Question P3–P4–P5–P6 Overlap and cancel
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A toy train is timed along two straight display tracks that both start at the same post and end at the same finishing post, so the two tracks are exactly the same length. The first track is made of 8 identical toy carriages joined end to end with no gaps. The second track is made of 5 of the same identical carriages joined end to end, plus a straight connector piece 63 cm long to reach the finishing post. Find the length of one carriage.
Answer
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Two shapes share a region, and the shared part cancels out.
In this one. When two equal totals share the same 5 carriages, cancel that common part; the 3 carriages left must equal the 63 cm connector left.
Shapes are joined, stacked, or have a piece cut off, and the question compares a perimeter or length before and after, rather than asking for an area from scratch.
Children assume perimeter changes the same way area does. Joining shapes or cutting off a corner can leave the perimeter unchanged, or change it by a different amount from the area.
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