NY Next Generation Math NY-3.MD.8.b

Math3rd GradeGeometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

The Standard

Identify rectangles with the same perimeter and different areas or with the same area and different perimeters.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students compare rectangles to find examples with equal perimeter but different areas and equal area but different perimeters. They calculate both measures and describe what changes.
What Mastery Looks Like: The student shows that 3-by-5 and 2-by-6 rectangles both have perimeter 16 but areas 15 and 12. The student also produces a valid equal-area pair with different perimeters.
Common Misconceptions: Students may assume equal perimeter forces equal area or confuse the formulas for the two measures. They may compare rectangles without verifying both values.
How to Assess It: Ask students to draw two whole-number rectangles with area 24 and different perimeters. Require labeled side lengths, areas, and perimeters.

Lesson moves

Build rectangles with square tiles and yarn borders, then record area and perimeter for each arrangement.
Ask students why rearranging 24 tiles can preserve area while changing perimeter.
Play rectangle-pair hunt for equal perimeter with different area, then equal area with different perimeter.
Compare garden designs that use the same fencing length but enclose different planting areas.

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