Reasoning · Grade 4-2 Counting Large and Small Figures
Problem
Each quadrilateral is two top-to-bottom lines.
Instead of looking for shapes you can see, you look for the two 'walls' that make each shape — and walls are much easier to keep track of than shapes.
4.G.A.1Draw A DiagramEvery quadrilateral in the strip is decided by which two of the slanting lines make its left and right walls.
The strip supplies the top and bottom sides for free, so a pair of walls names one quadrilateral and one quadrilateral has one pair of walls.
Counting shapes therefore becomes counting how many ways two lines can be chosen, which needs no drawing at all.
All the pairs give 36 quadrilaterals.
This is the same handshake-style count used for 'how many pairs' — list each line once and only count the partners to its right so nothing gets counted twice.
4.OA.A.3Make A Systematic ListBoth walls vertical gives 10 rectangles.
Choosing two of the five vertical lines is exactly the same pair-counting as before, just with a smaller set to choose from.
4.G.A.2Make A Systematic ListOf those, 3 are rhombuses.
A square has four equal sides, so it belongs in the rhombus list too — the categories overlap on purpose, and forgetting the squares is the classic slip here.
5.G.B.3Make A Systematic ListParallel walls give 12 parallelograms.
Every rectangle is also a parallelogram, so the 10 rectangles are all inside this count already; only the two genuinely slanted ones are new.
4.G.A.2Make A Systematic ListSubtracting leaves 24 trapezoids.
Counting what is left over is much safer than tracking down 24 lopsided shapes one at a time, and it uses the totals already worked out.
5.G.B.4Change Focus Count The ComplementCount the pairs of lines that make the shapes, not the shapes themselves — and remember a square answers to three names at once.