Solving simple linear equations with a multiplicative step | Maths

Starter quiz

Which of these equations can be written from this bar model?
- $x − 6.2 = 8.3$
- $x + 6.2 = 8.3$ ✓
- $x = 8.3 − x$
- $6.2 = 8.3 − x$ ✓
- $8.3 − 6.2 = x$ ✓
The solution to the equation $x + 3 = 17$ is when $x$ = ______
- '14' ✓
The solution to the equation $x − 8.6 = 10$ is when $x$ = ______
- '18.6' ✓
Any non-zero number multiplied by its reciprocal is equal to ______
- '1' ✓
Match each number to its reciprocal.
- $1\over 5$
  
  ⇔
  
  $5$ ✓
- $−{1\over 5}$
  
  ⇔
  
  $-5$ ✓
- $4\over 5$
  
  ⇔
  
  $5\over 4$ ✓
- $−{4\over 5}$
  
  ⇔
  
  $−{5\over 4}$ ✓
- $5$
  
  ⇔
  
  ${1\over 5}$ ✓
- $−5$
  
  ⇔
  
  $−{1\over 5}$ ✓
Match each calculation to an equivalent calculation.
- $\times {2\over 7}$
  
  ⇔
  
  $\div {7\over 2}$ ✓
- $\div (-{2\over 7})$
  
  ⇔
  
  $\times( −{7\over 2})$ ✓
- $\times (−7)$
  
  ⇔
  
  $\div( −{1\over 7})$ ✓
- $\times( −{1\over 7})$
  
  ⇔
  
  $\div( −7)$ ✓
- $\times {1\over 7}$
  
  ⇔
  
  $\div 7$ ✓
- $\div {1\over 7}$
  
  ⇔
  
  $\times 7$ ✓

Using this bar model, the solution to the equation $6x = 30$ is when $x=$ ______
- '5' ✓
$Using this bar model, the solution to the equation <Math>{1\over 4}x = 8</Math> is when <Math>x=</Math> <span class="blank">______</span>$

Using this bar model, the solution to the equation ${1\over 4}x = 8$ is when $x=$ ______
- '32' ✓
The solution to $3x = 396$ is when $x=$ ______
- '132' ✓
Which of these show the correct working to isolate one positive $x$ for the equation $0.5x = 3.5$ ?
The solution to $-9x = 36$ is when $x =$ ______
- '−4' ✓
Which of these is the solution to ${4\over 5} x = 20$ ?
- 4
- 5
- 16
- 25 ✓
- 28

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

When solving equations pupils may not use the inverse operation.

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

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