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A tray of ice blocks — large and small
A caterer packs a rectangular tray-box tightly with 12 identical large ice blocks and some identical small ice cubes, so that cubes of the same size are stacked directly on top of each other, filling the box exactly to the brim. The figure shows the first layer of cubes packed in the box.
- (a) How many small ice cubes does the caterer have?
- (b) The volume of the box is 1536 cm³. The total volume of the 12 large ice blocks is of the volume of the box. What is the length of one edge of the small ice cube?
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The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. The picture gives no lengths at all, but two large cubes and four small ones fill the same depth — that pins L : s = 2 : 1, and once the two cubes are tied together the whole box can be counted in cube-layers long before any measurement appears.
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
Standard Water — poured into a second container A rectangular tank measures 30 cm by 20 cm by 25 cm. It is 3/5 full of water. All the water is poured into a second rectangular co…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.
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