The pattern
Suppose and swap
Suppose everything is one kind, then swap one at a time until the total is right.
Suppose every animal is the same kind, work out the total that gives, and compare it with the real one. The shortfall is closed one swap at a time, chickens becoming cows, and each swap moves the total by the same fixed amount. Divide the shortfall by that amount to get the number of swaps.
How to spot it
Two kinds of thing are mixed together with a known total count and a known total of something else, such as legs or sweets, and neither kind's count is given on its own.
Common mistake
Children lose track of whether a swap adds to the total or takes away from it. Compare the starting total with the target first, then swap in the direction that closes the gap.
13 worked solutions
Standard
- Bicycles and tricycles — 58 wheels A cycling club has 25 vehicles parked outside, a mix of bicycles and tricycles. Bicycles have 2 wheels and tricycles have 3 wheels…
- Car park — cars and motorcycles, counting wheels A car park has 14 vehicles, only cars and motorcycles. Each car has 4 wheels and each motorcycle has 2 wheels. In total there are …
- Chickens and cows — 32 legs On a small farm there are 10 animals, a mix of chickens and cows. Each chicken has 2 legs and each cow has 4 legs. Together the an…
- Farm animals — chickens and cows A farmer has chickens and cows. There are 30 animals in total, with 96 legs altogether. How many chickens are there?
- Market stall baskets — small and large, loaves of bread A bakery packs 15 baskets of bread for a market stall. Each small basket holds 3 loaves and each large basket holds 5 loaves. Alto…
- Mrs Lim's stamps — 50-cent and 80-cent Mrs Lim buys 24 stamps at the post office, a mix of 50-cent stamps and 80-cent stamps. In total she pays $15.60. How many 80-cent …
- Spiders and beetles — 138 legs At a bug museum exhibit, there are 20 creatures on display, a mix of spiders and beetles. Spiders have 8 legs and beetles have 6 l…
- Sweets for twelve students — how many boys There are 12 students. Each girl gets 4 sweets, each boy gets 2 sweets. The total number of sweets distributed is 32. How many boy…
Challenging
- Baskets of fruit — adult and baby monkeys A zookeeper has 44 baskets of fruit for a troop of 58 monkeys, made up of adult monkeys and baby monkeys. Each adult monkey eats 2…
- Bowls of soup — teachers and students At a school lunch, there are 84 bowls of soup for 61 people made up of teachers and students. Each teacher eats 3 bowls of soup, a…
- Fried noodles — 80 people sharing 85 plates There are 85 plates of fried noodles for 80 people. Each adult eats 2 plates and every 3 children share 1 plate. How many adults a…
- Water bottles on a hike — adults and children On a hiking trip, there are 70 bottles of water for 65 hikers, made up of adults and children. Each adult drinks 3 bottles of wate…
- Wei Yang's money box — 20c and 50c coins Wei Yang started a savings plan by putting 2 coins in a money box every day. Each coin was either a 20c or 50c coin. His mother al…
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.