Cover the inside. Fence the outside.

SparkClass

Build with unit squares. Count every fence segment. What changes?

CCSS 3.MD.C.5–C.7 · 3.MD.D.8
Live Unit Grid
6 × 4 rectangle
A rectangle made from unit tiles and unit fence segments A 6 by 4 rectangle with 24 unit tiles inside and 20 unit fence segments around the outside.
01

6 columns × 4 rows. Count 24 tiles inside and 20 fence segments outside.

Area · Tiles Inside
24square units
A = 6 × 4 = 24
Perimeter · Fence Outside
20units
P = 2 × (6 + 4) = 20

Teacher notes — Area vs Perimeter

Keep the two units visible: square tiles measure coverage, while fence segments measure distance around the boundary.

1

Build before using formulas

Ask students to count tiles and fence segments, then connect the counts to A = w × h and P = 2(w + h). Use 1 × 10 and 10 × 10 to check both the counting and the side-length controls.

2

Hold area constant

In Same Area, only an on-target rectangle can be recorded. Ask for at least two different factor rectangles. Rotations are treated as the same shape. Compare what stayed equal and what changed.

3

Hold perimeter constant

In Same Perimeter, students keep the fence total fixed while changing the area. After each record, ask: “Where did the tiles go?” Revisit the collection before introducing any rule about square-like rectangles.

4

Treat min/max as a conjecture prompt

“Lowest so far” and “highest so far” describe only the saved collection, not a proven global minimum or maximum. Ask students to test whether another rectangle can extend the range and explain their reasoning.

CCSS alignment: 3.MD.C.5 — understand area and unit squares; 3.MD.C.6 — measure area by counting unit squares; 3.MD.C.7 — relate area to multiplication and rectangular tiling; 3.MD.D.8 — solve perimeter problems and investigate rectangles with the same area but different perimeters, or the same perimeter but different areas.