Reasoning · Grade 3-2 Circles and Counting Shapes
Problem
One centre per circle, so counting centres never double-counts.
Every circle, no matter how it overlaps, owns exactly one center point, so centers are a clean way to tag each circle once.
3.G.A.1Organize Information In More WaysCounting the centres counts the circles, because every circle owns exactly one centre no matter how it overlaps.
A circle is the points sitting one fixed radius from one point, so that point is the circle's own and no other circle's.
One centre marks one circle and one circle carries one centre, so tagging centres counts each circle exactly once.
Split the frame into bands and mark centres band by band.
Splitting the busy picture into a few calm bands makes a swarm of circles into a short, checkable list.
2.G.A.1Make A Systematic ListAdding the bands gives 24.
Adding small, carefully made partial counts is far safer than one big eyeball guess of a tangled picture.
3.NBT.A.2Make A Systematic ListEvery circle, even a half-hidden one, has just one center — so mark the centers and count those, and a messy tangle becomes an easy 24!