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Priya and Wei Jie's beads — glass and plastic
Priya and Wei Jie make bracelets, and each of them has the same total number of beads in his or her box: 200 beads, made up only of glass beads and plastic beads. Priya has 25 more glass beads than Wei Jie. Wei Jie has 60 glass beads in his box. Each glass bead costs $0.90 and each plastic bead costs $0.15. Each glass bead weighs 5 g and each plastic bead weighs 1 g.
- (a) Whose beads are worth more in total, and by how much?
- (b) What is the total weight of Wei Jie's beads, in kilograms?
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The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. When two equal totals contain only two types, 25 extra glass beads on one side must replace 25 plastic beads, so all matching beads cancel and only that swap affects the value difference.
How to spot it
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Common mistake
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Try one like it
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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.
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