Primary 5 Rate Study Guide
Primary 5 rate in four short steps: the amount for one unit, then using that rate to find a total or a number of units, reading a rate off a graph, and working out tiered charges. Each step has something to tap, with worked examples and a five-question check at the end.
Start here
What is a rate in maths?
A rate is an amount for each one of something.
Dollars for each bottle, litres for each minute, posters for each minute: each is a rate. To find one, share the total equally over the ones, so each one gets the same amount. Your child names the one first, because the one decides the rate. Then the rate does the rest of the work in this chapter.
In this chapter, your child learns to:
- find a rate by dividing a total by the number of units;
- multiply a rate to find a total, or divide by it to find how many units;
- read a rate off each part of a line graph, including when a second tap opens;
- work out charges where the first block costs a different amount.
Step 1
Finding the rate per unit
Divide the total by the number of ones. Cut the total into as many equal units as there are ones, and one unit is the rate. Write the rate with its one after "per": $1.50 per bottle, 4 ml per second. When the question names a different one, such as seconds when the time is given in minutes, change the time to that unit before dividing.
Tap Next step
A hose sprays 600 ml of water in 2 minutes. How much water does it spray each second?
Step 2
Finding the total amount or the number of units
First find the rate, then multiply or divide by it. A rate question has three quantities: the rate, the total amount and the number of units. When two are known, the third follows. The rate times the number of units is the total. The total divided by the rate is the number of units. Write the rate on its own line before using it.
Tap Next step
A machine fills 48 cans in 4 minutes. At the same rate, how many cans does it fill in 7 minutes?
Step 3
Reading a rate from a line graph
Read each stretch of the line on its own. A line graph of volume against time shows how much water is in a tank. On each straight stretch, find the litres added and the minutes taken, then divide. A steeper line means a faster rate. A flat line means no water goes in. When a second tap opens, the first tap keeps pouring, so the second tap's rate is the new rate minus the first.
Tap Next step
An empty tank is filled. Tap A runs on its own first. Then Tap B is turned on too, and both run until the tank is full. How many litres does Tap B add each minute?
Tap A fills a tank with 40 L in 5 minutes. Then Tap B is also turned on, and the water rises by 14 L each minute. How much water does Tap B add each minute?
Step 4
Working out parking charges from a rate table
Cut off the first block, then count the rest in blocks. A charges table can use one price for the first block and another for every block after it. Subtract the first block from the time, and charge it on its own. Cut the rest into blocks. When the table says "or part of one", a block that is only partly used is charged in full. Then add the two charges.
Tap Next step
| Parking time | Charge |
|---|---|
| First hour | $2.00 |
| Every further half hour or part of one | $0.80 |
Mrs Rahman parks her car for 2 h 50 min. How much does she pay?
A car park charges $1.20 for the first hour and $0.50 for every further half hour or part of one. Ben's father parks for 1 h 40 min. How much does he pay?
Primary 5 rate questions, worked step by stepWork each one out on paper first. Open the hint if you are stuck, then reveal the working a line at a time.
A pack of 8 pencils costs $3.60. What is the cost of 1 pencil?
- 8 pencils cost $3.60
- 1 pencil costs $3.60 ÷ 8 = $0.45
A machine packs 75 boxes in 5 minutes. At the same rate, how long will it take to pack 420 boxes?
- rate: 75 ÷ 5 = 15 boxes per minute
- number of minutes = 420 ÷ 15 = 28
A pump drains 3.6 L of water in 2 minutes. How many millilitres of water does it drain each second?
- 3.6 L = 3.6 × 1000 = 3600 ml
- 2 minutes = 2 × 60 = 120 seconds
- in 1 second: 3600 ÷ 120 = 30 ml
Tap P fills an empty tank on its own for 6 minutes and puts in 54 L. Tap Q is then turned on as well, and both taps run for 5 more minutes. The tank then holds 129 L. How much water does Tap Q put in each minute?
- Tap P in 1 minute = 54 ÷ 6 = 9 L
- water in the second stretch = 129 − 54 = 75 L
- both taps in 1 minute = 75 ÷ 5 = 15 L
- Tap Q in 1 minute = 15 − 9 = 6 L
A car park charges $1.80 for the first 2 hours and $0.70 for every further half hour or part of one. Mrs Koh parks from 9.15 a.m. to 1.05 p.m. How much does she pay?
- time parked: 9.15 a.m. to 1.05 p.m. = 3 h 50 min
- after the first 2 hours: 3 h 50 min − 2 h = 1 h 50 min = 110 min
- 110 ÷ 30 = 3 remainder 20, so 4 half hours are charged
- 4 × $0.70 = $2.80
- total = $1.80 + $2.80 = $4.60
Step 5
Check yourself
Five quick rate questions, one or two per step. Nothing is recorded, and each answer suggests the practice to try next.
1. 6 kg of rice cost $15. What is the cost per kilogram?
2. A pump moves 900 ml of water in 3 minutes. How many millilitres does it move each second?
3. A printer prints 16 pages per minute. How many minutes does it take to print 208 pages?
4. On a line graph, the water in a tank goes from 40 L at 2 minutes to 100 L at 6 minutes. What is the rate on that stretch?
5. A phone call costs $0.60 for the first 3 minutes and $0.15 for every further minute or part of one. How much does a call of 7 min 20 s cost?
Using this guide at home. Before any dividing, ask your child "for each what?" and let them say the one aloud: each bottle, each minute, each second. Writing the rate on a line by itself, with its unit, makes the next line easy to choose. When the time is in minutes and the question asks about seconds, the time changes first.
On graphs, cover all but one stretch of the line with a strip of paper so your child reads one stretch at a time. With charges tables, ask your child to sketch the stay as a strip, cut off the first block, and mark the last part block. A quick size check helps: a faster rate always gives a steeper line.
More study guides
P5 Rate lessons and practice
4 lesson videos and 38 questions across four subtopics, from Basic to Challenge, each with a worked solution.
Watch and practise →