# MA.3.NSO.2.4

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.)
Strand: Number Sense and Operations
Status: State Board Approved

## Benchmark Instructional Guide

### 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).

### 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.

• 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.

• 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.

• 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

This benchmark is part of these courses.
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

Alternate version of this benchmark for students with significant cognitive disabilities.
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

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Educational Game

Arithmetic Workout:

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

Type: Educational Game

## Educational Software / Tool

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.

Type: Educational Software / Tool

## Formative Assessments

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.

Type: Formative Assessment

Fluency with Multiplication:

Students are assessed for fluency with multiplication.

Type: Formative Assessment

Fluency with Division:

Students are assessed for fluency with division.

Type: Formative Assessment

Using Flexible Strategies:

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

Type: Formative Assessment

Fluency with Basic Multiplication Facts:

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

Type: Formative Assessment

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.

Type: Formative Assessment

## Lesson Plans

Bridging Multiplication with Word Problems:

This introductory lesson uses word problems to help students make connections between arrays and multiplication with single and two-digit factors within 100.

Type: Lesson Plan

How Long is Your Music Lesson?:

In this Model Eliciting Activity, MEA, students will be required to rank musical instrument lesson packages based on the price, the number of minutes of practice each week, and the quality of the instructor.

Part of the task involves students figuring out the elapsed time of the lessons based on their start and stop times. They will also need to figure out the total weekly cost of the lessons based on the number of lessons offered per week and the cost of each lesson based on its length.

The twist will require students to determine whether or not to revise their ranking based on new information about the cost of instrument rentals per lesson and the class size of each package.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

## Perspectives Video: Expert

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.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Idea

Representing Remainders as Fractions:

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

Type: Perspectives Video: Teaching Idea

## STEM Lessons - Model Eliciting Activity

How Long is Your Music Lesson?:

In this Model Eliciting Activity, MEA, students will be required to rank musical instrument lesson packages based on the price, the number of minutes of practice each week, and the quality of the instructor.

Part of the task involves students figuring out the elapsed time of the lessons based on their start and stop times. They will also need to figure out the total weekly cost of the lessons based on the number of lessons offered per week and the cost of each lesson based on its length.

The twist will require students to determine whether or not to revise their ranking based on new information about the cost of instrument rentals per lesson and the class size of each package.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

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.

## MFAS Formative Assessments

Fluency with Basic Multiplication Facts:

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

Fluency with Division:

Students are assessed for fluency with division.

Fluency with Multiplication:

Students are assessed for fluency with multiplication.

Using Flexible Strategies:

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

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.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Educational Game

Arithmetic Workout:

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

Type: Educational Game

## Educational Software / Tool

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.

Type: Educational Software / Tool

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.