3.MD.6: Measuring Area by Counting Unit Squares

Challenge Worksheet
I can measure areas by counting unit squares.

Problem 1

Design three different rectangles that all have an area of 36 square units. Compare their perimeters.

Problem 2

Explain why a 4×6 rectangle and a 3×8 rectangle have different areas even though 4+6 = 3+8.

Problem 3

Create a complex shape using exactly 20 unit squares. Calculate its area and explain your design.

Problem 4

Investigate: If you double the length and width of a rectangle, how does the area change?

Problem 5

A farmer wants to fence a rectangular garden with 28 square units of area. What dimensions minimize fencing?

Problem 6

Compare these methods for finding area: counting squares vs. using length × width. When is each better?

Problem 7

Design a floor plan for a room using unit squares. The room must have exactly 48 square units of area.

Problem 8

Analyze this pattern: 1×1=1, 2×2=4, 3×3=9, 4×4=16. Predict the next three terms and explain.

Problem 9

Create a word problem involving area measurement that requires counting unit squares to solve.

Problem 10

Explain how understanding area by counting unit squares helps in real-world situations. Give examples.