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

Grade 4 GT Multiplication and Division

5.NBT.5

About the Math

Full Standard

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

 

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, 4-digit by 2-digit factors and 3-digit by 3-digit factors.

 

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 the area model showing partial products to explain the standard algorithm

  • Use partial products to multiply multi-digit numbers.
  • Connect partial products to the standard algorithm for multiplication.

Understanding of the algorithm for multiplying numbers is grounded in understanding of place value, decomposition, and the meaning of multiplication. Students must connect the algorithm to partial products. This happens first as students demonstrate understanding of partial products with factors of different sizes and complexities. 

  • 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, 4-digit by 2-digit factors and 3-digit by 3-digit factors.

Students use the algorithm to multiply multi-digit factors. Students should be able to explain what is happening within the algorithm and why the algorithm was a good choice for the numbers being multiplied. 

 

Essential vocabulary for this standard includes: standard algorithm, multiply, product, and factor. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

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

 

 

 

 

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 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, 4-digit by 2-digit factors and 3-digit by 3-digit factors.

 

  

 

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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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

  • Write a 3-digit by 1-digit multiplication problem with a product close to 2,000?
  • List two numbers whose product is between 400 and 600.
  • Is 4,000 a reasonable estimate for 312 x 9? Explain your reasoning.
  • How does the order of the digits in the factors impact the product? (e.g. 452 x 7 compared to 425 x 7)
  • In a multiplication problem, what happens to the product if each factor is multiplied by 2? What happens to the product if one factor is doubled and the other factor is divided by 2?
  • Is the product of 42 x 63 over or under 2,400? Use what you know about place value in the standard algorithm to explain your answer.
  • You multiply two two-digit numbers and the product is close to 2,600.What two numbers did you multiply?
  • Use 1,2,3,4,5 to make the a multiplication problem with the greatest product? How does the placement of the numbers impact the product?

 

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 2 • Multiplication and Division

Multiply Multi-Digit Numbers by 1-Digit Factors; Connect to the Standard Algorithm:

Multiply Multi-Digit Numbers by 2-Digit Factors; Connect to the Standard Algorithm:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

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 3-5 Expanded Lesson: Area Model for Multiplication, Pages 129-130 
 Nimble with Numbers 4-5

75-79

83-85 
Nimble with Numbers 5-6 60-61 "Unaligned Products"
69 "Finding Products Practice"
67-68 "Products Galore"
  Groundworks: Reasoning about Number 5 8-15 "Place It Right"
88-95 "Globs of Goo"
Brain-Compatible Activities for Mathematics 4-5 9-12 "Guess-timate Estimates"
13-15 "Point and Play"

 

 

 

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Independent Work

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.

 

 

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Assessment

Learning Targets

rubric

  • 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, 4-digit by 2-digit factors and 3-digit by 3-digit factors.6

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

 

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.