Introduction to Algebra Tiles

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Presentation transcript:

Introduction to Algebra Tiles Created by Nancy McAlinden Numeracy Lead Teacher N.B. District 14

Remember how we modeled integers? Legend - + ? ?

What is this worth? (-2) Legend + - ZERO PAIRS

What is this worth? +2 Legend + -

Algebra Tiles work the same way! Legend + - +3

Algebra Tiles work the same way! Legend + - -6

Algebra Tiles work the same way! Legend + - -2

Model this question: (-2) + (+3) = Legend + - zero pairs +1

Algebra Tiles can show MORE! But… Algebra Tiles can show MORE!

+ - These tiles help us model the unknown! The variable! Legend + - These tiles help us model the unknown! The variable! The mystery number!

+ - These tiles represent x! (Or n) (or whatever letter you’re using Legend + - These tiles represent x! (Or n) (or whatever letter you’re using for the variable or unknown amount.)

+ - One side represents a positive variable; Legend + - One side represents a positive variable; the other side represents a negative.

What does this show? Legend + - 3x

What does this show? Legend + - -9x

What does this show? Legend + - -2x

What does this show? Legend + - 2x + 4

What does this show? Legend + - x - 6

What does this show? Legend + - -2x + 5

What does this show? x + 3

But what is x worth? We don’t know until: 1.) someone tells us the value of x Or 2.) we have some information about the other side of the equation!

3x = 9 This line represents the = sign, or the middle of the balance scale.

If 3x = 9, …what is one x worth?

3x = 9

3x = 9 x = 3

Solve for x: x + 2 = 6

Solve for x: X + 2 = 6 We want a single x alone on one side and its value (the number of units or squares) on the other.

Solve for x: x + 2 = 6 We can subtract the 2 units (or squares) from the left IF we also subtract 2 units from the right. This keeps the balance.

Solve for x: x + 2 = 6 x + 2 – 2 = 6 - 2

Solve for x: x = 4

Solve for x: 2x + 4 = 8

Solve for x: 2x + 4 = 8 We want a single x alone on one side and its value (the number of units or squares) on the other.

Solve for x: 2x + 4 = 8 We can remove the 4 positive units from the left as long as we keep the balance and remove 4 positives from the right too. 2x + 4 - 4 = 8 - 4

2x + 4 = 8 2x = 4 Solve for x: We want one x. Now we have 2 x on one side and 4 on the other. 2x = 4 We want one x.

2x + 4 = 8 2x = 4 Solve for x: We can’t subtract an x from the left because we don’t have an x to subtract from the right, but…

Solve for x: 2x = 4 We can divide them and share fairly:

Solve for x: 2x = 4

Solve for x: ___ = __ 2 2 2x = 4

Solve for x: x = 2

What about the big squares?

They represent x2 and (-x2).

We’ll use them in high school!

Not all sets of algebra tiles are the same colours as the set we’ve seen here. How can you tell which side is negative?

The negative side is the colour that is the same for all sizes of tiles in the set: White = negative

The negative side is the colour that is the same for all the tiles in the set: Black = negative