5.NBT.5 - About the Math, Learning Targets, and Rigor

Grade 5 Place Value and Decimals

5.NBT.5

Full Standard

Fluently multiply multi-digit whole numbers using the standard algorithm.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

5th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of multiplication and division of different number types.

 

 
4th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

 

 

 

Learning Targets (I can)

  • Use partial products to multiply multi-digit numbers.
  • Connect partial products to the standard algorithm for multiplication.
  • Explain the standard algorithm for multiplication of multi-digit numbers.
  • Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, and 4-digit by 2-digit factors.
  • Solve problems using multi-digit multiplication.

 

About the Math

Multiplication can be represented by arrays, area models, or by equal jumps on a number line. In order to teach the multiplication algorithm with understanding, models must be used to explain the procedure for using the standard algorithm.

  • Use partial products to multiply multi-digit numbers.

The Distributive Property can be applied to expressions to find partial products. Students should show a deep understanding of partial products and various decompositions of factors. Partial products can be recorded as an algorithm as well. However, as the number of place values grows partial products can lose its efficiency. 

  • Connect partial products to the standard algorithm for multiplication.

Students must be able to use the standard algorithm and explain how it works. To do this, students should connect the standard algorithm process to partial products. Essentially, the standard algorithm consolidates partial products into a single step per place value. See the linked article for more information.

  • Explain the standard algorithm for multiplication of multi-digit numbers.

The standard algorithm consolidates steps. It is a digit-based process. It relies on use of single-digit factors as values are not expanded. In the image to the right, one sees 6 x 9 but the actual computation is 6 x 9 tens or 6 x 90. Students should speak to place value as they progress through the algorithm. 

  • Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, 4-digit by 2-digit factors and 3-digit by 3-digit factors.

As noted above, students must be able to use and explain the standard algorithm. Additionally, students should be challenged to determine when the standard algorithm is or isn't efficient. For example, 32 x 3 might be more efficiently thought of as 30 x 3 (90) + 2 x 3 (6). The paper/pencil algorithm for this computation is likely inefficient for most students.

Essential vocabulary for this standard includes: standard algorithm, multiply, product, and factor

 

 Read more about standard algorithms in Fuson and Beckmann's NCSM article (pictured). Links to an external site.

 

 

 

 

 

Progression of Standard within Grade 5

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
  • Use partial products to multiply multi-digit numbers.
  • Connect partial products to the standard algorithm for multiplication.
  • Explain the standard algorithm for multiplication of multi-digit numbers.
  • Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, and 4-digit by 2-digit factors.
  • Multiply multi-digit numbers using the standard algorithm.


  • Revisit with routines and independent work.

 

  • Revisit with routines and independent work. Make connections when teaching multiplying decimals and volume.
  • Revisit with routines and independent work. Make connections when teaching multiplying decimals and volume.

 

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 4 Grade 6
  • Fluently add and subtract multi-digit whole numbers using the standard algorithm (4.NBT.4)
  • Multiplication with multi-digit factors (4.NBT.5)
  • Fluently add, subtract, multiply, and divide decimals using the standard algorithm (6.NS.3)

 

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