Lesson 12: Rectangles with the Same Area

Rectangles with the Same Area

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to divide fluently within 100.

When students use properties of operations and quotients with a value of 10 to find other quotients, they look for and make use of structure (MP7).

Launch

Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time

Teacher Instructions

Record answers and strategies.
Keep expressions and work displayed.
Repeat with each expression.

Student Task

Find the value of each expression mentally.

$40 \div 4$
$60 \div 4$
$80 \div 4$
$96 \div 4$

Sample Response

10: I just know it.
15: I know that 60 is $40 + 20$ . I also know that $40 \div 4$ is 10 and $20 \div 4$ is 5, so $60 \div 4$ is $10 + 5$ or 15.
20: 80 is double 40, so it’s like having 2 groups of 10 for 20.
24: The last problem shows $80 \div 4 = 20$ . I know that 96 is $80 + 16$ and $16 \div 4 = 4$ , so $96 \div 4$ is $20 +4$ or 24.

Activity Synthesis (Teacher Notes)

“How does knowing the first fact help you find other facts?”
Consider asking:
- “Who can restate _____’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone approach the problem in a different way?”
- “Does anyone want to add on to _____’s strategy?”

Standards

Addressing

3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that $8 \times 5 = 40$, one knows $40 \div 5 = 8$) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

15 min

20 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Rectangles with the Same Area

10 min

Narrative

When students use properties of operations and quotients with a value of 10 to find other quotients, they look for and make use of structure (MP7).

Launch

Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time

Teacher Instructions

Record answers and strategies.
Keep expressions and work displayed.
Repeat with each expression.

Student Task

Find the value of each expression mentally.

$40 \div 4$
$60 \div 4$
$80 \div 4$
$96 \div 4$

Sample Response

10: I just know it.
15: I know that 60 is $40 + 20$ . I also know that $40 \div 4$ is 10 and $20 \div 4$ is 5, so $60 \div 4$ is $10 + 5$ or 15.
20: 80 is double 40, so it’s like having 2 groups of 10 for 20.
24: The last problem shows $80 \div 4 = 20$ . I know that 96 is $80 + 16$ and $16 \div 4 = 4$ , so $96 \div 4$ is $20 +4$ or 24.

Activity Synthesis (Teacher Notes)

“How does knowing the first fact help you find other facts?”
Consider asking:
- “Who can restate _____’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone approach the problem in a different way?”
- “Does anyone want to add on to _____’s strategy?”

Standards

Addressing

3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that $8 \times 5 = 40$, one knows $40 \div 5 = 8$) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Rectangles with the Same Area

Warm-up Number Talk: Divide in Parts 10 minKCs

Narrative

Launch

Student Task

Sample Response

Activity Area of 24 15 minKCs

ActivitySame Area, Different Perimeter 20 minKCs

Knowledge Components

Rectangles with the Same Area

Warm-up Number Talk: Divide in Parts 10 minKCs

Narrative

Launch

Student Task

Sample Response

Activity Area of 24 15 minKCs

ActivitySame Area, Different Perimeter 20 minKCs

10 min

15 min

20 min

10 min

15 min

20 min