Perimeter by Tracing Every Side
The perimeter of a composite or overlapped figure is found by following its boundary and summing each side, using rectangle/square side equalities and overlap relations to recover unknown segments. Learners trace joined rectangles, ribbons around boxes, and overlapped polygons, later with fractional and decimal side lengths. The discipline is accounting for every boundary segment exactly once.
grade 2–4 GeometryMeasurement & dataBase-ten numbersFractionsOperations Draw a DiagramIdentify Subproblems
Progression (11)
g3 1. Ribbon around a box: four equal parts Measurement & data
g4 2. Find a side from equal perimeters Measurement & dataOperations
g4 3. Side lengths from overlapping rectangles Measurement & dataOperations
g4 4. Perimeter plus tiles needed to build it Measurement & dataOperations
g4 5. Perimeter by tracing every side Measurement & data
g3 6. Find perimeter path length by multiplication Measurement & dataOperations
g3 7. Perimeter as side length times side count Measurement & dataOperations
g4 8. Find a missing side, then sum sides as fractions FractionsMeasurement & data
g5 9. Perimeter as decimal side sums minus overlaps Base-ten numbersMeasurement & data
g4 10. Perimeter of overlapped squares and rectangles Measurement & dataGeometry
g4 11. Distance between parallel sides equals the side length GeometryMeasurement & data
Bridges to competition (1)
Reasoning problems that extend this idea toward competition:
Perimeter of a figure built from squares Invariant