# Algebra Tiles

Look at the section on Number to Algebra for ideas on how to introduce Algebra Tiles.

**Expressions with algebra tiles**

**Expressions with algebra tiles**

This activity introduces expressions with unknown variables and constant terms.

Also available expressions with variable -10<x <10

Ask students to match the models to the statements. Ideally they should already be familiar with base blocks and algebra tiles.

Next move the change x slider above to show that x is variable and the units are constant.

The expressions can be manipulated using Mathsbot to highlight the distributive property 2(x+3) = 2x + 6.

Using the rectangle representation links to the area model for multiplication and division and highlights the common factor of 2.

**Equal expressions**

**Equal expressions**

Move the slider to change the value of x. When does 3x + 2 = x + 6?

When is 3x+2 > x+6?

When is 3x+2 < x+6?

**Algebra tiles and graphs**

**Algebra tiles and graphs**

Making connections between the bar model and the graph model.

Change the number bars, size of constant term and position using the sliders.

**Compare expressions**

**Compare expressions**

Compare 3x and x+3

Change the value of x by moving the sliders

**Equations and graphs**

**Equations and graphs**

Solve equations and inequalities by moving the slider and comparing the bar model to the graph.

**Solving Linear Equations**

**Solving Linear Equations**

**Algebra tiles do not show equality and inequality.**

**Before using algebra tiles to solve equations represent equality and inequality using a bar model or a dynamic ****model like ****equal expressions**** above****.**

**B****alance/elimination method**

**B**

**alance/elimination method**

**Add multiples of x’s, -x’s, 1’s or -1’s to both expressions to isolate x on one side of the equation. **

This method will always work and leads to the standard balancing method.

**3 - x + x = x - 4 + x**

**3 + 4 = 2x - 4 + ****4**

**Simultaneous Equations **

**Simultaneous Equations**

Change x and y until the bars are equal.

**Simultaneous equations by elimination**

**Simultaneous equations by elimination**

The elimination method is clear to see using algebra tiles and zero pairs when the coefficients have opposite signs.

2x + y = 7

x - y = 2

Add the two equations together to get the image below.

3x **+ y - y** = 9

The zero pair highlights the elimination.

3x = 9

x = 3

Substitute into 2x + y = 7

6 + y = 7

y = 1

x = 3 and y = 1

From here you can move on to multiplying one and then both equations before eliminating by adding the equations.

Difficulties and misconceptions start when the coefficients are the same sign.

### Method 1 – subtracting the two equations or finding the difference

### Method 2 – elimination using zero pairs

Method 2 also avoids the difficulties that arise in questions that involve subtracting negatives.