# Solving Equations Small Steps

The equations below have been represented using algebra tiles and equations solver on MathsBot.

## One step equations (x +/- a = b)

Solve the following equations

x + 3 = 5

x + 3 = 4

x + 3 = 3

x + 3 = 2

x + 3 = 1

x + 3 = 0

x + 3 = -1

x + 3 = -5

x + 5 = 7

x + 5 = 5

x + 5 = 0

x + 5 = -2

x + 5 = -5

x + 5 = -12

x + 5 = 100

x + 5 = -100

If a is a positive integer,

x + 3 = a, x > 0 when a ...... 3

x + 3 = a, x = 0 when a ...... 3

x + 3 = a, x < 0 when a ...... 3

x + 5 = a, x > 0 when a ...... 5

x + 5 = a, x = 0 when a ...... 5

x + 5 = a, x < 0 when a ...... 5

### Using MathsBot Equation Solver

Add the same number of tiles to both sides of the equation to eliminate x's and 1's. The aim is to leave x (or x's) on its own.

This representation uses zero pairs.

Notice that in this method we add -3 to both sides rather than subtract 3.

1x + 3 = 5

0x - 3 -3

1x + 0 = 2

Represent the written solution as a column addition.

1x + 0x = 1x 3 + -3 = 0 5 + -3 = 2

or adding to both sides of the equation

1x + 3 = 5

1x + 3 - 3 = 5 - 3

1x = 2

x + 0.3 = 0.5

x + 0.3 = 0.4

x + 0.3 = 0.3

x + 0.3 = 3

x + 0.3 = 0.33

x + 0.3 = 0.2

x + 0.3 = 0.03

x + 0.3 = -0.3

Interweave retrieval practice

What misconceptions might these questions reveal?

How will you address them?

Compare the following equations

3 + x = 7

7 = x + 3

x + 3 = 7

7 = 3 + x

What is the same?

What is different?

Ask students to draw a diagram for each equation. This activity draws out misconceptions and allows students to see the similarities and differences in these equations. This is an important step and worth spending time on to avoid misconceptions later.

Solve the following equations

x - 5 = 1

x - 5 = 3

x - 5 = 0

x - 5 = -1

x - 5 = -5

x - 5 = -7

If a is a positive or negative integer,

x - 5 = a, x > 0 when a ...... ......

x - 5 = a, x = 0 when a ...... ......

x - 5 = a, x < 0 when a ...... ......

Compare the following equations

x - 5 = 3

-5 + x = 3

5 - x = 3

-5x = 3

What is the same?

What is different?

Can you draw a model to represent each equation?

Solve the following equations

x - 3 = 5

-3 + x = 5

5 = x - 3

5 = 3 - x

5 = -3 + x

What do you notice?

### Intelligent Practice

4x = 12

x = 12

4

1 x = 12

4

0.25x = 12

Draw a diagram to represent each equation.

What do you notice?

## Two step equations

2x + 3 = 15

3 + 2x = 15

2x - 3 = 15

-3 + 2x = 15

3 - 2x = 15

Draw a diagram to represent each equation.

What do you notice?

Solve the following equations

Compare the diagrams above.

The first diagram represents x + 3 = 21.

Write equations for the other two diagrams.