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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
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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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Share activities with pupils
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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?

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 (2024), 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:$$5(2y+2)-5(6-y)$$,$$5(3y-4)$$

$$5(3y-4)$$