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Year 7

Representing a multiplicative relationship

I can use a double number line to represent a multiplicative relationship and connect to other known representations.

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New
New
Year 7

Representing a multiplicative relationship

I can use a double number line to represent a multiplicative relationship and connect to other known representations.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A bar model is a representation of a multiplicative relationship.
  2. A double number line is a representation of a multiplicative relationship.
  3. A straight line graph is a representation of a multiplicative relationship.

Common misconception

Both lines of a double number line must start at zero and these zeros must be aligned.

When drawing double number lines, ensure to align the zeros and the known equivalents. Showing how a graph is formed from a DNL can help.

Keywords

  • Proportionality - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.

  • Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

From one ratio, pupils can create a DNL, a ratio table, bar model and graph. Get pupils to create their own ratio and draw up the matching DNL, ratio table, bar model and graph.
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 the following show this ratio or an equivalent ratio?
An image in a quiz
Correct answer: For every 1 star, there are 3 hearts.
Correct answer: $$\frac{1}{4}$$ are stars
Correct answer: For every 3 star, there are 9 hearts.
For every 3 stars, there is 1 heart.
$$\frac{1}{3}$$ are stars
Q2.
A __________ shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
Correct answer: ratio
additive inverse
postive integer
multiplier
Q3.
Identify the equivalent ratios.
An image in a quiz
a) and b)
a) and c)
a), b) and c)
All are equivalent.
Correct answer: a), b) and d)
Q4.
The table shows the proportion of red to green. Which of these also correctly describe this proportion?
An image in a quiz
Correct answer: For every 2 reds, there are 5 greens.
For every 5 reds, there are 2 greens.
Correct answer: Red(s) $$\times\frac{5}{2}=$$ Green(s)
Red(s) $$\times\frac{2}{5}=$$ Green(s)
Q5.
For every 2 As there are 5 Bs. If there are 35 letters in total, how many Bs are there?
Correct Answer: 25, twenty five, twentyfive, twenty-five
Q6.
For every 12 As there are 4 Bs. If there are 4 letters in total, how many Bs are there?
Correct Answer: 1, one

Exit quiz

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6 Questions

Q1.
Which shows the ratio "For every 2 rabbits (R), there is 1 carrot(C)" ?
An image in a quiz
a)
b)
Correct answer: c)
None of them
Q2.
Select the correct statement for drawing double number lines.
Correct answer: Each line should be parallel.
Correct answer: Chosen interval should be equally spaced.
Each number on each interval increases by 1.
Numbers can be placed anywhere on the line.
Q3.
Using the double number line, identify the correct ratio.
An image in a quiz
For every £1, there are 315₹
For every £315, there is 1₹
For every £2, there are 315₹
Correct answer: For every £3, there are 315₹
Q4.
Here is a double number line. Which of the following are equivalent to this double number line?
An image in a quiz
Correct answer: For every 20 As there are 16 Bs.
Correct answer: For every 10 As there are 8 Bs.
For every 16 As there are 20 Bs.
For every 8 As there are 10 Bs.
Correct answer: For every 5 As there are 4 Bs.
Q5.
Match the graph with the proportion it represents.
An image in a quiz
Correct Answer:a),For every $$x$$, there is 1 $$y$$

For every $$x$$, there is 1 $$y$$

Correct Answer:b),For every 6 $$x$$s, there are 21 $$y$$s

For every 6 $$x$$s, there are 21 $$y$$s

Correct Answer:c),For every 6 $$x$$s, there are 42 $$y$$s

For every 6 $$x$$s, there are 42 $$y$$s

Correct Answer:d),For every 6 $$x$$s, there are 9 $$y$$s

For every 6 $$x$$s, there are 9 $$y$$s

Q6.
Which of the double number lines are equivalent to the graph?
An image in a quiz
a)
b)
c)
d)
Correct answer: None of the double number lines