New
New
Year 8

Solving simple linear equations with an additive step

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

New
New
Year 8

Solving simple linear equations with an additive step

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

Lesson details

Key learning points

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

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.

Keywords

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

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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6 Questions

Q1.
Which equations are represented by this bar model?
An image in a quiz
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?
An image in a quiz
$$a + 8 = 33$$
$$33 − 8 = a$$
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?
An image in a quiz
$$\times 2$$
$$\times 3$$
Correct answer: $$+9$$
$$+ 12$$
$$+ 18$$

6 Questions

Q1.
What is the value of the unknown in this bar model? $$x=$$
An image in a quiz
Correct Answer: 10, ten
Q2.
Which best describes the mistake that has been made when solving the equation below?
An image in a quiz
15 add (−8) does not equal 7
The same operation has not been applied to both sides of the equation.
Correct answer: The correct additive inverse has not been added.
The (−8) has not been added to the $$x$$ term and the constant term on the LHS.
Q3.
The solution to the equation $$x − 5 = 15$$ is when $$x$$ =
Correct Answer: 20, twenty
Q4.
Which of these shows the correct working to solve the equation $$x + 3.8 = 2.3$$ in one additive step?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q5.
The solution to the equation $$x + 7.2 = 14.6$$ is when $$x$$ =
Correct Answer: 7.4
Q6.
Which of these is the solution to the equation $$x − {2\over 3} = {5\over 6}$$ ?
$$x = {1\over 6}$$
$$x = {3\over 4}$$
$$x = {7\over 9}$$
$$x = 1$$
Correct answer: $$x = {3\over 2}$$