Montana Math MT.7.G.3
The Standard
Know and use the formulas for the area and circumference of a circle and give an informal derivation of the relationship between the circumference and area of a circle. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the distance around a circle and the space inside it from a radius or diameter. They rearrange circle wedges to show why area is half the circumference times the radius.
What Mastery Looks Like
- Students use the circumference and area formulas with the correct radius and units. They explain that rearranged wedges form a near-rectangle with a base of half the circumference and a height of one radius.
Common Misconceptions
- Students may use the diameter in place of the radius or use the circumference formula to find area. They may give square units for circumference or think the wedges form an exact rectangle.
How to Assess It
- Exit ticket: A circle has a diameter of 12 m. Find its circumference and area in terms of π, include units, and sketch how rearranged wedges explain the area.
Lesson moves
Ways to Teach It
Cut a paper circle into 12 wedges, alternate them into a strip, and label its approximate base and height.
Ask students to write why narrower wedges make the strip closer to a rectangle and what that shows about circle area.
Give pairs radius and diameter cards, then have students match each card to the correct circumference and area expressions.
Show a public photo of a Montana tribal powwow arena; model it as a 20-meter-radius circle and calculate approximate perimeter and area.
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Printable MT.7.G.3 Worksheet
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