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Year 7

Multiplying an expression by a constant

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

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New

Year 7

Multiplying an expression by a constant

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

Download all resources

Share activities with pupils

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Lesson details

Key learning points

The distributive law can make multiplication easier.
The distributive law can be understood using an area model.
A bar model can be used to represent the distributive law.
The distributive law can help us multiply an expression by a constant.

Keywords

Constant - A constant is a term that does not change; it contains no variables.

Common misconception

3(y+2) expands to 3y+2.

3 lots of 12 isn't 3x10+2 so 3 lots of (y+2) isn't 3y+2. Get students to draw this out. To visualise it.

Visually representations are really powerful here. If you can use concrete manipulatives, or get students to make some, or draw them. That will support their learning.

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).

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Starter quiz

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6 Questions

Q1.

The expression $$2x+5y-1$$ can not be further.

Correct Answer: simplified

Q2.

Match each expression to its simplified form.

Correct Answer:$$5 \times y$$,$$5y$$

$$5y$$

Correct Answer:$$5 \times x$$,$$5x$$

$$5x$$

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

$$xy$$

Correct Answer:$$-5 \times y$$,$$-5y$$

$$-5y$$

Correct Answer:$$x \times -5$$,$$-5x$$

$$-5x$$

Q3.

Which of the below will correctly evaluate $$6 \times 82$$?

$$6 \times 8 + 2$$

$$6 \times 8 + 6 \times 2$$

$$6 \times 80 + 2$$

Correct answer: $$6 \times 80 +6 \times 2$$

Q4.

Simplify $$4 \times 2a$$.

$$6a$$

Correct answer: $$8a$$

$$4a^2$$

$$6a^2$$

$$8a^2$$

Q5.

Match the expressions.

Correct Answer:$$3 \times -4a$$,$$-12a$$

$$-12a$$

Correct Answer:$$3 \times -4b$$,$$-12b$$

$$-12b$$

Correct Answer:$$-3 \times -4a$$,$$12a$$

$$12a$$

Correct Answer:$$-6b \times -2$$,$$12b$$

$$12b$$

Correct Answer:$$-3 \times 2a \times -2b$$,$$12ab$$

$$12ab$$

Correct Answer:$$-3 \times -2a \times -2b$$,$$-12ab$$

$$-12ab$$

Q6.

Which of these is the correct simplification of the expression $$ -y \times y + 5 \times y \times (-3) \times y$$?

$$15y^4$$

Correct answer: $$-16y^2$$

$$-y^2+2y$$

$$16y^2$$

Exit quiz

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6 Questions

Q1.

In the expression $$y+8$$, the $$y$$ term is a variable and the $$8$$ term is a .

Correct Answer: constant, Constant

Q2.

Which of these identities match the bar model shown?

$$4 \times e + 7 \equiv 4e + 7$$

Correct answer: $$4(e + 7) \equiv 4e + 28$$

$$e + 7\times 4 \equiv e + 28$$

Correct answer: $$(e+7) \times 4 \equiv 4e + 28$$

Q3.

In this area model, what is under these two ink splats?

$$5 +x$$ and $$8$$

$$5x$$ and $$3$$

$$5x$$ and $$8$$

Correct answer: $$5x$$ and $$15$$

$$3x$$ and $$15$$

Q4.

Match the expressions.

Correct Answer:$$5(x+4)$$,$$5x+20$$

$$5x+20$$

Correct Answer:$$4(x+5)$$,$$4x+20$$

$$4x+20$$

Correct Answer:$$10(x+2)$$,$$10x+20$$

$$10x+20$$

Correct Answer:$$2(x+10)$$,$$2x+20$$

$$2x+20$$

Correct Answer:$$10(x+4)$$,$$10x+40$$

$$10x+40$$

Correct Answer:$$4(x+10)$$,$$4x+40$$

$$4x+40$$

Q5.

Expand $$4(t-7)$$

Correct answer: $$4t-28$$

$$4t-7$$

$$-4t-28$$

$$4t-3$$

Q6.

Match the expressions.

Correct Answer:$$-2(-x-5)$$,$$2x+10$$

$$2x+10$$

Correct Answer:$$-2(x+5)$$,$$-2x-10$$

$$-2x-10$$

Correct Answer:$$-2(x-5)$$,$$-2x+10$$

$$-2x+10$$

Correct Answer:$$-2(5-x)$$,$$2x-10$$

$$2x-10$$