Equality in an equation

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Lesson details

Learning outcome

I can appreciate that in an equation the two sides of the equals sign balance.

Key learning points

The equals sign means that the two sides of the equation have the same value.
This can be described as the expressions balancing.
The equality of the expressions can be represented with a bar model.
It is possible to rearrange equations to find the family of alternative versions of the equation.

Keywords

Equation - An equation is used to show two expressions that are equal to each other.

Common misconception

10 - x = 2 means that 2 - x = 10

Using bar models can help pupils understand rearranging additive relationships at an early stage.

Teacher tip

Manipulable algebra tiles would allow pupils to make their own equations and think about how they can maintain equality. This can be a nice step between using the balances and moving to the abstract as negative algebra tiles can be used too.

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0

except where otherwise stated. See Oak's terms & conditions

(Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Which expression is represented by this bar model?

$$3x + 6$$

$$6x + 6$$

Correct answer: $$6x + 12$$

Correct answer: $$2(3x + 6)$$

$$3(x + 6)$$

Q2.
Select the bar model that correctly represents the equation $$3x + 15 = x + 32$$.

Correct Answer: An image in a quiz

Q3.
Given that $$2.4 + 3.7 = 6.1$$, which of these are also true?

$$2.4 + 6.1 = 3.7$$

Correct answer: $$6.1 - 2.4 = 3.7$$

$$3.7 - 2.4 = 6.1$$

Correct answer: $$2.4 = 6.1 - 3.7$$

Q4.
This bar model represents the initial equation $$x + 16 = 27$$. What needs to be done to the top bar to maintain equality?

$$ + 2$$

$$ + 16$$

Correct answer: $$ + (x + 16) $$

Correct answer: $$ + 27$$

$$+ x$$

Q5.
This bar model represents the initial equation $$2x + 5 = 9$$. What needs to be done to the top bar to maintain equality?

$$+9$$

$$+ (2x + 10)$$

Correct answer: $$+ (4x + 10)$$

$$\times 2$$

Correct answer: $$\times 3$$

Q6.
These 4 bar models represent operations performed on the equation $$x + 12 = 19$$. Match the bar models labelled A, B, C, D with the equivalent equation they represent .

Correct Answer:A,$$3(x + 12) = 57$$

$$3(x + 12) = 57$$

Correct Answer:B,$$x + 12 + 2x + 24 = 19 + 2x + 24$$

$$x + 12 + 2x + 24 = 19 + 2x + 24$$

Correct Answer:C,$$x + 12 + 38 = 19 + 38$$

$$x + 12 + 38 = 19 + 38$$

Correct Answer:D,$$4(x + 12) = 76$$

$$4(x + 12) = 76$$

Assessment exit quiz

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6 Questions

Q1.
Which equations are represented by this bar model?

$$a + c = 12$$

Correct answer: $$a − c = 12$$

$$c − a = 12$$

$$12 + a = c$$

Correct answer: $$c = a − 12$$

Q2.
Which equations are represented by this bar model?

$$3x + 18 = 28$$

Correct answer: $$3x + 18 - 28 = x$$

$$x + 28 − 3x + 18 = 0$$

Correct answer: $$x = x + 28 − 18 − 2x$$

$$2x = 28 − 18 − x$$

Q3.
If $$31 − x = 17$$, which of these equations are also true?

Correct answer: $$31 − 17 = x$$

$$17 − x = 31$$

Correct answer: $$x + 17 =31$$

$$x = 31 + 17$$

$$x = 17 − 31 $$

Q4.
These scales are not balanced. The mass of all the square objects are the same. Which statements are definitely true?

The triangle is lighter than 1 square.

Correct answer: The triangle is lighter than 2 squares.

The triangle has the same mass as 1 square.

The triangle has the same mass as 2 squares.

The triangle is heavier than 1 square.

Q5.
The diagram shows a balanced scale on the left. When an operation is performed to the RHS, it is not balanced. What operation must be performed to the LHS to maintain equality?

$$+1$$

Correct answer: $$+3$$

$$+x$$

$$\times 2$$

$$\times 3$$

Q6.
The diagram shows a balanced scale on the left. When an operation is performed to the LHS, it is not balanced. What operation must be performed to the RHS to maintain equality?

$$+1$$

$$−1$$

$$+x$$ and $$−1$$

Correct answer: $$−2x $$ and $$−1$$

Correct answer: $$\times {1\over 2}$$

To help you plan your 8 maths lesson on: Equality in an equation, download all teaching resources for free and adapt to suit your pupils' needs...

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Equality in an equation

Lesson slides

Lesson details

Learning outcome

Key learning points

Keywords

Common misconception

Teacher tip

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which expression is represented by this bar model?

Q2.Select the bar model that correctly represents the equation $$3x + 15 = x + 32$$.

Q3.Given that $$2.4 + 3.7 = 6.1$$, which of these are also true?

Q4.This bar model represents the initial equation $$x + 16 = 27$$. What needs to be done to the top bar to maintain equality?

Q5.This bar model represents the initial equation $$2x + 5 = 9$$. What needs to be done to the top bar to maintain equality?

Q6.These 4 bar models represent operations performed on the equation $$x + 12 = 19$$. Match the bar models labelled A, B, C, D with the equivalent equation they represent .

Assessment exit quiz

6 Questions

Q1.Which equations are represented by this bar model?

Q2.Which equations are represented by this bar model?

Q3.If $$31 − x = 17$$, which of these equations are also true?

Q4.These scales are not balanced. The mass of all the square objects are the same. Which statements are definitely true?

Q5.The diagram shows a balanced scale on the left. When an operation is performed to the RHS, it is not balanced. What operation must be performed to the LHS to maintain equality?

Q6.The diagram shows a balanced scale on the left. When an operation is performed to the LHS, it is not balanced. What operation must be performed to the RHS to maintain equality?

How to plan a lesson using our resources

Q1.
Which expression is represented by this bar model?

Q2.
Select the bar model that correctly represents the equation $$3x + 15 = x + 32$$.

Q3.
Given that $$2.4 + 3.7 = 6.1$$, which of these are also true?

Q4.
This bar model represents the initial equation $$x + 16 = 27$$. What needs to be done to the top bar to maintain equality?

Q5.
This bar model represents the initial equation $$2x + 5 = 9$$. What needs to be done to the top bar to maintain equality?

Q6.
These 4 bar models represent operations performed on the equation $$x + 12 = 19$$. Match the bar models labelled A, B, C, D with the equivalent equation they represent .

Q1.
Which equations are represented by this bar model?

Q2.
Which equations are represented by this bar model?

Q3.
If $$31 − x = 17$$, which of these equations are also true?

Q4.
These scales are not balanced. The mass of all the square objects are the same. Which statements are definitely true?

Q5.
The diagram shows a balanced scale on the left. When an operation is performed to the RHS, it is not balanced. What operation must be performed to the LHS to maintain equality?

Q6.
The diagram shows a balanced scale on the left. When an operation is performed to the LHS, it is not balanced. What operation must be performed to the RHS to maintain equality?