Grade 4 Multiplication and Division

4.NBT.5

About the Math

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 549 Multiplication 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).

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. 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)

Back to Top

Instructional Tasks

TASKS

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

Instructional Materials for the various computation strategies can be found in Figuring Out Fluency Multiplication and Division with Whole Numbers (this book has been provided to schools) as follows:

Screenshot 2023-10-10 at 11.47.13 AM.png — Book Cover for Figuring Out Fluency Multiplication and Division with Whole Numbers

- Break Apart to Multiply-- pages 22-30
- Halve and Double to Multiply-- pages 44-50
- Compensation-- pages 62-67
- Partial Products-- pages 80-88

Use the beta version of the Partial Product Finder to create a 2 digit by 2 digit equation. Allow students to explore by manipulating the horizontal and vertical bars on the virtual mantipulative. What do they notice, what do they wonder? Allow students to make connections to what they remember about multi-digit multiplication computation.
Give students base ten blocks and ask them to represent 3x8 with a rectangular array (3 rows of 8 or 8 rows of 3 unit cubes). Have students push the unit cubes together and discuss how this is now a representation of area (no gaps showing 8x3/3x8). Ask students to now use the base ten blocks to represent 15x6. Repeat with other 2 digit x 1 digit and 3 digit x 1 digit examples. The purpose of these representations is for students to connect their previously taught concepts of area and distributive property to multi-digit multiplication and the partial products strategy. Representations with 2-digit by 2-digit can be made when working in module 12.
How many different ways can you solve 289 x 8? 94 x 64?
What two factors can be multiplied to result in a product of 126?
Create two multiplication sentences that could create a product between 200 and 500?
How does the order of the digits in the factors impact the product? (e.g., 452 x 7 compared to 425 x 7)
Is the product of 29 x 34 over or under 900? Explain how you know.
Think of an example in life when you might multiply two numbers? An example is, when might you multiply two two-digit numbers? Or a three-digit number by a one digit number.

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 6 • Multiplication and Division (2-Digit by 1-Digit) and Connect Basic Facts Review (8s) to Factors and Multiples

Multiply 2-digit numbers by 1-digit numbers using representations and partial products:

Module 7 • Multiplication & Division (3- and 4-Digit by 1-Digit)

Multiply 3-digit by 1-digit numbers using representations and partial products:

Module 12 • Multiplication (2-Digit by 2-Digit) & Division and Solve Multiplication and Division Problems

Multiply 2-digit by 2-digit factors using representations and partial products:

Module 15 • Measurement and Problem Solving

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

Multiply 2-digit by 2-digit factors:

Additional Tasks

These links provide instructional ideas connected to this standard.

Array-bow of Colors (3 Act Task, G.Fletcher)
Place Value Understanding (ppt)
Brain Only! (Georgia Dept. of Education, pg. 85-89)
Boxes and Rolls (Georgia Dept. of Education, pg.96-102)
Storing Fossils (Utah Core Academy Lesson)
Recess Refreshments (Utah Core Academy Lesson)
Collection Conundrum (Utah Core Academy Lesson)
Supply List (Utah Core Academy Lesson)
Pioneer Packing (Utah Core Academy Lesson)
Long Journey (Utah Core Academy Lesson)

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 Title	Grade	Pages
Teaching Student-Centered Mathematics	3-5	Expanded Lesson Area Model for Multiplication, Page 129
Hands-On Standards	3-4	104-105 (Commutative Property) 108-109 (Associative Property) 30-31 (Multiplication with Two-Digit Numbers)
20 Thinking Questions for Base 10 Blocks		78
Developing Mathematics with Base Ten	2-6	44-46 67-70
Fundamentals	3-4	40 (Climb the Ladders)
Math Intervention: Building Number Power	3-5	118-120 124-128
NumberSense	4-6 3-4	36-37 and 40-42 92-96
Roads to Reasoning	4	5, 7, 10, 11 61 and 69
Mental Math in the Middle Grades		79-84 (Understanding Trailing Zeros) 97-98 (Halving and Doubling)
Math In Practice Teaching Fourth-Grade Math	4	Module 5

Back to Top

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Area Model Puzzles (2-digit by 1-digit and 2-digit by 2-digit) (HCPSS created)
Doubles and Halves (HCPSS-adapted print resource)
Break Apart a Factor to Multiply (HCPSS-adapted print resource)
Greatest Product (2x2) (HCPSS-adapted print resource)
Greatest Product (3x1) (HCPSS-adapted print resource)
Greatest Product (4x1) (HCPSS-adapted print resource)
Multiplication Pop (HCPSS-adapted print resource)
Multiplication Show and Tell (HCPSS-adapted print resource)
Least Product (2x2) (HCPSS-adapted print resource)
Least Product (3x1) (HCPSS-adapted print resource)
Least Product (4x1) (HCPSS-adapted print resource)
The Great Chase Race (HCPSS-adapted print resource)
Tic Tac Times (HCPSS-adapted print resource)
Partial Products Tutorial (LearnZillion ppt)

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.

Multiply 2-digit numbers by 1-digit numbers using representations and partial products:

Multiply 3-digit and 4-digit numbers by 1-digit numbers using representations and partial products:

Multiply 2-digit numbers by 2-digit numbers using representations and partial products:

Review: Apply Strategies to Multiply Efficiently

Back to Top

Assessment

Learning Targets

rubric

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.

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

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

Back to Top