Virginia SOL 8.MG.5.b
The Standard
Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, and semicircles. Use the attributes of the subdivisions to determine the perimeter 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 break an irregular figure into familiar shapes and use side relationships to find missing lengths. They add only the lengths along the outside boundary, including curved semicircle edges when present.
What Mastery Looks Like
- Students label all outer edges and use shape properties to find missing lengths. They calculate straight and curved boundary lengths accurately and explain why interior segments are excluded.
Common Misconceptions
- Students may add interior divider lengths or shared edges to the perimeter. They may use area formulas instead of adding boundary lengths. For semicircles, they may use the full circumference or forget to include the diameter when it is exposed.
How to Assess It
- Exit ticket: An 8 cm by 6 cm rectangle has a 4 cm by 2 cm rectangle cut from its top-right corner. Sketch it, label every outer edge, and find the perimeter.
Lesson moves
Ways to Teach It
Give pairs cardstock composite shapes and rulers, then have them draw subdivisions, label side lengths, and calculate only the outside boundary.
Display a subdivided figure and ask, "Which segments count toward perimeter, and which do not?" Students justify each choice in writing.
Use perimeter detective cards with missing side lengths, and have teams solve and match each figure to its correct perimeter.
Plan the edging for a garden made from a rectangle and semicircle, then calculate the total length and estimated material cost.
Keep exploring
Related Standards
- 8.MG.5.a
Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles. Determine the area of subdivisions and combi...
- 1.MG.2.c
Draw and name the plane figure (circle, square, rectangle, triangle) when given information about the number of sides, vertices, and angles.
- 1.MG.2.f
Compose larger plane figures by combining two or three simple plane figures (triangles, squares, and/or rectangles).
- 1.MG.2
The student will describe, sort, draw, and name plane figures (circles, triangles, squares, and rectangles), and compose larger plane figures by combining simpl...
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