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Year 8

Equality in an equation

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

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New
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Year 8

Equality in an equation

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

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The equals sign means that the two sides of the equation have the same value.
  2. This can be described as the expressions balancing.
  3. The equality of the expressions can be represented with a bar model.
  4. 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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which expression is represented by this bar model?
An image in a quiz
$$3x + 6$$
$$6x + 6$$
Correct answer: $$6x + 12$$
Correct answer: $$2(3x + 6)$$
$$3(x + 6)$$
Q2.
Select the bar model that correctly represents the equation $$3x + 15 = x + 32$$.
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
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?
An image in a quiz
$$ + 2$$
$$ + 16$$
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?
An image in a quiz
$$+9$$
$$+ (2x + 10)$$
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 .
An image in a quiz
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,$$4(x + 12) = 76$$

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

Exit quiz

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6 Questions

Q1.
Which equations are represented by this bar model?
An image in a quiz
$$a + c = 12$$
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?
An image in a quiz
$$3x + 18 = 28$$
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?
An image in a quiz
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?
An image in a quiz
$$+1$$
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?
An image in a quiz
$$+1$$
$$−1$$
$$+x$$ and $$−1$$
Correct answer: $$−2x $$ and $$−1$$
Correct answer: $$\times {1\over 2}$$