Lesson 11: Dividing Numbers that Result in Decimals
About this lesson
So far, students have divided whole numbers that result in whole-number quotients. In the next three lessons, they work toward performing division in which the divisor, dividend, and quotient are decimals. In this lesson, they perform division of two whole numbers that result in a terminating decimal. Students divide using all three techniques introduced in this unit: base-ten diagrams, partial quotients, and long division. They apply this skill to calculate the (terminating) decimal expansion of some fractions.
Students analyze, explain, and critique various ways of reasoning about division (MP3).
Lesson overview
- 11.1 Warm-up: Number Talk: Evaluating Quotients (5 minutes)
- 11.2 Optional Activity: Keep Dividing (20 minutes)
- 11.3 Activity: Using Long Division to Calculate Quotients (25 minutes)
- Lesson Synthesis
- 11.4 Cool-down: Calculating Quotients (5 minutes)
Learning goals:
- Interpret different methods for computing a quotient that is not a whole number, and express it (orally and in writing) in terms of “unbundling.”
- Use long division to divide whole numbers that result in a quotient with a decimal, and explain (orally) the solution method.
Learning goals (student facing):
- Let’s find quotients that are not whole numbers.
Learning targets (student facing):
- I can use long division to find the quotient of two whole numbers when the quotient is not a whole number.
Required preparation:
- Students may choose to draw base-ten diagrams in this lesson.
- If drawing them is a challenge, consider giving students access to:
- Commercially produced base-ten blocks, if available.
- Paper copies of squares and rectangles (to represent base-ten units), cut up from copies of the blackline master of the second lesson in the unit.
- Digital applet of base-ten representations https://ggbm.at/NJPVks38.
- Some students might find it helpful to use graph paper to help them align the digits as they divide using long division and the partial quotients method.
- Consider having graph paper accessible throughout the lesson.
Glossary:
- Access the complete Grade 6 glossary.
Standards
- This lesson builds on the standard: CCSS.4.NBT.B.6MS.4.NBT.6MO.4.NBT.A.7
- This lesson builds towards the standard: CCSS.6.EE.AMO.6.EEI.A
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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