Virginia SOL 8.MG.5.a
The Standard
Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles. Determine the area of subdivisions and combine to determine the area of the composite plane figure.
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 split a composite figure into familiar shapes such as rectangles, triangles, trapezoids, and semicircles. They find each area, then add the parts without leaving gaps or creating overlaps.
What Mastery Looks Like
- A student can choose a valid way to split a composite figure and find any missing dimensions. They calculate each part accurately, combine the areas, and label the answer in square units.
Common Misconceptions
- Students may confuse area with perimeter or use the wrong formula for a piece. They may treat a diameter as a radius or forget to halve a circle. Some leave gaps or count overlapping regions twice.
How to Assess It
- Give this exit ticket: A 10-by-6 rectangle has a semicircle with diameter 10 attached along one side. Find the total area and show each part.
Lesson moves
Ways to Teach It
Give pairs paper composite figures to cut into familiar shapes, label dimensions, and reassemble while recording each area.
Ask students to compare two different subdivisions of one figure and explain why both methods give the same total area.
Play a matching game with composite figure cards, subdivision diagrams, area expressions, and final answers.
Plan a patio made from a rectangle and semicircle, then calculate the square footage of paving material needed.
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Printable 8.MG.5.a Worksheet
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Related Standards
- 8.MG.5.c
Apply perimeter, circumference, and area formulas to solve contextual problems involving composite plane figures.
- 8.MG.5.b
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