Virginia SOL 6.MG.2.a
The Standard
Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives (e.g., two-dimensional diagrams, grid paper).
Virginia Standards of Learning for Mathematics · The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students cut, move, or redraw parts of shapes to connect parallelograms with rectangles and triangles with parallelograms. They use those models to justify the area rules, including the one-half factor for triangles.
What Mastery Looks Like
- Students can cut or redraw a parallelogram as a rectangle and explain why both shapes have equal area. They can pair a base with its perpendicular height and show why a matching triangle has half the area.
Common Misconceptions
- Students often use the slanted side as the height instead of the perpendicular distance. They may forget to divide a triangle’s base times height by two, or confuse area with perimeter.
How to Assess It
- Exit ticket: Draw a parallelogram with base 8 units and perpendicular height 5 units. Show how to rearrange it into a rectangle, then explain how the model gives the area formula.
Lesson moves
Ways to Teach It
Give pairs paper parallelograms to cut along a height, move the triangle, and label the resulting rectangle’s base and height.
Ask students to explain, with a sketch, why a triangle with base b and height h has half the matching parallelogram’s area.
Play a matching game with diagram cards, dimension cards, rearranged shapes, and area expressions for triangles and parallelograms.
Use a slanted garden plot on grid paper, then compare fencing needed with soil coverage to separate perimeter from area.
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Related Standards
- 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.
- 6.MG.2.b
Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.
- 4.MG.3.a
Use concrete materials and pictorial models to develop a formula for the area and perimeter of a rectangle (including a square).
- 7.MG.1.b
Develop the formulas for determining the surface area of rectangular prisms and right cylinders and solve problems, including those in contextual situations, us...
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