Practice a Partial-Quotients Algorithm
10 min
Narrative
This Warm-up prompts students to carefully analyze and compare a variety of ways to use partial quotients to find a single quotient. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about the characteristics of the different strategies shown.
As students use partial quotients to find more complex quotients, they need to be strategic about which multiples of the divisor to subtract. Small multiples may be easier for finding the partial quotients, but it takes more of them to give a sum that is equivalent to the dividend.
Launch
- Groups of 2
- Display the image.
- “Pick 3 strategies that go together. Be ready to share why they go together.”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
Which 3 go together?
Sample Response
Sample responses:
A, B, and C go together because they start with a multiple of 5 in the quotient.
A, B, and D go together because they show the value of the quotient.
A, C, and D go together because they subtract 10 groups of 82.
B, C, and D go together because they show work, not just an answer.
Activity Synthesis (Teacher Notes)
- “Which strategy do you prefer for finding the value of 1,312÷82?” (I like Method C because it begins by taking out a pretty big multiple of 82.)
Standards
- 5.NBT.6·Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
- 5.NBT.B.6·Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
20 min
15 min
Knowledge Components
All skills for this lesson
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Practice a Partial-Quotients Algorithm
10 min
Narrative
This Warm-up prompts students to carefully analyze and compare a variety of ways to use partial quotients to find a single quotient. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about the characteristics of the different strategies shown.
As students use partial quotients to find more complex quotients, they need to be strategic about which multiples of the divisor to subtract. Small multiples may be easier for finding the partial quotients, but it takes more of them to give a sum that is equivalent to the dividend.
Launch
- Groups of 2
- Display the image.
- “Pick 3 strategies that go together. Be ready to share why they go together.”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
Which 3 go together?
Sample Response
Sample responses:
A, B, and C go together because they start with a multiple of 5 in the quotient.
A, B, and D go together because they show the value of the quotient.
A, C, and D go together because they subtract 10 groups of 82.
B, C, and D go together because they show work, not just an answer.
Activity Synthesis (Teacher Notes)
- “Which strategy do you prefer for finding the value of 1,312÷82?” (I like Method C because it begins by taking out a pretty big multiple of 82.)
Standards
- 5.NBT.6·Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
- 5.NBT.B.6·Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.