Today’s problem — free all day, every step. Every day has one.
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 using 38 circular tiles of diameter 50 cm, following the pattern shown. Each tile is in contact with those next to it.
- (a) What is the area of the footpath not covered by the tiles? (Take pi = 3.14)
- (b) What is the perimeter of the grass patch?
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MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
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65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Number × value
One batch repeats. Work out one batch, then multiply.
In this one. Each 50 cm square of footpath loses the same corner area to its tile, so part (a) is one small subtraction done once and multiplied by 38 — never one big area minus 38 circles.
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.
Try one like it
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…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.