The pattern

Area and volume foundations

Choose the matching base and perpendicular height, or count equal cube layers before multiplying dimensions.

Grid dots turn a fiddly geometry proof into counting. If two lines move the same number of squares across and up for every step, they run in the same direction, so they are parallel; parallel lines sitting the same distance apart give two shapes equal height. Once the heights match, a triangle's area is half its base times that height, and a trapezium's area comes from the same base-and-height reading, no protractor needed.

How to spot it

Look for shapes drawn on a dotted or squared grid, sharing a side or a vertex, with names like ABCD and ABE. Words like "grid", "dots" or "squares" alongside a request to compare areas or heights are the giveaway.

Common mistake

Children measure height by eye along the slanted side of a shape instead of counting the straight up-down grid distance from the base to the opposite vertex, which gives the wrong height whenever a side leans.

19 worked solutions

Standard

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.