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Lesson 1 of 12
  • Year 9

Checking and securing understanding of the distributive law with algebraic terms

I can use the distributive law to multiply an expression by a term.

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Lesson 1 of 12
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  • Year 9

Checking and securing understanding of the distributive law with algebraic terms

I can use the distributive law to multiply an expression by a term.

Download all resources
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

  1. The distributive law can be understood using an area model.
  2. The distributive law can help us multiply an expression by a term.
  3. The expression may contain any number of terms.

Keywords

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

Common misconception

Pupils forget to multiply every term in the bracket by the term outside the bracket.

Remind pupils about the distributive law with numerical examples, e.g. 4(3 + 7) and show that this is not equivalent to 12 + 7. Using algebra tiles can also help pupils to make sense of this skill.


To help you plan your year 9 maths lesson on: Checking and securing understanding of the distributive law with algebraic terms, download all teaching resources for free and adapt to suit your pupils' needs...

If you don't have algebra tiles, pupils can still sketch them (mini-whiteboards may be good for this) or they can be used as a visual aid for explanation.
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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).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
What does the symbol $$\equiv$$ represent in the identity $$x + x + x \equiv 3x$$ ?

There is a value for $$x$$ which makes both sides equal.
Correct answer: Both sides are equivalent expressions.
The left hand side does not equal the right hand side.
The identity can be solved to find the value of $$x$$

Q2.
Which of these examples show two like terms?

Correct answer: $$2x$$ and $$0.4x$$
$$x^2$$ and $$x$$
$$5xy$$ and $$5y$$
Correct answer: $$3xy$$ and $$3yx$$
$$8x$$ and $$4$$

Q3.
Which of these bar models represents 3 lots of the expression $$2x + 1$$ ?

An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz

Q4.
Match the product of two terms with its simplified expression.

Correct Answer:$$3 \times 2x$$,$$6x$$

$$6x$$

Correct Answer:$$3 \times -2x$$,$$-6x$$

$$-6x$$

Correct Answer:$$-3 \times -x$$,$$3x$$

$$3x$$

Correct Answer:$$x \times 2x$$,$$2x^2$$

$$2x^2$$

Correct Answer:$$-x \times 2x$$,$$-2x^2$$

$$-2x^2$$

Correct Answer:$$-3x \times -2x$$,$$6x^2$$

$$6x^2$$

Q5.
Which of these is an equivalent calculation to $$44\times 12$$ ?

$$(11\times 3) + (4\times 4)$$
$$(44\times 6) + (44\times 2)$$
Correct answer: $$(44\times 8) + (44\times 4)$$
$$(40\times 10) + (4\times 2)$$
Correct answer: $$(44\times 10) + (44\times 2)$$

Q6.
Match each product of two terms with its simplified expression.

Correct Answer:$$-x \times -x$$,$$x^2$$

$$x^2$$

Correct Answer:$$2x \times x$$,$$2x^2$$

$$2x^2$$

Correct Answer:$$2x \times y$$,$$2xy$$

$$2xy$$

Correct Answer:$$-2y \times x$$,$$-2xy$$

$$-2xy$$

Correct Answer:$$x \times -y$$ ,$$-xy$$

$$-xy$$

Assessment exit quiz

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6 Questions

Q1.
Use the area model to select the correct expanded form for the expression $$5(3x + 4)$$.

An image in a quiz
$$8x + 4$$
$$8x + 20$$
$$15x + 4$$
Correct answer: $$15x + 20$$
$$20 - 15x$$

Q2.
Use the area model to select the correct expanded form for the expression $$-3(4x - 6)$$.

An image in a quiz
$$-12x - 18$$
$$-12x - 6$$
Correct answer: $$-12x + 18$$
$$12x - 18$$
$$12x + 6$$

Q3.
Use the area model to select the correct expanded form for the expression $$x(x - 1)$$.

An image in a quiz
$$x$$
$$2x - 1$$
$$x^2 + x$$
Correct answer: $$x^2 - x$$
$$2x^2 - x$$

Q4.
Match up each bracketed expression with its equivalent expression in expanded form.

Correct Answer:$$4x(x - 6)$$,$$4x^2 - 24x$$

$$4x^2 - 24x$$

Correct Answer:$$4x(x + 6)$$,$$4x^2 + 24x$$

$$4x^2 + 24x$$

Correct Answer:$$-4x(x - 6)$$,$$-4x^2 + 24x$$

$$-4x^2 + 24x$$

Correct Answer:$$-2x(-2x + 3)$$,$$4x^2 -6x$$

$$4x^2 -6x$$

Correct Answer:$$-2x(2x - 3)$$,$$-4x^2 + 6x$$

$$-4x^2 + 6x$$

Correct Answer:$$2x(2x+ 3)$$,$$4x^2 + 6x$$

$$4x^2 + 6x$$

Q5.
Select the correct expanded and simplified form of the expression $$3(2x + 4) + 7(x - 6).$$

$$10x - 30$$
$$10x + 6$$
Correct answer: $$13x - 30$$
$$13x - 2$$
$$13x + 54$$

Q6.
Select the correct expanded and simplified form of the expression $$8(5x - 3) - 6(5x - 3).$$

$$2x - 6$$
Correct answer: $$10x - 6$$
$$10x - 42$$
$$70x - 42$$
$$70x + 42$$