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.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • 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.
  

 

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.

Progression Across Grades
Grade 5 Grade 7
  • Divide multi-digit dividends   (5.NBT.6)
  • Solve problems with the four operations with rational numbers (7.NS.3)

 

 

 

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