6.NS.2 - About the Math, Learning Targets, and Increasing Rigor
Grade 5AGL The Number System
6.NS.2
Full Standard
Fluently divide multi-digit numbers using the standard algorithm.
Learning Targets (I can)
- Explain division of multi-digit numbers with representations.
- Connect representations of multi-digit numbers to partial quotient algorithms.
- Use partial quotient algorithms.
- Connect partial quotient algorithms with the standard algorithm.
- Estimate quotients to determine if results of algorithms are accurate.
About the Math
- Explain division of multi-digit numbers with representations.
In the elementary grades, students were introduced to division through concrete models and various strategies to develop an understanding of this mathematical operation (limited to 4-digit numbers divided by 2-digit numbers). In 6th grade, students become fluent in the use of the standard algorithm, continuing to use their understanding of place value to describe what they are doing. Place value has been a major emphasis in the elementary standards. This standard is the end of this progression to address students' understanding of division procedurally. Students should work with remainders as well.
- Use partial quotient algorithms.
- Connect representations of multi-digit numbers to partial quotient algorithms.
- Connect partial quotient algorithms with the standard algorithm.
The standard algorithm for division is closely related to the partial quotients algorithm. Students should work with both simultaneously to determine how they are related in order to see how the standard algorithm works. Some students may need to go back further to a physical tool or drawing to understand the algorithm. That is fine. However, many students should be able to build on their understanding of partial quotients. Keep in mind that with partial quotients students can take away a single group of something or multiple groups of something at a time. The standard algorithm takes away the maximum number of groups possible. Students may need work understanding that one can take away single groups or groups of groups with the partial algorithm before transitioning to the maximum number of groups and ultimately to the standard algorithm.
- Estimate quotients to determine if results of algorithms are accurate.
Estimating quotients helps students determine if their calculations are reasonable. It's wise to have students estimate a quotient before computing most of the time - if not always. Students can compare their estimates to actuals after computing. The discussion should be had about how estimates are made and the strategies used for estimates. In some cases, one might round numbers. In other cases, a range might be found. Still, in others friendly compatible numbers might be used.
Essential vocabulary for this standard includes quotient, dividend, divisor, place value, and algorithm, partial quotients, remainder.
Progression of Standard within Grade 6 (5 AGL)
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Progression of this Standard Across Grades
This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.
Grade 5 | Grade 7 |
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TASKS
These tasks can be used with small group or whole group instruction.
- Create a word problem that can be solved by dividing a four-digit number by a two-digit number?
- The quotient is 118, what is the problem? Show how you know.
- 557 soccer fans need to take a bus to see the USA soccer team play Germany. Each bus holds 32 people. John thinks the fans would need to take 17 buses. Lisa thinks they will need more buses. Who is correct? Explain your thinking.
- Use the digits 3, 6, 7, 2, and 8 to create a division problem with the smallest possible quotient.
- What is the relationship between multiplication and division? Provide examples to show your thinking.
- Solve 1,481 ÷ 5 using the standard algorithm and then explain, using what you know about place value, why that strategy works.
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
Module 3 • Multiplication and Division
Connect the Division Algorithm to Partial Quotient Division:
- Comparing Division Links to an external site.
- Carnival Rides Links to an external site.
- Interpreting Division Links to an external site.
- Summer Reading Links to an external site.
Estimate and Divide Multi-Digit Numbers Using the Standard Algorithm:
Additional Tasks
These links provide instructional ideas connected to this standard.
- Size of the Divisor and Size of the Quotients Links to an external site. (Illustrative Mathematics: Lesson 4.1
- Meanings of Division Links to an external site. (Illustrative Mathematics: Lesson 4.2)
- Interpreting Division Situations Links to an external site. (Illustrative Mathematics: Lesson 4.3)
- Interpreting a Division Computation ( Links to an external site.Illustrative Mathematics)
- Using Long Division Links to an external site. (Illustrative Mathematics: Lesson 5.10)
- African Elephants Download African Elephants (Rich Task)
- Dance Show Download Dance Show (Rich Task)
- Division of Whole Numbers Download Division of Whole Numbers (MSDE Lesson)
- Division PPT Download Division PPT
Tasks From Print Resources
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Book Thumbnail | Book Title | Grade | Pages |
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Teaching Student-Centered mathematics |
6-8 | Where does The Decimal Go? Division, Activity 9.13, Page 162 |
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Nimble With Numbers
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5-6 | 56-70 | |
Nimble with Numbers |
4-5 | 56-59 | |
Hands-On Standards |
5-6 | 48 | |
Developing Mathematics with |
2-6 | 71-73 | |
Puddle Questions |
6 | 68-75 (Investigation 8) | |
Roads to Reasoning |
5 | 11 |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
- Partial Products Links to an external site.
- Multiply with the Standard Algorithm Links to an external site.
- Partial Quotients a Links to an external site.
- Partial Quotients b Links to an external site.
- Divide Multi-Digit Numbers with the Standard Algorithm a Links to an external site.
- Divide Multi-Digit Numbers with the Standard Algorithm b Links to an external site.
- Division Word Problems a Links to an external site.
- Division Word Problems b Links to an external site.
- Multiply and Divide with the Standard Algorithm Links to an external site.
- Represent Division in Varied Ways Links to an external site.
- Divide to Solve Word Problems Links to an external site.
- Divide to Solve Word Problems_2 Links to an external site.
- Divide to Solve Word Problems_3 Links to an external site.
- Divide to Solve Word Problems_4 Links to an external site.
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Learning Targets
- Explain division of multi-digit numbers with representations.
- Connect representations of multi-digit numbers to partial quotient algorithms.
- Use partial quotient algorithms.
- Connect partial quotient algorithms with the standard algorithm.
- Estimate quotients to determine if results of algorithms are accurate.
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.
Rubric for Tasks Links to an external site.
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.