Problems about Perimeter and Area
10 min
Narrative
The purpose of this How Many Do You See? routine is to prompt students to decompose a rectilinear figure to find its area and to recognize that there are many ways to do so. Students are also reminded that area is additive. The reasoning in this routine prepares students to reason flexibly about the area of rectilinear figures later in the lesson.
Launch
- Groups of 2
- “How many do you see? How do you see them?”
- Flash the image.
Teacher Instructions
- 30 seconds: quiet think time
- Display the image.
- 1 minute: partner discussion
- Record responses.
Student Task
How many shaded squares do you see? How do you see them?
Sample Response
27 squares. Sample responses:
- I see a 2-by-2 square, a 7-by-3 rectangle, and a 2-by-1 square. (2×2)+(7×3)+(2×1)=27
- I see a 2-by-5 rectangle, a 3-by-3 square, and a 2-by-4 rectangle. (2×5)+(3×3)+(2×4)=27
- I see a 6-by-7 rectangle with two corners cut out. The corners are rectangles, 5 by 1 and 5 by 2. (6×7)−(5×1)−(5×2)=42−5−10=27
Activity Synthesis (Teacher Notes)
- “We’ve seen how helpful it is to decompose the figure into rectangles. In how many ways could we do that here?” (Many ways)
- As students share each way, record the thinking for all to see.
- “Are there ways to partition that are more helpful than others?” (Partitioning into larger rectangles is more efficient than smaller ones. The latter would mean more multiplication and more partial areas to add up.)
Standards
- 4.OA.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 4.OA.A.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Problems about Perimeter and Area
10 min
Narrative
The purpose of this How Many Do You See? routine is to prompt students to decompose a rectilinear figure to find its area and to recognize that there are many ways to do so. Students are also reminded that area is additive. The reasoning in this routine prepares students to reason flexibly about the area of rectilinear figures later in the lesson.
Launch
- Groups of 2
- “How many do you see? How do you see them?”
- Flash the image.
Teacher Instructions
- 30 seconds: quiet think time
- Display the image.
- 1 minute: partner discussion
- Record responses.
Student Task
How many shaded squares do you see? How do you see them?
Sample Response
27 squares. Sample responses:
- I see a 2-by-2 square, a 7-by-3 rectangle, and a 2-by-1 square. (2×2)+(7×3)+(2×1)=27
- I see a 2-by-5 rectangle, a 3-by-3 square, and a 2-by-4 rectangle. (2×5)+(3×3)+(2×4)=27
- I see a 6-by-7 rectangle with two corners cut out. The corners are rectangles, 5 by 1 and 5 by 2. (6×7)−(5×1)−(5×2)=42−5−10=27
Activity Synthesis (Teacher Notes)
- “We’ve seen how helpful it is to decompose the figure into rectangles. In how many ways could we do that here?” (Many ways)
- As students share each way, record the thinking for all to see.
- “Are there ways to partition that are more helpful than others?” (Partitioning into larger rectangles is more efficient than smaller ones. The latter would mean more multiplication and more partial areas to add up.)
Standards
- 4.OA.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 4.OA.A.3·Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.