A formula is a rule linking sets of physical variables in context. The plural of formula is formulae.

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.

Changing the subject with simple formula

Maths

Checking and securing understanding of the distributive law with algebraic terms

Checking and securing solving linear equations

The product of two binomials

Difference of two squares

More complex binomial products

Additive relationships

Multiplicative relationships between terms

Changing the subject with more complex formula

Changing the subject to suit the context

Evaluating expressions with and without changing the subject

Problem solving with expressions and formulae

In this unit, pupils use the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

In the prior unit, pupils learnt how to rearrange an equation to find a specific value that satisfied the equation. In expressions and formulae, pupils use their understanding of rearrangement to change the subject of a formula.

This unit develops pupil understanding of formulae and how to rearrange them. Pupils will learn how to recognise and manipulate binomials and learn to recognise the difference of two squares.

Expressions and formulae

The __________ of a formula is a variable expressed in terms of other variables.

$$y^2$$ is not the subject of the equation $$y^2=25-x^2$$. Why not?

Laura wants to make $$x$$ the subject of the equation $$x+3y=17$$. Which operation should she apply to both sides of the equation?

The formula for the volume of a cylinder is  $$V=\pi{r^2}h$$. Select the correct arrangement of the formula to make $$h$$ the subject.

Division in the __________ operation of multiplication.

Select the rearrangements of the additive relationship 389.16 + 417.4 = 806.56.

Select the rearrangements of the multiplicative relationship $$y=5x$$.

The solution to $$x-13=63$$ is $$x=$${{}}.

Laura has only performed the operation $$+12$$ to one side of the equation.

The answer is obviously just $$1$$. Laura doesn't need a method here.

Laura begins to solve the equation $$x-12=13$$ by writing $$x-12+12=13$$.  What error has Laura made?

Which of the below are rearrangements of the equation $$17-x=2y$$ ?

Starter Quiz

Division in the __________ operation of multiplication.