Maryland Math 3.GR.C.9
The Standard
Solve problems in contexts involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and finding rectangles with the same perimeter and different areas or with the same area and different perimeters.
Maryland College and Career Ready Standards for Mathematics (2025) · UNDERSTAND CONCEPTS OF AREA AND PERIMETER.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students add side lengths to find the distance around a polygon. They use a known perimeter to find a missing side. They draw rectangles to see how perimeter and area can change separately.
What Mastery Looks Like
- A student adds every side, including any unlabeled sides they can work out. If a rectangle has sides of 3 cm, 5 cm, 3 cm, and an unknown length, with a perimeter of 16 cm, they find the missing side is 5 cm. They can draw two rectangles with the same area but different perimeters, and check both measurements.
Common Misconceptions
- Some students count the squares inside a shape instead of adding its outside edges. Others skip a side or add the known sides to the perimeter when finding a missing length. They may think rectangles with the same area always have the same perimeter.
How to Assess It
- Exit ticket: A rectangle is 4 cm wide and has a perimeter of 18 cm. Find its length, then draw a rectangle with the same perimeter but a different area, and label both areas.
Lesson moves
Ways to Teach It
Give pairs square tiles to build 2-by-6 and 3-by-5 rectangles, then trace each outline and count its perimeter.
Ask students to explain why 2-by-6 and 3-by-4 rectangles cover the same area but have different perimeters.
Play missing-side match with polygon cards showing side lengths and a total perimeter, plus cards showing possible missing lengths.
Plan a garden using 20 feet of fencing; sketch two rectangular layouts and compare their planting areas.
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Printable 3.GR.C.9 Worksheet
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Related Standards
- 7.GR.B.4
Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensional objects.
- 7.GR.B.4.a
Solve problems involving area, surface area, and volume of polygonal figures and polyhedral solids, including triangles, quadrilaterals, other polygons, cubes, ...
- 6.GR.A.1
Find the area of triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and quadrilaterals to solve problems.
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