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Using the Partial Quotients Method: IM 6.5.9
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1. Lesson 6.5.9
- IM 6.5.9 Lesson: Using the Partial Quotients Method
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2. Practice 6.5.9
- IM 6.5.9 Practice: Using the Partial Quotients Method
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Using the Partial Quotients Method: IM 6.5.9
IM 6 – 8 Math, GeoGebra Classroom Activities, Aug 13, 2020
“Using the Partial Quotients Method” from IM Grade 6 by Open Up Resources and Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 license.
Table of Contents
- Lesson 6.5.9
- IM 6.5.9 Lesson: Using the Partial Quotients Method
- Practice 6.5.9
- IM 6.5.9 Practice: Using the Partial Quotients Method
IM 6.5.9 Lesson: Using the Partial Quotients Method
Elena used base-ten diagrams to find . She started by representing 372.
She made 3 groups, each with 1 hundred. Then, she put the tens and ones in each of the 3 groups. Here is her diagram for .
Discuss with a partner:
Elena’s diagram for 372 has 7 tens. The one for has only 6 tens. Why?
She made 3 groups, each with 1 hundred. Then, she put the tens and ones in each of the 3 groups. Here is her diagram for .
Discuss with a partner:
Elena’s diagram for 372 has 7 tens. The one for has only 6 tens. Why?Font sizeFont size
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Discuss with a partner:
Where did the extra ones (small squares) come from?
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Andre calculated using a method that was different from Elena’s.
Andre subtracted 600 from 657. What does the 600 represent?
Andre subtracted 600 from 657. What does the 600 represent?
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Andre wrote 10 above the 200, and then subtracted 30 from 57. How is the 30 related to the 10?
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What do the numbers 200, 10, and 9 represent?
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What is the meaning of the 0 at the bottom of Andre’s work?
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How might Andre calculate ? Explain your reasoning.
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Find the quotient of 1,332 ÷ 9 using one of the methods you have seen so far. Show your reasoning.
Find each quotient and show your reasoning. Use the partial quotients method at least once with the following 3 problems: 1,115 ÷ 5
665 ÷ 7
432 ÷ 16
IM 6.5.9 Practice: Using the Partial Quotients Method
Here is one way to find 2,105 ÷ 5 using partial quotients. Show a different way of using partial quotients to divide 2,105 by 5.
Show or explain a different way of using partial quotients to divide 2,105 by 5.
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Andre and Jada both found using the partial quotients method, but they did the calculations differently, as shown here.
How is Jada's work the same as Andre’s work? How is it different?
How is Jada's work the same as Andre’s work? How is it different?
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Explain why they have the same answer.
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Which might be a better way to evaluate : drawing base-ten diagrams or using the partial quotients method? Explain your reasoning.
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Here is an incomplete calculation of 534 : 6. Write the missing numbers (marked with “?”) that would make the calculation complete.
Use the partial quotients method to find 1,032 ÷ 43.
Which of the polygons has the greatest area?
One micrometer is a millionth of a meter. A certain spider web is 4 micrometers thick. A fiber in a shirt is 1 hundred-thousandth of a meter thick.
Which is wider, the spider web or the fiber? How many meters wider? Explain your reasoning.
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