New
New
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.

New
New
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.

## 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.

### 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.

### Keywords

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

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.
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.
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 $$2x + 1$$ ?
Correct Answer: 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:$$x \times -y$$ ,$$-xy$$

$$-xy$$

## Exit quiz

### 6 Questions

Q1.
Use the area model to select the correct expanded form for the expression $$5(3x + 4)$$.
$$8x + 4$$
$$8x + 20$$
$$15x + 4$$
Correct answer: $$15x + 20$$
$$20 - 15x$$
Q2.
Use the area model to select the correct expanded form for the expression $$-3(4x - 6)$$.
$$-12x - 18$$
$$-12x - 6$$
Correct answer: $$-12x + 18$$
$$12x - 18$$
$$12x + 6$$
Q3.
Use the area model to select the correct expanded form for the expression $$x(x - 1)$$.
$$x$$
$$2x - 1$$
$$x^2 + x$$
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: $$10x - 6$$
$$10x - 42$$
$$70x - 42$$
$$70x + 42$$