).
MODEL
X＋2
×
ALGEBRA
(x2 + 5x + 6) ÷(x + 2)
Try to form a rectangle
with a length of x + 2.
X+3
=x+3
Try This
Topic 8. Use algebra tiles to find each quotient.
1. (x2 + 5x + 4) ÷(x + 1)
2. (x2 + 4x – 5)÷(x – 1)
3. (x2 - 6x + 8)÷(x - 2)
4. (2x2 + 5x + 2) ÷(x + 2)
Topic 6.
Model Factoring (by GCF)
Activity 1
Use algebra tiles to factor 4x+8
MODEL
ALGEBRA
X＋2
×
4x + 8
= 4(x + 2)
4
Activity 2
Use algebra tiles to factor x2 – 2x
MODEL
ALGEBRA
X-2
×
x2 – 2x
= x (x – 2)
x
Try This
Topic 5.
Use algebra tiles to factor each polynomial.
1. 3x – 12
2. 3x2 – 3x
Topic 7.
Model Factorization of
Trinomials
Activity 1
Use algebra tiles to factor x2 + 7x + 6
MODEL
×
ALGEBRA
x2 + 7x + 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 x2 + 7x + 6
MODEL
ALGEBRA
X＋6
×
x2 + 7x + 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.
x2 + 6x + 8
Activity 2
Use algebra tiles to factor x2 + x - 2
MODEL
X＋2
×
X-1
ALGEBRA
x2 + 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. x2 - 2x - 3
2. x2 - 5x + 4
3. x2 - 2x + 1
4. x2 + 3x – 4
5. x2 + 3x - 10
Topic 8.
Model Completing the
Square
Activity
Use algebra tiles to model x2 + 6x. Add unit tiles to complete a perfectsquare trinomial. Then write the new expression in factored form.
MODEL
X＋3
×
ALGEBRA
9
x2 + 6x + ____
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.
x2 + 8x
Marshall Island High School Open Class
Grade 10
Thank you for joining.
See you again.
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
Topic1&2
Topic6
1. X – 5 = 3
1. 3x – 12
2. 3x2 – 3x
2. X = -2X + 9
Topic3
(3x2 + 2x + 5) + (x2 – x – 4)
Topic4
Topic7
1. 3(x + 2)
x2 + 6x + 8
2. x (2x-1)
3. (x – 1)(x + 3)
Topic5
Topic8
x2 + 8x
1. (x2 + 5x + 4) ÷(x + 1)
2. (x2 + 4x – 5)÷(x – 1)
3. (x2 - 6x + 8)÷(x - 2)
4. (2x2 + 5x + 2) ÷(x + 2)