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Year 7

Expressing multiplicative relationships as ratios and fractions

I can express a multiplicative relationship as a ratio or as a fraction.

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Share activities with pupils
New
New
Year 7

Expressing multiplicative relationships as ratios and fractions

I can express a multiplicative relationship as a ratio or as a fraction.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. By expressing the multiplicative relationship as a ratio, it can be easier to scale further.
  2. The relationship can be represented using a bar model.
  3. A bar model shows both parts of the ratio as well as the whole.
  4. A multiplicative relationship can be expressed as a fraction.
  5. There are many different ways to express the relationship.

Common misconception

Pupils see the bar model and/or fraction as the whole as opposed to the proportion of the whole.

Emphasise equivalent fractions and equivalent bar models which show different parts to whole, but are the same proportion. e.g 3/5 = 60/100

Keywords

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

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

  • Fraction - shows us how many equal parts in a whole.

Using MWB, get pupils to represent the ratio of 2 circles to 1 square in as many different ways. Asking: what are the total shapes, how many circles and/or squares do you have? Emphasising the proportion is the same but totals are different.
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.
If two things are proportional then the ratio of part to whole is maintained and the __________ relationship between parts is also maintained.
subtractive
additive
Correct answer: multiplicative
inverse
opposite
Q2.
The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Pizza sauce $$\times$$ = Puree.
An image in a quiz
Correct Answer: 120
Q3.
The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Garlic $$\times$$ = Puree.
An image in a quiz
Correct Answer: 30, thirty
Q4.
A bowl of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 15 apples in the bowl. There are bananas in the bowl.
Correct Answer: 25, twenty five, twentyfive, twenty-five
Q5.
A box of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 80 pieces of fruit in total. How many bananas are there? bananas.
Correct Answer: 50, fifty
Q6.
Which are equivalent ratios to: "For every 3 circles there are 5 squares."
"For every 9 circles there are 14 squares."
Correct answer: "For every 9 circles there are 15 squares."
Correct answer: "For every 36 circles there are 60 squares."
Correct answer: "For every 1.5 circles there are 2.5 squares."
"For every 1 circle there are 1.5 squares."

Exit quiz

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6 Questions

Q1.
Which are equivalent to this ratio?
An image in a quiz
Correct answer: For every 1 t-shirt, there is 1 pair of shorts.
For every 1 t-shirt, there are 2 pairs of shorts.
Correct answer: Number of pairs of shorts × 1 = Number of t-shirts
Number of pairs of shorts × 0.5 = Number of t-shirts
Q2.
Which are equivalent to this ratio?
An image in a quiz
Correct answer: For every cat, there are 4 mice.
For every 2 cats, there are 9 mice.
Correct answer: For every 2 cats, there are 8 mice.
Correct answer: Number of cats × 4 = Number of mice
Number of cats × 5 = Number of mice
Q3.
Which are equivalent to this ratio?
An image in a quiz
For every 4 phones, there are 3 houses.
Correct answer: For every 4 houses, there are 3 phones.
Correct answer: Number of houses $$\times \frac{3}{4}=$$ Number of phones
Number of phones $$\times \frac{3}{4}=$$ Number of houses
Correct answer: Number of phones $$\times \frac{4}{3}=$$ Number of houses
Q4.
A quantity is divided into two parts: A and B. Match each ratio with the correct fraction.
Correct Answer:For every 2 As, there are 3 Bs,Fraction of A is $$\frac{2}{5}$$

Fraction of A is $$\frac{2}{5}$$

Correct Answer:For every 2 As, there are 5 Bs,Fraction of A is $$\frac{2}{7}$$

Fraction of A is $$\frac{2}{7}$$

Correct Answer:For every 2 As, there are 2 Bs,Fraction of A is $$\frac{1}{2}$$

Fraction of A is $$\frac{1}{2}$$

Correct Answer:For every 1 As, there are 2 Bs,Fraction of A is $$\frac{1}{3}$$

Fraction of A is $$\frac{1}{3}$$

Q5.
A quantity is divided into two parts: A and B. Match each ratio with the correct formula.
Correct Answer:For every 2 As, there are 3 Bs.,A $$\times\frac{3}{2} $$ = B

A $$\times\frac{3}{2} $$ = B

Correct Answer:For every 2 As, there are 5 Bs.,A $$\times\frac{5}{2}$$ = B

A $$\times\frac{5}{2}$$ = B

Correct Answer:For every 2 As, there are 2 Bs.,A $$\times1 $$ = B

A $$\times1 $$ = B

Correct Answer:For every 1 As, there are 2 Bs.,A $$\times2$$ = B

A $$\times2$$ = B

Q6.
A quantity is divided into two parts: A and B. Match each fraction with the correct formula to find B.
Correct Answer:A is $$\frac{2}{3}$$,A $$\times\frac{1}{2} $$ = B

A $$\times\frac{1}{2} $$ = B

Correct Answer:A is $$\frac{3}{5}$$,A $$\times\frac{2}{3} $$ = B

A $$\times\frac{2}{3} $$ = B

Correct Answer:A is $$\frac{4}{7}$$,A $$\times\frac{3}{4} $$ = B

A $$\times\frac{3}{4} $$ = B

Correct Answer:A is $$\frac{1}{3}$$,A $$\times 2 $$ = B

A $$\times 2 $$ = B