Situations Involving Area
10 min
Narrative
The purpose of this Warm-up is to elicit students’ understandings of the relationship between the side lengths of a rectangle and its area. These understandings prepare students to reason about an unknown length or width of rectangles in the activities.
Students use their understanding about the relationship between multiplication and division, and their understanding of multiples of 10 to divide beyond 100.
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Task
Estimate: What is the length of the soccer field in meters?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
- Too low: 40–50 meters
- About right: 55–60 meters
- Too high: 60 meters
Activity Synthesis (Teacher Notes)
- “How did you make your estimate? How did you know it’s reasonable?” (I know that the area is about 2,300 and one of the side lengths is 40. I know that 40×60=2,400 and 40×50=2,000, so the estimate is between 50 and 60, but closer to 60.)
- “Is anyone’s estimate less than 40 meters? Is anyone’s estimate greater than 60 meters?”
- “Based on this discussion does anyone want to revise their estimate?”
Standards
Building On
- 3.MD.7·Relate area to the operations of multiplication and addition.
- 3.MD.C.7·Relate area to the operations of multiplication and addition.
- 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Building Toward
- 4.MD.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <em>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</em>
- 4.MD.A.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <span>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</span>
- 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Situations Involving Area
10 min
Narrative
The purpose of this Warm-up is to elicit students’ understandings of the relationship between the side lengths of a rectangle and its area. These understandings prepare students to reason about an unknown length or width of rectangles in the activities.
Students use their understanding about the relationship between multiplication and division, and their understanding of multiples of 10 to divide beyond 100.
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Task
Estimate: What is the length of the soccer field in meters?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
- Too low: 40–50 meters
- About right: 55–60 meters
- Too high: 60 meters
Activity Synthesis (Teacher Notes)
- “How did you make your estimate? How did you know it’s reasonable?” (I know that the area is about 2,300 and one of the side lengths is 40. I know that 40×60=2,400 and 40×50=2,000, so the estimate is between 50 and 60, but closer to 60.)
- “Is anyone’s estimate less than 40 meters? Is anyone’s estimate greater than 60 meters?”
- “Based on this discussion does anyone want to revise their estimate?”
Standards
Building On
- 3.MD.7·Relate area to the operations of multiplication and addition.
- 3.MD.C.7·Relate area to the operations of multiplication and addition.
- 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Building Toward
- 4.MD.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <em>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</em>
- 4.MD.A.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <span>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</span>
- 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.