P3–P4–P5–P6 Overlap and cancel
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Paper flags — two strings, one courtyard
Two strings of identical paper flags are hung across a courtyard, each string tied from the same starting wall to the same opposite wall, so both strings cover exactly the same distance. The first string is made of 7 identical flags placed edge to edge with no gaps. The second string is made of 5 of the same identical flags placed edge to edge, plus a plain ribbon 48 cm long added on to reach the opposite wall. Find the length of one flag.
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The pattern behind it: Overlap and cancel
Two shapes share a region, and the shared part cancels out.
In this one. When two totals are equal and share a common part, you may take that part off both sides — what is left is still equal, and now it is an equation in the unknown alone.
How to spot it
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.
Common mistake
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.
Try one like it
Challenging Toy train tracks — matching carriages to a connector 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…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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