Montana Math MT.3.MD.8
The Standard
Solve problems in context involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students add the side lengths of a polygon to find its perimeter. They use a known perimeter to find a missing side. They draw rectangles to compare area and perimeter.
What Mastery Looks Like
- Students add every side of a polygon once and use the correct length unit. They find an unknown side by subtracting the known sides from the perimeter. They can show that 2-by-6 and 3-by-4 rectangles have the same area but different perimeters.
Common Misconceptions
- Some students count squares inside a shape when asked for perimeter, or leave out a side when adding. Others think rectangles with the same area must have the same perimeter, or subtract a known rectangle side only once.
How to Assess It
- Exit ticket: A rectangular garden is 3 feet wide and has a perimeter of 14 feet. Find its length, then draw a different rectangle with the same area and label its perimeter.
Lesson moves
Ways to Teach It
Give pairs 12 square tiles to build 2-by-6 and 3-by-4 rectangles; have them count tiles inside and tile edges around each shape.
Have students sketch two rectangular gardens with equal fencing but different areas and explain which holds more 1-foot-square stepping stones.
Deal cards labeled "perimeter 18 cm, width 4 cm"; partners find the missing length and check by adding all four sides.
Give students a 20-foot garden edging budget; have them sketch 4-by-6-foot and 3-by-7-foot beds and compare planting areas.
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