Checking and securing understanding of real world ratios | Maths

Starter quiz

There are only red and green sweets in a bag. If the ratio of red to green is 4 : 7, what fraction of the sweets in the bag are red?

$\frac{4}{11}$ ✓

$\frac{4}{7}$

$\frac{7}{4}$

$\frac{11}{4}$
There are only cars or bikes in a car park. If 40% are bikes, what is the ratio of cars : bikes?

3 : 2 ✓

40 : 100

100 : 40

2 : 3
There are only red, yellow and green marbles in a bag. $\frac{1}{3}$ are red, $\frac{2}{5}$ are yellow, write the ratio of red to yellow to green marbles.

'5 : 6 : 4' ✓
A bag of sweets contains red, yellow and green sweets. There are 250 sweets in the bag. 30% of them are red. The rest are yellow and green in the ratio 3 : 4. How many green sweets are there?

'100' ✓
Laura and Sofia share some money in the ratio 2 : 7. Laura gives $\frac{3}{8}$ of her money to Jacob. If Jacob gets £33, how much does Sofia get?

'£308' ✓
Jacob, Andeep and Lucas receive some money. Jacob gets $\frac{2}{7}$ of the money. Andeep and Lucas share the rest in the ratio 4 : 7. What proportion of the prize money does Andeep get?

$\frac{5}{7}$

$\frac{4}{11}$

$\frac{20}{77}$ ✓

$\frac{8}{77}$

Exit quiz

Select the units of measure that are metric.

inches

centimetre ✓

millilitres ✓

miles

grams ✓
A recipe for a stir-fry uses 30 ml of soy sauce. The recipe is for 4 people. How many millilitres of soy sauce would you need to make the recipe for 12 people?

'90' ✓
A recipe for a stir-fry uses 36 ml of soy sauce. The recipe is for 6 people. How many millilitres of soy sauce would you need to make the recipe for 10 people?

'60' ✓
A recipe for soup for 8 people uses 200 g of carrots. Andeep is making the soup for more people and has correctly scaled the recipe. He is using 375 g of carrots. How many people will this serve?

'15' ✓
A scale on a map is 1 : 250 000. How long would something that measured 3 cm on the map be in real life?

7.5 km ✓

7.5 cm

750 000 m

750 000 km
A scale on a map is 1 : 50 000. How long would something that is 4 km in real life measure on the map?

8 cm ✓

200 000 cm

2 m

0.08 cm

8 km

Worksheet

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Lesson Details

Key learning points

Bar models, ratio tables and double number lines can help with ratios.
Real-life scaling involves writing a ratio involving the parts which are dependent on each other.
A recipe is an example as to scale the recipe up or down requires keeping the proportions of the ingredients the same.

Common misconception

Not converting the units correctly in a question or forgetting to have the same units before simplifying a ratio

help pupils to set out ratio tables where they include the units and work through step by step to convert correctly before simplifying. The ratio table can help organise this working.

Keywords

Proportion - A part to whole (sometimes part to part) comparison. If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.