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Checking and securing understanding of changing the subject

I can apply an understanding of inverse operations to a formula in order to make a specific variable the subject.

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Lesson 8 of 16

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Year 10

Checking and securing understanding of changing the subject

I can apply an understanding of inverse operations to a formula in order to make a specific variable the subject.

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Lesson details

Key learning points

Rearranging the formula may be beneficial when what you wish to calculate is not the subject.
You can compare rearranging the formula to solving for one unknown.
Instead of finding a value though, you will find an expression that the variable is equal to.

Keywords

Subject of an equation - The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1.

Common misconception

When rearranging multiplicative relationships, the values just 'swap'

Pupils should understand how to manipulate multiplicative relationships properly instead of relying on a 'trick'. This will be useful in other subject areas as well.

There are opportunities to see the importance of changing the subject in a range of topic areas. For example when rearranging trigonometric ratios, or using geometric formula. There are also examples of linear relationships between x and y which can be linked to identifying the gradient of a line.

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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.
If the side of an equilateral triangle is $$3n+1$$, write an expression for the perimeter.

Correct Answer: 3(3n+1), 9n + 3

Q2.
If the side of a regular pentagon is $$14y - a$$ write an expression for the perimeter.

Correct Answer: 5(14y - a), 70y - 5a

Q3.
Which of the following is an expression for the area of a square with side length $$3x$$

$$3x^2$$

$$(3x^2)$$

Correct answer: $$(3x)^2$$

Q4.
What is the value of $$x$$ for $$5(x + 7) = 30$$?

Correct Answer: -1

Q5.
If $$x$$ is a positive integer, what is the value of $$x$$ for $$x^2 - 4 = 0$$?

Correct Answer: 2

Q6.
What is the value of $$x$$ for $$2x - 3 = 7$$?

Correct Answer: 5

Assessment exit quiz

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6 Questions

Q1.
Make $$x$$ the subject of $$3y - x = 15$$

Correct answer: $$x = 3y - 15$$

$$x = 15 - 3y$$

$$x = 3y + 15$$

$$x = -3y - 15$$

Q2.
Make $$y$$ the subject of $$4x + 2y = 8$$

$$y = 2x + 4$$

$$y = -2x - 4$$

Correct answer: $$y = 4 - 2x$$

$$y = 2 - 4x$$

Q3.
Make $$z$$ the subject of $$\frac{z}{2} + 3x = 7$$

$$z = 7 - 3x$$

$$z = 4 - 3x$$

$$z = 14 - 3x$$

Correct answer: $$z = 14 - 6x$$

Q4.
Make $$a$$ the subject of $$b = 3(a - 4) + 2$$

$$a = \frac{b + 2}{3} - 4$$

Correct answer: $$a = \frac{b - 2}{3} + 4$$

$$a = \frac{b - 2}{3} - 4$$

$$a = \frac{b + 6}{3}$$

Q5.
Make $$m$$ the subject of $$\frac{4m + 5}{3} = n$$

$$m = 3n + 5$$

$$m = \frac{3n + 5}{4}$$

Correct answer: $$m = \frac{3n - 5}{4}$$

$$m = \frac{n - 5}{3}$$

Q6.
Make $$p$$ the subject of $$2p + \frac{q}{3} = 4$$

$$p = \frac{8 - q}{6}$$

$$p = 2 - \frac{q}{3}$$

$$p = \frac{4 - q}{3}$$

Correct answer: $$p = 2 - \frac{q}{6}$$

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

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Checking and securing understanding of changing the subject

Checking and securing understanding of changing the subject

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.If the side of an equilateral triangle is $$3n+1$$, write an expression for the perimeter.

Q2.If the side of a regular pentagon is $$14y - a$$ write an expression for the perimeter.

Q3.Which of the following is an expression for the area of a square with side length $$3x$$

Q4.What is the value of $$x$$ for $$5(x + 7) = 30$$?

Q5.If $$x$$ is a positive integer, what is the value of $$x$$ for $$x^2 - 4 = 0$$?

Q6.What is the value of $$x$$ for $$2x - 3 = 7$$?

Assessment exit quiz

6 Questions

Q1.Make $$x$$ the subject of $$3y - x = 15$$

Q2.Make $$y$$ the subject of $$4x + 2y = 8$$

Q3.Make $$z$$ the subject of $$\frac{z}{2} + 3x = 7$$

Q4.Make $$a$$ the subject of $$b = 3(a - 4) + 2$$

Q5.Make $$m$$ the subject of $$\frac{4m + 5}{3} = n$$

Q6.Make $$p$$ the subject of $$2p + \frac{q}{3} = 4$$

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

Q1.
If the side of an equilateral triangle is $$3n+1$$, write an expression for the perimeter.

Q2.
If the side of a regular pentagon is $$14y - a$$ write an expression for the perimeter.

Q3.
Which of the following is an expression for the area of a square with side length $$3x$$

Q4.
What is the value of $$x$$ for $$5(x + 7) = 30$$?

Q5.
If $$x$$ is a positive integer, what is the value of $$x$$ for $$x^2 - 4 = 0$$?

Q6.
What is the value of $$x$$ for $$2x - 3 = 7$$?

Q1.
Make $$x$$ the subject of $$3y - x = 15$$

Q2.
Make $$y$$ the subject of $$4x + 2y = 8$$

Q3.
Make $$z$$ the subject of $$\frac{z}{2} + 3x = 7$$

Q4.
Make $$a$$ the subject of $$b = 3(a - 4) + 2$$

Q5.
Make $$m$$ the subject of $$\frac{4m + 5}{3} = n$$

Q6.
Make $$p$$ the subject of $$2p + \frac{q}{3} = 4$$