Multiplication of Multi-digit Numbers
10 min
Narrative
In this Warm-up, students practice estimating a reasonable answer, using known information, rounding, and multiplicative reasoning strategies. For example, students may create a diagram and arrive at 7×7×7×7 as an estimate of the number of fish. Then they may approximate (7×7)×(7×7) with 50×50, or estimate (7×7×7)×7 with (50×7)×7 or 350×7. Some students may notice that the question is vague and ask: “How many are going to the park?” rather than “How many people are going to the park?” and account only for the number of children and teachers in their estimation. If students ask for clarification, ask them to make their own assumptions and explain why they made those assumptions when they share their estimates.
Launch
- Groups of 2
- Display the description.
Teacher Instructions
- “What is an estimate that’s too high? Too low? About right?”
- 2 minutes: quiet think time
- 1 minute: partner discussion
- Record responses.
Student Task
- Seven teachers go to the park.
- Each teacher takes 7 students.
- Each student brings 7 fishbowls.
- Each fishbowl has 7 fish.
How many go to the park?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
- Too low: 1,500–2,000
- About right: 2,400–2,500
- Too high: 2,600–3,000
Activity Synthesis (Teacher Notes)
- Consider asking:
- “Is anyone’s estimate less than 500? Greater than 5,000?”
- “Did anyone include the number of teachers and students in their estimate?”
- Invite students to share their estimation strategies. After each explanation, ask if others reasoned the same way.
- Consider revealing the actual value of 2,457 teachers, students, and fish.
Standards
- 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.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Multiplication of Multi-digit Numbers
10 min
Narrative
In this Warm-up, students practice estimating a reasonable answer, using known information, rounding, and multiplicative reasoning strategies. For example, students may create a diagram and arrive at 7×7×7×7 as an estimate of the number of fish. Then they may approximate (7×7)×(7×7) with 50×50, or estimate (7×7×7)×7 with (50×7)×7 or 350×7. Some students may notice that the question is vague and ask: “How many are going to the park?” rather than “How many people are going to the park?” and account only for the number of children and teachers in their estimation. If students ask for clarification, ask them to make their own assumptions and explain why they made those assumptions when they share their estimates.
Launch
- Groups of 2
- Display the description.
Teacher Instructions
- “What is an estimate that’s too high? Too low? About right?”
- 2 minutes: quiet think time
- 1 minute: partner discussion
- Record responses.
Student Task
- Seven teachers go to the park.
- Each teacher takes 7 students.
- Each student brings 7 fishbowls.
- Each fishbowl has 7 fish.
How many go to the park?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
- Too low: 1,500–2,000
- About right: 2,400–2,500
- Too high: 2,600–3,000
Activity Synthesis (Teacher Notes)
- Consider asking:
- “Is anyone’s estimate less than 500? Greater than 5,000?”
- “Did anyone include the number of teachers and students in their estimate?”
- Invite students to share their estimation strategies. After each explanation, ask if others reasoned the same way.
- Consider revealing the actual value of 2,457 teachers, students, and fish.
Standards
- 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.