Question P6 Repeated identity
Today’s problem — free all day, every step. Every day has one.
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.
Answer
See all 10 steps
MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
I have a code → See a free one like it
65 worked examples are free without a code, two from every pattern. No account, either way.
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.
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.
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Worked examples of all 33 patterns and skills, in a booklet you can print.