Standard #: MA.3.NSO.2.4


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Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.


Examples


Example: The product of 5 and 6 is 30.

Example: The quotient of 27 and 9 is 3.



Clarifications


Clarification 1: Instruction focuses on helping a student choose a method they can use reliably.

General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Number Sense and Operations
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

Terms from the K-12 Glossary

  • Expression 
  • Equation 
  • Factor 
  • Dividend 
  • Divisor 
  • Commutative property of multiplication 
  • Associative property of multiplication 
  • Distributive property of multiplication

Vertical Alignment

Previous Benchmarks

Next Benchmarks

Purpose and Instructional Strategies

The purpose of this benchmark is for students to utilize skills from the exploration stage of multiplication and division (MA.3.NSO.2.2) to develop an accurate, reliable method that aligns with the student’s understanding and learning style. Procedural fluency of multiplication facts with factors up to 12 and their related division facts is not expected until Grade 4 (MTR.2.1, MTR.3.1). 
  • This benchmark provides the opportunity for students to generalize patterns they see within the tools used during the exploration stage (e.g., rectangular arrays, equal groups) to then identify multiplication and related division facts (MTR.4.1). 
  • Instruction that builds procedural reliability should connect multiplication understanding with the properties of multiplication (commutative, associative and distributive). The patterns students recognize help them relate facts to one another, and to use the related facts to find the products and quotients of unknown facts. In this benchmark, students should be able to explain how they know facts and how they can find products of unknown facts (MTR.5.1). For example, students should recognize that 4 x 6 and 6 x 4 have the same product of 24 and identify this pattern as evidence of the commutative property of multiplication. This can also be discovered through arrays for multiplication using objects or drawings, where students can observe that the arrays contain the same total number of squares, but the orientation of the array has just rotated so the rows and columns are switched as shown below (MTR.5.1).

counters

Common Misconceptions or Errors

  • This benchmark does not support students’ memorization of multiplication and division facts. Memorization does not indicate work toward multiplication and division fact fluency. Students should be able to explain how they know multiplication and division facts, and how they can find products and quotients of unknown facts.

Strategies to Support Tiered Instruction

  • Instruction includes opportunities to experience the properties of multiplication and division. Students use and apply properties to build procedural fluency. Students should understand that multiplication and division both involve grouping equal sets of numbers or objects. 
    • For example, the teacher shows students an array of 8 × 6 = 48 and has them describe what they see with rows and columns. This learning can be connected to the concept of “groups of” objects, 8 groups of 6 is the same as 8 jumps of 6 on the number line.

an array of 8 × 6 = 48

  • Teacher provides opportunities to build and manipulate what a multiplication fact looks like and then relates how it looks as division. 
    • For example, students model 3 x 4 as 3 rows of 4 with counters. 

 rows of 4 with counters

    • The teacher then relates the multiplication model to division by separating the rows into groups. 12 = 4 groups of 3 counters, or 12 divided by 4 = 3.

3 groups of 4 counters

Instructional Tasks

Instructional Task 1 

  • Part A. Show how to find the product of 6 × 7 in two different ways. 
  • Part B. Identify the related division facts from your equation in Part A.

Instructional Items

Instructional Item 1 

  • What is the product of 11 and 4? 

Instructional Item 2 

  • Provide two division facts that have a quotient of 8. 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.


Related Courses

Course Number1111 Course Title222
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.3.NSO.2.AP.4 Explore the relationship between multiplication and division in order to multiply and divide. Multiplication may not exceed two single-digit whole numbers and their related division facts.


Related Resources

Educational Game

Name Description
Arithmetic Workout

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game. 

Educational Software / Tool

Name Description
Arithmetic Quiz

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Formative Assessments

Name Description
What Does the Six Mean?

Students are given division word problem and asked to determine how it might have been solved and what the quotient means.

Fluency with Multiplication

Students are assessed for fluency with multiplication.

Fluency with Division

Students are assessed for fluency with division.

Using Flexible Strategies

Students are asked to describe two different ways to find the product of two numbers.

Fluency with Basic Multiplication Facts

Students are assessed on their fluency with multiplication facts for the products of two one-digit numbers.

What does the 21 mean?

Students are given a context for a multiplication problem and asked to determine how to solve it and what the product means.

Lesson Plans

Name Description
Kites for Education MEA

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

Amazing Arrays

This is a hands-on lesson for introducing and practicing building arrays to create models that represent the distributive property of multiplication, and then using those arrays to draw models of the equations they represent.

Way Too Much!

In this lesson, students will learn that in some word problems too much information is given. They will learn to identify what information is needed to solve a single digit multiplication problem and what is "additional information" or way too much! With this information, they will represent their answers using arrays and explain their thinking. This is a good lesson to use after students have become comfortable with multiplication and prior to introducing multi-step problems.

Perspectives Video: Expert

Name Description
B.E.S.T. Journey

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Perspectives Video: Teaching Idea

Name Description
Representing Remainders as Fractions

Unlock an effective teaching strategy for representing remainders as fractions in this Teacher Perspectives video for educators.

Student Resources

Educational Game

Name Description
Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game. 

Educational Software / Tool

Name Description
Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.



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