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Year 8

Solving simple linear equations with a multiplicative step

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

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New
New
Year 8

Solving simple linear equations with a multiplicative step

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

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. An equation involving an multiplicative step can be represented with a bar model.
  2. Using the bar model you can write all the arrangements of the equation with an multiplicative 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 equations pupils may not use the inverse operation.

Working out should include each step then pupils can check each step using substitution.

Keywords

  • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number.

This is a great chance to consolidate fraction skills, including the use of reciprocals. Pupils should understand the equivalence of multiplication and division by the reciprocal and use these interchangeably to suit the question.
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).

Video

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Starter quiz

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6 Questions

Q1.
Which of these equations can be written from this bar model?
An image in a quiz
$$x − 6.2 = 8.3$$
Correct answer: $$x + 6.2 = 8.3$$
$$x = 8.3 − x$$
Correct answer: $$6.2 = 8.3 − x$$
Correct answer: $$8.3 − 6.2 = x$$
Q2.
The solution to the equation $$x + 3 = 17$$ is when $$x$$ =
Correct Answer: 14, fourteen
Q3.
The solution to the equation $$x − 8.6 = 10$$ is when $$x$$ =
Correct Answer: 18.6
Q4.
Any non-zero number multiplied by its reciprocal is equal to
Correct Answer: 1, one
Q5.
Match each number to its reciprocal.
Correct Answer:$$1\over 5$$,$$5$$

$$5$$

Correct Answer:$$−{1\over 5}$$,$$-5$$

$$-5$$

Correct Answer:$$4\over 5$$,$$5\over 4$$

$$5\over 4$$

Correct Answer:$$−{4\over 5}$$,$$−{5\over 4}$$

$$−{5\over 4}$$

Correct Answer:$$5$$,$${1\over 5}$$

$${1\over 5}$$

Correct Answer:$$−5$$,$$−{1\over 5}$$

$$−{1\over 5}$$

Q6.
Match each calculation to an equivalent calculation.
Correct Answer:$$\times {2\over 7}$$,$$\div {7\over 2}$$

$$\div {7\over 2}$$

Correct Answer:$$\div (-{2\over 7})$$,$$\times( −{7\over 2})$$

$$\times( −{7\over 2})$$

Correct Answer:$$\times (−7)$$,$$\div( −{1\over 7})$$

$$\div( −{1\over 7})$$

Correct Answer:$$\times( −{1\over 7})$$,$$\div( −7)$$

$$\div( −7)$$

Correct Answer:$$\times {1\over 7}$$,$$\div 7$$

$$\div 7$$

Correct Answer:$$\div {1\over 7}$$,$$\times 7$$

$$\times 7$$

Exit quiz

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6 Questions

Q1.
Using this bar model, the solution to the equation $$6x = 30$$ is when $$x= $$
An image in a quiz
Correct Answer: 5, five
Q2.
Using this bar model, the solution to the equation $${1\over 4}x = 8$$ is when $$x=$$
An image in a quiz
Correct Answer: 32
Q3.
The solution to $$3x = 396$$ is when $$x=$$
Correct Answer: 132
Q4.
Which of these show the correct working to isolate one positive $$x$$ for the equation $$0.5x = 3.5$$?
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q5.
The solution to $$-9x = 36$$ is when $$x =$$
Correct Answer: −4, - 4, − 4, -4
Q6.
Which of these is the solution to $${4\over 5} x = 20$$?
4
5
16
Correct answer: 25
28