6.NS.2 - About the Math, Learning Targets, and Increasing Rigor

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

Beginning in third grade, students are 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 place value.

• Explain division of multi-digit numbers with representations.
• Connect representations of multi-digit numbers to partial quotient algorithms.
• Use partial quotient algorithms.

Before working with the standard division algorithm, students must demonstrate understanding of division with multi-digit divisors and dividends. This understanding should then be used as a springboard for working with the algorithm.

• Connect partial quotient algorithms with the standard algorithm.

As the algorithm is introduced, it should be connected to students' understanding of division and partial quotients. Students should be able to articulate how the algorithm is similar and different than the partial quotients algorithm. Tricks, acronyms, and chants should not be used for students to memorize the division algorithm. It should be intuitive and well understood. 

• Estimate quotients to determine if results of algorithms are accurate.

Proficiency with the algorithm is connected to students' ability to determine if their results are reasonable. One way to develop this in students is to consistently ask them to estimate quotients. To do this, students estimate quotients, apply the algorithm, and compare results. 

Essential vocabulary for this standard includes: quotient, dividend, divisor, place value, and remainder. 

Progression of Standard within Grade 4 G/T

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

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.

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.

Additional Tasks

  These links provide instructional ideas connected to this standard. 

• Interpreting a Division Computation Links to an external site. (Illustrative Mathematics)
• Using the Partial Quotients Method Links to an external site. (IM Open-Up Resources: Lesson 5.9)
• Using Long Division Links to an external site. (IM Open-Up Resources: 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
• Rubiks- Large Number Division Links to an external site. (cc = colleague created tasks)

CC Indicates colleague created HCPSS instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.

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. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered mathematics	6-8	Where does The Decimal Go? Division, Activity 9.13, Page 162
	Nimble With Numbers	5-6	56-70
	Nimble with Numbers	4-5	56-59
	Hands-On Standards	5-6	48
	Developing Mathematics with Base Ten	2-6	71-73
	Puddle Questions	6	68-75 (Investigation 8)
	Roads to Reasoning	5	11

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.

• Divide with the Standard Algorithm a Links to an external site.
• Divide with the Standard Algorithm b Links to an external site.

• Represent Division in Varied WaysLinks to an external site.
• Divide to Solve Word ProblemsLinks to an external site.
• Divide to Solve Word Problems_2Links to an external site.
• Divide to Solve Word Problems_3Links to an external site.
• Divide to Solve Word Problems_4Links to an external site.

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.