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Year 8

Solving simple linear equations with an additive step

I can solve a linear equation requiring a single additive step.

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New

Year 8

Solving simple linear equations with an additive step

I can solve a linear equation requiring a single additive step.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

An equation involving an additive step can be represented with a bar model.
Using the bar model you can write all the arrangements of the equation with an additive step.
One of the arrangements will give the solution to the equation.
This can be written algebraically to find the solution.

Keywords

Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0

Common misconception

When solving x - 5 = 10 pupils may see the -5 and calculate 10 - 5 = 5

Focus on understanding zero pairs and why adding the additive inverse gives the solution. Bar models are a helpful representation here.

Pupils with good numeracy often want to spot the answer. Use this as an opportunity to focus on presentation and stressing the importance of writing mathematically. It's not just about finding the solution but constructing an argument to show why.

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.

Which equations are represented by this bar model?

Correct answer: $$12 + x = 21$$

$$21 + x = 12$$

Correct answer: $$21 − 12 = x$$

$$21 + 12 = x$$

Correct answer: $$12 = 21 − x$$

Q2.

Which equations are represented by this bar model?

$$a + 8 = 33$$

$$33 − 8 = a$$

Correct answer: $$a = 8 + 33$$

Correct answer: $$33 = a − 8$$

$$8 = 33 − a$$

Q3.

Match each value with its additive inverse.

Correct Answer:$$3$$,$$−3$$

$$−3$$

Correct Answer:$$-3$$,$$3$$

$$3$$

Correct Answer:$$1\over 3$$,$$−{1\over 3}$$

$$−{1\over 3}$$

Correct Answer:$$−{1\over 3}$$,$$1\over 3$$

$$1\over 3$$

Correct Answer:$$0.3$$,$$−0.3$$

$$−0.3$$

Correct Answer:$$10\over 3$$,$$−{10\over 3}$$

$$−{10\over 3}$$

Q4.

Which of these are zero pairs?

Correct answer: 5 and (−5)

(−3) and (−3)

1 and (−0.1)

$$1\over 2$$ and $$2$$

Correct answer: $$2\over 5$$ and $$(−0.4)$$

Q5.

What is the value of the expression $$2(3x + 5)$$ when $$x = −3$$ ?

Correct Answer: −8, -8, − 8, - 8

Q6.

The diagram shows a balanced scale on the left. When an operation is performed to the RHS, it is not balanced. What operation must be performed to the LHS to maintain equality?