The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Checking and securing understanding of the distributive law with algebraic terms

Maths

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 simple formula

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

Use the area model to select the correct expanded form for the expression $$5(3x + 4)$$.

Use the area model to select the correct expanded form for the expression $$-3(4x - 6)$$.

Use the area model to select the correct expanded form for the expression $$x(x - 1)$$.

Match up each bracketed expression with its equivalent expression in expanded form.

Select the correct expanded and simplified form of the expression $$3(2x + 4) + 7(x - 6).$$

Select the correct expanded and simplified form of the expression $$8(5x - 3) - 6(5x - 3).$$

There is a value for $$x$$ which makes both sides equal. 

The left hand side does not equal the right hand side.

The identity can be solved to find the value of $$x$$

What does the symbol $$\equiv$$ represent in the identity $$x + x + x \equiv 3x$$ ?

Which of these examples show two like terms?

Which of these bar models represents 3 lots of the expression $$2x + 1$$ ?

Match the product of two terms with its simplified expression.

Which of these is an equivalent calculation to $$44\times 12$$ ?

Match each product of two terms with its simplified expression.

Starter Quiz

What does the symbol $$\equiv$$ represent in the identity $$x + x + x \equiv 3x$$ ?