Today’s problem — free all day, every step. Every day has one.
Average height — a class of 40 pupils
In a class of 40 students, the average height is 142 cm. 15 of the students have an average height of 138 cm. What is the average height of the remaining students?
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The pattern behind it: An average is a total
Turn the average back into a total before doing anything with it.
In this one. An average is a total in disguise — total = average × how many — and totals can be added and subtracted, while averages cannot; so convert every average to a total, do the arithmetic there, and convert back at the end.
How to spot it
The word 'average' appears alongside a group being split into two parts, or two separate journeys or trips being combined into one overall figure.
Common mistake
Children average two averages directly, such as averaging two speeds or two group averages, without weighting by how many, or how long, each part actually covers.
Try one like it
Standard A bakery's week — average daily sales A bakery recorded its sales over 5 days: $42, $48, $55, $51 and $44. What was the average daily sales amount over the 5 days?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.