Systematically Count Shapes in a Figure
Small pieces combine into larger ones, so counting all triangles, quadrilaterals, segments, or vertices in a composite figure requires an organized sweep by size or type to avoid missing or double-counting. Learners count hidden shapes in grids and composites and tally dots, lines, and faces. The discipline is exhaustive, non-overlapping enumeration.
grade 3–4 GeometryOperations Make a Systematic ListDraw a Diagram
Progression (5)
g3 1. Count all shapes hidden in a grid GeometryOperations
g4 2. Count segments between points on a line GeometryOperations
g4 3. Express counts of dots, lines, faces Operations
g4 4. Systematically count all triangles in a composite Geometry
g4 5. Count all the rhombuses in a figure of small triangles Geometry
Bridges to competition (14)
Reasoning problems that extend this idea toward competition:
Counting non-square rectangles Shape enumeration
Counting right triangles in a figure Shape enumeration
Counting squares in a figure Shape enumeration
Counting right triangles on a dot grid Shape enumeration
Counting segments, lines, and rays Counting
Counting squares including tilted ones Shape enumeration
Count circles in an overlapping figure Shape enumeration
Overlap shapes and count figures Shape enumeration
Count all large and small shapes Shape enumeration
Draw lines to hit a target shape count Shape enumeration
Trace target shapes along straight lines Shape enumeration
Count segments joining points on a loop Counting
Count shapes from points on open lines Shape enumeration
Count all shapes on a dot grid Shape enumeration