Virginia SOL 8.MG.5.c
The Standard
Apply perimeter, circumference, and area formulas to solve contextual problems involving composite plane figures.
Virginia Standards of Learning for Mathematics · The student will solve area and perimeter problems involving composite plane figures, including those in context.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students break irregular figures into rectangles, triangles, circles, or parts of circles. They apply area, perimeter, and circumference formulas to solve real situations and report suitable units.
What Mastery Looks Like
- Students split a composite figure into familiar shapes and choose the correct formulas. They find missing measures, include only outside edges for perimeter, and label answers with correct units.
Common Misconceptions
- Students may add internal segment lengths when finding perimeter or omit curved edges. They may confuse radius with diameter, use perimeter formulas for area, or add unlike units.
How to Assess It
- Give students a rectangle with a semicircle attached: rectangle 10 cm by 6 cm, semicircle diameter 6 cm. Ask for total area and outside perimeter.
Lesson moves
Ways to Teach It
Cut paper rectangles, triangles, and circles, combine them into one figure, then calculate its area and outside perimeter.
Show two solution methods for the same composite figure and ask students to explain why both produce the same area.
Play Formula Match, pairing composite figure cards with decomposition sketches, needed formulas, and correctly labeled answers.
Plan flooring and border trim for an L-shaped room, using a scale drawing to calculate square feet and linear feet.
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Related Standards
- 5.MG.2.g
Solve contextual problems that involve perimeter, area, and volume in standard units of measure.
- 4.MG.3.f
Solve contextual problems involving area and perimeter of rectangles and squares.
- 6.MG.2.b
Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.
- 8.MG.5
The student will solve area and perimeter problems involving composite plane figures, including those in context.
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