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Year 7

Simplifying before multiplying with multiple expressions

I can recognise when I can simplify before multiplying expressions by their respective terms.

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New
New
Year 7

Simplifying before multiplying with multiple expressions

I can recognise when I can simplify before multiplying expressions by their respective terms.

Download all resources
Share activities with pupils

Link copied to clipboard

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Lesson details

Key learning points

  1. Collecting together like terms simplifies the expression.
  2. Simplifying may be possible before multiplication.

Keywords

  • Term - A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –

  • Expression - An expression contains one or more terms where each term is separated by an operator.

Common misconception

2(z+7)+3(z+7)+5(z+7) must be expanded first before simplifying.

Think of 'Unitising'. What is it we are adding together? In this case, we are summing multiples of (z+7). How many lots do we have?


To help you plan your year 7 maths lesson on: Simplifying before multiplying with multiple expressions, download all teaching resources for free and adapt to suit your pupils' needs...

Coherence is the key here. What does this resemble from their prior learning with which they are very comfortable? 3 tens + 2 tens + 4 tens makes 9 tens. 3m + 2m + 4m makes 9m.
Teacher tip

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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Starter quiz

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6 Questions

Q1.
Look at $$4(y-7)+8(y-7)$$. Inside each bracket you can see matching __________.
equations
Correct answer: expressions
formulas
answers
Q2.
Which of the below is equivalent to $$6 \times 7+2 \times 7$$?
Correct answer: $$(6+2)\times 7$$
$$42 \times 14$$
$$(6+2) \times 14$$
Q3.
Expand $$5(x-3)$$
$$5x-3$$
$$5x+3$$
$$5x+15$$
Correct answer: $$5x-15$$
Q4.
Which of the below are equivalent to $$11 \times 6 + 11 \times 4$$?
$$66 \times 44$$
Correct answer: $$11 \times 10$$
$$22 \times (6+4)$$
$$22 \times 10$$
Correct answer: $$11 \times (6+4)$$
Q5.
Expand and simplify $$6(e-f)+2(f-e)$$
$$8e+8f$$
$$8e+4f$$
$$4e+8f$$
$$4e+4f$$
Correct answer: $$4e-4f$$
Q6.
Match the expressions to the correct first step when expanding before simpifying.
Correct Answer:$$5(a+3)+2(a-8)$$,$$5a+15+2a-16$$

$$5a+15+2a-16$$

Correct Answer:$$5(a-3)+2(a-8)$$,$$5a-15+2a-16$$

$$5a-15+2a-16$$

Correct Answer:$$5(a+3)-2(a+8)$$,$$5a+15-2a-16$$

$$5a+15-2a-16$$

Correct Answer:$$5(2a+3)+2(a-8)$$,$$10a+15+2a-16$$

$$10a+15+2a-16$$

Correct Answer:$$5a(a+3)+2(a-8)$$,$$5a^2+15a+2a-16$$

$$5a^2+15a+2a-16$$

Exit quiz

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6 Questions

Q1.
When you write $$3(y-8)+9(y-8)$$ as $$12(y-8)$$ you have __________ the expression.
solved
Correct answer: simplified
expanded
factorised
Q2.
Use this bar model to help you simplify the expression $$5(x+6)+2(x+6)$$
An image in a quiz
$$7(2x+12)$$
Correct answer: $$7(x+6)$$
$$7x+6$$
$$5x+6+2x+6 \equiv 7x+12$$
Q3.
Which of the below cannot be simplified before it is expanded?
$$5(x+8)+7(x+8)$$
$$5(y-3)+7(y-3)$$
Correct answer: $$5(x-3)+7(y-3)$$
$$5(x+8)-7(x+8)$$
$$5(x+8)+7(x+8)+3(x+8)$$
Q4.
Match each expression with a simplified expression.
Correct Answer:$$4(e+2)+6(e+2)$$,$$10(e+2)$$

$$10(e+2)$$

Correct Answer:$$4(e+2)+5(e+2)$$,$$9(e+2)$$

$$9(e+2)$$

Correct Answer:$$7(e+2)+3(e+2)-5(e+2)$$,$$5(e+2)$$

$$5(e+2)$$

Correct Answer:$$4(e+2)-5(e+2)$$,$$-e-2$$

$$-e-2$$

Correct Answer:$$4(e-2)-5(e-2)$$,$$2-e$$

$$2-e$$

Q5.
Which of the below is true for $$8y(x-4)+8y(x-5)$$?
$$x-4$$ and $$x-5$$ are not matching expressions so you can not simplify.
You have to expand first before simplifying.
Correct answer: Matching multipliers means you can simplify before expanding.
Q6.
Match each expression with a simplified expression.
Correct Answer:$$5(y+2)+5(y+6)$$,$$5(2y+8)$$

$$5(2y+8)$$

Correct Answer:$$5(y+2)+5(2y+6)$$,$$5(3y+8)$$

$$5(3y+8)$$

Correct Answer:$$5(y-1)+5(y+6)$$,$$5(2y+5)$$

$$5(2y+5)$$

Correct Answer:$$5(2y+2)-5(y+6)$$,$$5(y-4)$$

$$5(y-4)$$

Correct Answer:$$5(2y+2)-5(6-y)$$,$$5(3y-4)$$

$$5(3y-4)$$