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

Grade 4 Multiplication and Division

4.NBT.5

Full Standard

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

 

Measurement Topic

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

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

 

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Report Card Measurement Topic: Demonstrates understanding of multiplication.

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

 

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Learning Target

  • Explain and represent multiplication of a multi-digit factor by a one-digit factor.
  • Use partial products to multiply a multi-digit factor by a one-digit factor (decomposing one or both factors).
  • Explain and represent multiplication of a two-digit factor by a two-digit factor.
  • Use partial products to multiply a two-digit factor by a two-digit factor (decomposing one or both factors).
  • Write an equation for multiplication situations.

 

About the Math

Array/Area drawing of 8 x 549Multiplication can be represented by arrays, area models, or by equal jumps on a number line. Note that as factors change the notion of repeated addition loses its value and efficiency. Use of repeated addition with multi-digit factors should be avoided.  In order to teach the multiplication algorithm in 5th grade with understanding, models must be used to explain the procedure for using the standard algorithm. The area model can be used to model partial products. Students should also record partial products with equations or the partial products algorithm.

  • Explain and represent multiplication of a multi-digit factor by a one-digit factor.

There is a clear progression of the size of factors across grade 4 beginning with 2-digit factors and proceeding to 3 and 4-digits.

  • Use partial products to multiply a multi-digit factor by a one-digit factor (decomposing one or both factors).

We can decompose one or both factors to find partial products. Factors can be decomposed in a myriad of ways. Students should be able to justify the decompositions that they make. For example, 26 x 4 can be thought of as (20 x 4) + (6 x 4). However, it is likely more efficient to think of it as (25 x 4) + (1 x 4).

  • Explain and represent multiplication of a two-digit factor by a two-digit factor.
  • Use partial products to multiply a two-digit factor by a two-digit factor (decomposing one or both factors).

Multiplication in grade 4 progresses to two, two-digit factors. Students should use partial products with these factors. One or both factors can be decomposed. It makes sense to decompose both factors at first before beginning to work with the decomposition of one (as appropriate). 

  • Write an equation for multiplication situations.

Students represent multiplication situations and problems with equations. Students should connect their equations to their representations and problems. This is especially needed for developing an understanding of partial products. It is also important that multiplicative comparison is featured in this work. 

Essential vocabulary for this standard includes: partial products,  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 4

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 and represent multiplication of a two-digit factor by a one-digit factor.
  • Use partial products to multiply a two-digit factor by a one-digit factor (decomposing one or both factors).
  • Write an equation for multiplication situations.

 

Multiply 2-digit factors by 1-digit factors, 3-digit factors by 1-digit factors, and 4-digit by 1-digit

  • Explain and represent multiplication of a multi-digit factor by a one-digit factor.
  • Explain and represent multiplication of a two-digit factor by a two-digit factor.
  • Use partial products to multiply a multi-digit factor by a one-digit factor and a two-digit factor by a two-digit factor (decomposing one or both factors).

 

Multiply 3-digit factors by 1-digit factors, 4-digit by 1-digit and 2-digit by 2-digit factors

  • Use partial products to multiply a multi-digit factor by a one-digit factor (decomposing one or both factors).
  • Use partial products to multiply a two-digit factor by a two-digit factor (decomposing one or both factors).

 

Multiply 2-digit, 3-digit, or 4-digit factors by 1-digit factors and 2-digit by 2-digit numbers

 

 

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 3 Grade 5
  • Add/subtract within 1000 (3.NBT.2)
  • Multiply one-digit whole numbers by multiples of 10-90 (3.NBT.3)
  • Commutative, Associative, Distributive Properties (3.OA.5
  • Fluently x/÷ facts (3.OA.7)
  • Fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5)

 

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