Today’s problem — free all day, every step. Every day has one.
Marbles — red and blue boxes, matching fractions
of a box of red marbles equals of a box of blue marbles. The box of red marbles contains 30 marbles. How many blue marbles are there?
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27 blue marbles.
The pattern behind it: The equal concept
The question tells you a part of one pile equals a part of another.
In this one. When two fractions of two different wholes are equal, work out the number they both equal from the side you know, then climb back up the other side.
How to spot it
Two different groups each get their own fraction or percentage, and the question links them with 'the same as', 'twice as many as', or a shared cost across different units.
Common mistake
Children compare the two fractions without first relating them to a common whole. A smaller fraction of a larger group can be bigger than a larger fraction of a smaller group.
Try one like it
Standard Files and pens — the cost of 1 pen The total cost of 2 identical files and 1 pen is $19.05. The total cost of 3 such files and 5 such pens is $44.50. Find the cost o…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.