The pattern
Rate as an amount per unit
Say both units aloud, then connect amount, rate and number of units.
A rate is an amount for one of something: a price for one ticket, a distance covered in one hour. When the rate is known, multiply it by the number of tickets or hours to find the total. When the total and the number of tickets or hours are known instead, divide the total by that count to find the rate itself, the amount for one alone.
How to spot it
The word 'each' or 'per' next to a ticket, item, or hour marks this. The question asks for a total, or asks for the rate itself.
Common mistake
Children multiply when they should divide, especially when the question gives the total and the number of hours and asks for the rate per hour rather than a bigger total.
8 worked solutions
Standard
- Find a rate A vehicle travels 350 km in 5 hours. Find its rate in kilometres per hour.
- Find a rate A vehicle travels 180 km in 3 hours. Find its rate in kilometres per hour.
- Find an amount from a rate Tickets cost $8 each. Find the cost of 15 tickets.
- Find an amount from a rate Tickets cost $12 each. Find the cost of 18 tickets.
- Find units from an amount and rate Ribbon costs $4 per metre. How many metres can be bought for $36?
- Find units from an amount and rate Ribbon costs $12 per metre. How many metres can be bought for $180?
- Rate — 45 pages per minute A printer makes 45 pages per minute. Explain what this rate means.
- Rate — 75 pages per minute A printer makes 75 pages per minute. Explain what this rate means.
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.