Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Purpose and Instructional Strategies
The purpose of this benchmark is for students to connect perimeter and area problems to algebraic concepts to find the measures of unknown side lengths. This new idea builds from solving area and perimeter problems with whole number side lengths when using models and formulas in grade 3 (MA.3.GR.2.3
) and will form the foundation for problems involving fractional and decimal side lengths in grade 5 (MA.5.GR.2.1
- During instruction, students should use a letter (variable) to represent the missing side length and have experiences solving for unknowns in perimeter situations with a given area and vice-versa.
- Instruction includes having students use the fact that opposite sides in rectangles and squares are equal when solving problems involving area and perimeter.
Common Misconceptions or Errors
- Students frequently confuse area and perimeter. Instruction should provide lots of opportunity for students to work with both measures on the same object and have them explain which measure is area and which is perimeter and why? Instruction should also focus on naming the units properly.
Strategies to Support Tiered Instruction
- Instruction provides many opportunities for students to work with both measures on the same object and explain which measure is area and which is perimeter and why. Instruction should also focus on naming the units properly
- Instruction includes finding both the area and perimeter in real world examples and having students explain how they solved for both.
- For example, when provided with examples like the following, students use the measurements provided to create an equation to find area and perimeter and explain the difference. “A rectangular garden is being built at the school. The dimensions for the garden are 8 feet by 4 feet. Write and solve an equation to find the area of the garden and an equation to find the perimeter of the garden.”
- The teacher provides students with images created using square tiles. Student count and labels the side lengths based on the tiles, then write equations to show how they would find the area and how they would find the perimeter.
- For example: When provided with an image like the one shown below, students label each side length based on the number of tiles and write an equation for perimeter and then count the units around the outside of the figure to confirm their solution. Students multiply the length and width to find area and then count the number of squares that make up the figure to confirm their solution.
Instructional Task 1 (MTR.7.1)
The perimeter of the patio below is 98 square feet.
What is the area of the patio?
Instructional Item 1
A soccer field with its dimensions is shown.
Which equation can be used to find the area of the soccer field?
- a. 75 yards + 120 yards = A yards
- b. 75 yards + 75 yards + 120 yards + 120 yards = A yards
- c. 75 yards× 120 yards = A square yards
- d. 75 yards × 120 yards × 75 yards × 120 yards = A square yards
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.