Proportional Reasoning: The Right Words

Mathematics · Ratio & Proportion · ages 11-14

Name ______________________ Date ____________

A car travels 180 miles in 3 hours at a steady speed. What is its speed in mph?
Answer: ______________
Which pair shows direct proportion?
- More pages printed, more ink used at the same rate per page
- More workers on a job, more days to finish
- Faster driving, more time for the trip
- Bigger discount, higher price
Which unit correctly measures a rate of distance over time?
- Kilometres
- Hours
- Kilometres per hour
- Kilometres times hours
Which unit correctly measures speed?
- Miles per hour
- Miles
- Hours per minute
4 kg of apples cost £6. What is the unit rate per kg in £?
Answer: ______________
Zoe says that in direct proportion, tripling one quantity triples the other. Is Zoe right?
Circle one: True False
Which unit correctly measures density?
- Cubic centimetres per gram
- Grams and cubic centimetres added
- Square grams
- Grams per cubic centimetre
Density is calculated by dividing mass by:
- Volume
- Time
- Distance
A recipe needs 2 cups of flour to make 8 cookies. Using direct proportion, how many cups of flour make 24 cookies?
Answer: ______________
Leo says, 'A runner's speed is 10, so she is fast.' What is missing from Leo's statement?
- The distance she ran
- The time she took to finish the race
- The unit, like meters per second

Answer key

For grown-ups. Fold this page away before handing over the rest.

60 · Speed equals distance divided by time: 180 / 3 = 60 mph.
More pages printed, more ink used at the same rate per page · Pages and ink rise together at the same rate: direct proportion.
Kilometres per hour · Speed divides distance by time: kilometres per hour.
Miles per hour · Speed is a quantity measured in a compound unit: distance divided by time, written as miles per hour.
1.5 · 4 kg of apples cost £6, so one kg costs £1.50.
True · Direct proportion scales both sides together: tripling works.
Grams per cubic centimetre · Density divides mass by volume: grams per cubic centimetre.
Volume · Density is mass divided by volume, so more mass packed into the same volume means higher density.
6 · 24 cookies is 3 times as many as 8, so you need 3 times as much flour: 2 × 3 = 6 cups.
The unit, like meters per second · A number alone doesn't tell you speed. You need the unit, like meters per second, to know how fast something is really going.