This lesson introduces students to long division. Students see that in long division the meaning of each digit is intimately tied to its place value, and that it is an efficient way to find quotients. In the partial quotients method, all numbers and their meaning are fully and explicitly written out. For example, to find \(657 \div 3\) we write that there are at least 3 groups of 200, record a subtraction of 600, and show a difference of 57. In long division, instead of writing out all the digits, we rely on the position of any digit—of the quotient, of the number being subtracted, or of a difference—to convey its meaning, which simplifies the calculation.
In addition to making sense of long division and using it to calculate quotients, students also analyze some place-value errors commonly made in long division (MP3).
Lesson overview
- 10.1 Warm-up: Number Talk: Estimating Quotients (5 minutes)
- 10.2 Activity: Lin Uses Long Division (25 minutes)
- 10.3 Optional Activity: Dividing Whole Numbers (10 minutes)
- Lesson Synthesis
- 10.4 Cool-down: Dividing by 15 (5 minutes)
Learning goals:
- Interpret the long division method, and compare and contrast it (orally) with other methods for computing the quotient of whole numbers.
- Recognize and explain (orally) that long division is an efficient strategy for dividing numbers, especially with multi-digit dividends.
- Use long division to divide whole numbers that result in a whole-number quotient, and multiply the quotient by the divisor to check the answer.
Learning goals (student facing):
- Let’s use long division.
Learning targets (student facing):
- I can use long division to find a quotient of two whole numbers when the quotient is a whole number.
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:
- long division - Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right. For example, here is the long division for \(57 \div 4\).
- 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 building 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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