This lesson serves two purposes. The first is to show that we can divide a decimal by a whole number the same way we divide two whole numbers. Students first represent a decimal dividend with baseten diagrams. They see that, just like the units representing powers of 10, those for powers of 0.1 can also be divided into groups. They then divide using another method—partial quotients or long division—and notice that the principle of placing baseten units into equalsize groups is likewise applicable.
The second is to uncover the idea that the value of a quotient does not change if both the divisor and dividend are multiplied by the same factor. Students begin exploring this idea in problems where the factor is a multiple of 10 (e.g. \(8\div 1= 80\div 10\)). This work prepares students to divide two decimals in the next lesson.
Lesson overview
 12.1 Warmup: Number Talk: Dividing by 4 (5 minutes)

12.2 Activity: Using Diagrams to Represent Division (15 minutes)
 Includes "Are you Ready for More?" extension problem
 12.3 Activity: Dividends and Divisors (15 minutes)
 Lesson Synthesis
 12.4 Cooldown: The Same Quotient (5 minutes)
Learning goals:
 Compare and contrast (orally and using other representations) division problems with wholenumber and decimal dividends
 Divide decimals by whole numbers, and explain the reasoning (orally and using other representations).
 Generalize (orally and in writing) that multiplying both the dividend and the divisor by the same factor does not change the quotient.
Learning goals (student facing):
 Let’s divide decimals by whole numbers.
Learning targets (student facing):
 I can divide a decimal by a whole number.
 I can explain the division of a decimal by a whole number in terms of equalsized groups.
 I know how multiplying both the dividend and the divisor by the same factor affects the quotient.
Required preparation:
 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.5.NBT.B.7MS.5.NBT.7MO.5.NBT.A.6MO.5.NBT.A.7MO.5.NBT.A.8
 This lesson builds towards the standards:CCSS.6.EE.AMO.6.EEI.ACCSS.6.NS.B.2MS.6.NS.2MO.6.NS.B.2 MS.6.EE
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 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/mathcurriculum/.
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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