Virginia SOL 8.MG.5

8.MG.5 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 8.MG.5.a

  Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles. Determine the area of subdivisions and combi...

• 8.MG.5.b

  Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, and semicircles. Use the attributes of the subdivisions to determine t...

• 8.MG.5.c

  Apply perimeter, circumference, and area formulas to solve contextual problems involving composite plane figures.

01

What Students Need to Do

Students break a composite figure into familiar shapes and calculate each part. They add the parts for total area and trace the outside edges for perimeter.

02

What Mastery Looks Like

Students choose useful subdivisions, find any missing lengths, and apply the correct formulas. They combine areas without overlap and trace only the outside boundary for perimeter.

03

Common Misconceptions

Students often add the perimeters of every smaller shape, counting shared edges twice. They may use diameter as radius, include a semicircle’s full circumference, or confuse square units with linear units.

04

How to Assess It

Give this exit ticket: A 12 by 8 rectangle has a semicircle with diameter 8 attached to one short side. Find the total area and outside perimeter in terms of pi.

1. 01

   Give pairs a composite figure on grid paper to cut into shapes, label dimensions, and calculate its area and perimeter.

2. 02

   Ask students to explain why shared edges count when finding area dimensions but do not count in the outside perimeter.

3. 03

   Run a card match with composite diagrams, subdivision sketches, area expressions, and perimeter expressions.

4. 04

   Have students design a patio using a rectangle and semicircle, then calculate paving area and the length of border needed.

• 5.MG.2

  The student will use multiple representations to solve problems, including those in context, involving perimeter, area, and volume.

• 6.MG.2

  The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.

• 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...