New
New
Year 9

# Evaluating expressions with and without changing the subject

I can evaluate an expression where the subject has been changed and where it has not.

New
New
Year 9

# Evaluating expressions with and without changing the subject

I can evaluate an expression where the subject has been changed and where it has not.

## Lesson details

### Key learning points

1. Changing the subject can make it easier to evaluate a formula.
2. It is possible to evaluate a formula without changing the subject.
3. Both forms of the formula give the same result.

### Common misconception

Changing the subject of an equation or formula is only done when you are told to.

Having students practise rearranging before substituting and vice versa allows them to decide when the skill could be useful.

### Keywords

• Subject of an equation/formula - 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.

This is a good opportunity for pupils to practise using key formulae and this could include those from other subjects. You could ask the pupils to share formulas they have seen or used in other lessons or outside of school.
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).

## Starter quiz

### 6 Questions

Q1.
Substitute means to put in place of another. In algebra, substitution can be used to replace __________ with values.
constants
equations
solutions
Q2.
$$A={1\over2}(a+b)h$$ is the formula for area of a trapezium. It can be rearranged to $${2A\over{h}}-a=b$$ in order to make $$b$$ the of the formula.
Q3.
The formula for area of a triangle is $$A={1\over2}bh$$. The area of a triangle with base 7.5 cm and height 6 cm is cm²
Q4.
The formula $$s={d\over{t}}$$ can be rearranged to $$t={d\over{s}}$$ or $$d=s\times {t}$$. If $$d=12$$ and $$s=3$$, find $$t$$.
$$36$$
Correct answer: $$4$$
$${1\over{4}}$$
Q5.
Find the area of a trapezium with $$h=7$$, $$a=3.2$$, $$b=4.8$$.
$$A={1\over2}(3.2+4.8)+7=11$$ square units
Correct answer: $$A={1\over2}(3.2+4.8)\times7=28$$ square units
$$A=2(3.2+4.8)\times7=112$$ square units
$$A={1\over2}(3.2\times4.8)\times7=53.76$$ square units
Q6.
$$A={1\over2}(a+b)h$$ is the formula for area of a trapezium. Select all the correct rearrangements of this formula.
Correct answer: $${2A\over{h}}-b=a$$
$${Ah\over{2}}-a=b$$
$${A\over{2h}}-a=b$$
$${2h\over{A}}-a=b$$
Correct answer: $${2A\over{a+b}}=h$$

## Exit quiz

### 6 Questions

Q1.
$$a=\sqrt{{c^2}-b^2}$$ is a __________ of $$a^2+b^2=c^2$$.
expression
solution
substitution
variable
Q2.
Which arrangement of the formula for area of a triangle makes it quickest for you to find $$b$$ if you know $$A$$ and $$h$$?
$$A={1\over2}bh$$
$${2A\over{b}}=h$$
Correct answer: $${2A\over{h}}=b$$
$${h\over{2A}}=b$$
Q3.
The formula for the area of a triangle is $$A={1\over2}bh$$. The base $$b$$ of a triangle with area 24 m² and height 8 m is m.
Q4.
Rearrange the formula $$C=2{\pi}{r}$$ to find the radius of a circle with circumference 42 cm. Leave your answer in terms of $$\pi$$.
$$r=2C\pi=2\times 42\times \pi=84\pi$$
$$r={2\pi\over{{C}}}={2\pi\over{{42}}}={\pi\over{21}}$$
$$r={2C\over{{\pi}}}={2\times 42\over{{\pi}}}={84\over{\pi}}$$
Correct answer: $$r={C\over{2{\pi}}}={42\over{2{\pi}}}={21\over{\pi}}$$
Q5.
Which rearrangement makes it easiest to find length $$b$$ if you know lengths $$a$$ and $$c$$?
$$a=\sqrt{{c^2}-b^2}$$
Correct answer: $$b=\sqrt{{c^2}-a^2}$$
$$b^2=c^2-a^2$$
$$b=\sqrt{{a^2}-c^2}$$
$$b=\sqrt{{c^2}+a^2}$$
Q6.
Jun says "You have to rearrange the formula $$a^2+b^2=c^2$$ into the form $$b=\sqrt{{c^2}-a^2}$$ with $$b$$ as the subject if you want to find $$b$$ given that $$a=6$$ and $$c=10$$." Is Jun right?
Yes, $$b$$ must be the subject before you can substitute.
Yes, because $$b=\sqrt{{10^2}-6^2}$$ is the fastest way to find $$b$$.
Correct answer: No, you can substitute $$a$$ and $$c$$ into $$a^2+b^2=c^2$$ before evaluating.