Virginia SOL 6.MG.2.b
The Standard
Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.
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 find perimeter by adding side lengths and find area using a base and its perpendicular height. They solve diagram and word problems, choose the right measurements, and report suitable units.
What Mastery Looks Like
- Students choose the needed measurements from a diagram and use the correct formula. They label perimeter with linear units and area with square units, and they can explain each step.
Common Misconceptions
- Students may use a slanted side as the height, even when it is not perpendicular to the base. They may forget to halve a triangle's area, halve a parallelogram's area, or confuse square units with linear units.
How to Assess It
- Give a parallelogram with base 9 cm, side 5 cm, and height 4 cm. Ask students to find its area and perimeter, then explain why the side and height have different uses.
Lesson moves
Ways to Teach It
Give pairs grid paper and scissors to cut a triangle from a parallelogram, rearrange it, and label base, height, and area.
Ask, “Why can two parallelograms have the same perimeter but different areas?” Students sketch examples and defend their measurements.
Run a formula-sort relay with diagram cards; teams match each figure to needed measurements, formula, calculation, and correct units.
Have students price fencing and sod for a drawn triangular dog run, using perimeter for fencing and area for sod.
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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.
- 8.MG.5.c
Apply perimeter, circumference, and area formulas to solve contextual problems involving composite plane figures.
- 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.
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