The pattern
Number × value
One batch repeats. Work out one batch, then multiply.
A batch keeps repeating, four chips with two cookies, or one tile with its patch of footpath, and every batch is worth the same. Work out what one batch costs or covers, then multiply by how many batches there are. One batch stands for all of them, which is what makes the multiplication safe.
How to spot it
Items are described as a fixed group or ratio that repeats, such as tiles following a pattern, snacks sold in a fixed mix, or a rate given per hour or per item.
Common mistake
Children start from the grand total instead of first working out what one batch is worth. In rate questions they also confuse a duration with a clock time.
17 worked solutions
Standard
- Buns and muffins — 3 : 5 worth $55 A bakery sells buns and muffins in the ratio of 3 buns to 5 muffins. Each bun costs $2, and each muffin costs $1. If the total val…
- Chickens and ducks — 3 : 2 worth $180 A farm keeps chickens and ducks in the ratio of 3 chickens to 2 ducks. Each chicken is worth $6, and each duck is worth $9. If the…
- Flags for a parade — reels of string A scout troop is preparing 320 flags for a parade. Each flag needs 45 cm of string to tie it to a pole. String is sold in reels of…
- Mr Lee's drive — Town A to Town B Town A and Town B are 240 km apart. Mr Lee drives from A to B at 60 km/h. At what time will he arrive if he departs at 9:30 am?
- Pencils and erasers — 5 : 3 worth $27.50 A stationery shop sells pencils and erasers in the ratio of 5 pencils to 3 erasers. Each pencil costs $0.50, and each eraser costs…
- Ribbon length Jess needs 200 ribbons, each 110 cm long. Ribbon is sold in tapes of 25 m (2500 cm). How many tapes does she need?
- Shelf brackets — a carpenter buys webbing tape A carpenter is making straps for 140 shelf brackets. Each strap needs 65 cm of webbing tape. The tape is sold in rolls of 15 m. Ho…
- Siti cycles to the beach — arrival time Siti cycles from her house to the beach, a distance of 45 km, at a steady speed of 15 km/h. If she sets off at 7:15 am, at what ti…
- The express train — arrival time An express train travels from Central Station to Hillview Station, a distance of 360 km, at a constant speed of 90 km/h. If the tr…
- The ferry to Coral Island — arrival time A ferry sails from Jetty Town to Coral Island, a distance of 84 km, at a speed of 24 km/h. If it leaves at 8:50 am, at what time w…
- Two pipes — filling a tank together Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 4 hours. Both pipes are turned on at the same time. How long w…
- Two workers — finishing a job together Worker A can complete a job in 5 days. Worker B can complete the same job in 10 days. They work together for 2 days, then Worker A…
- Vending machine — chips and cookies A vending machine dispenses snacks in the ratio of 4 chips to 2 cookies. Each chip costs $1, and each cookie costs $2. If the tota…
Challenging
- Bakery countertop — coasters around the display case The figure shows a rectangular display case and an L-shaped countertop border around it in a bakery. The width of the border is 40…
- Footpath — circular tiles The figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 100 cm. The footpath is tiled us…
- PSLE 2024 — Jamie oliver egg tarts Jamie and Oliver used $61.20 each to buy some egg tarts. Jamie has a 15% discount coupon and bought 6 more egg tarts than Oliver. …
Very challenging
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.