Standard

Solve real world and mathematical problems 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.

Student language:

• "I can solve real world math problems using what I know about the perimeter of shapes."

Explanation

About the Math, Learning Targets, and Rigor

Students develop an understanding of the concept of perimeter (the distance around the outside of a shape) through hands on experiences:

• Walking around the perimeter of a room
• Using rubber bands to represent the perimeter of a plane figure on a geoboard
• Tracing around a shape on an interactive whiteboard.

Have students use a piece of non-stretchy string. Have them wrap the string around a shape then measure the string. The measurement is the perimeter, or distance around the outside of the shape.

In this standard, students need to find:

• The perimeter of objects
  • Examples
    • Perimeter of a rectangle = length + length + width + width or (2 x length) + ( 2 x width)
    • Perimeter of a pentagon (5-sided shape) = length + length + length + length + length
• Unknown side lengths in which the perimeter and side lengths are known.
  • Example
    • Rectangle: Perimeter 45cm, side lengths of 12cm, 15cm, 8cm
      • 12 + 15 + 8 = 35; 45 - 35 = 10. The unknown side length is 10 cm.

Common Misconception

Students think that when they are presented with a drawing of a rectangle with only two of the side lengths shown or a problem situation with only two of the side lengths provided, these are the only dimensions they should add to find the perimeter. Encourage students to include the appropriate dimensions on the other sides of the rectangle.

Resources

Videos

• Khan Academy
  • scroll to 3.MD.8, click on a skill, watch videos on left side in each skill
• Learn Zillion
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 3rd grade at bottom, then 3.MD.8
• Common Core Sheets

Released Assessment Questions

PARCC

3.MD.8

Solve real world and mathematical problems 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.

Performance Indicators: 3.MD.8

Level 5: Exceeds Expectations

• Solves real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and provides examples of rectangles with the same perimeter and different areas or with the same area and different perimeters. A substantial addition, subtraction, or multiplication step with number values towards the higher end of the acceptable values for each operation.
• Partitions shapes into parts with equal areas and expresses the area as a unit fraction of the whole.

Level 4: Meets Expectations

• Solves mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and provides examples of rectangles with the same area and different perimeters.

Integrated Standards

3.Int.3

Solve real world and mathematical problems involving perimeters of polygons requiring a substantial addition, subtraction, or multiplication step, drawing on knowledge and skills articulated in 3.NBT. (Content Scope: 3.MD.8, 3.NBT.2, and 3.NBT.3)

• Tasks must be aligned to the first standard and 1 or more of the subsequent standards listed in the content scope. Substantial (def.) – Values should be towards the higher end of the numbers identified in the standards.

Performance Indicators: 3.Int.3

Level 5: Exceeds Expectations

• Solves real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and provides examples of rectangles with the same perimeter and different areas or with the same area and different perimeters. A substantial addition, subtraction, or multiplication step with number values towards the higher end of the acceptable values for each operation.
• Partitions shapes into parts with equal areas and expresses the area as a unit fraction of the whole.

Level 4: Meets Expectations

• Solves mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and provides examples of rectangles with the same area and different perimeters.