# MA.4.NSO.2.1

Recall multiplication facts with factors up to 12 and related division facts with automaticity.
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

• Associative Property of Multiplication
• Commutative Property of Multiplication
• Distributive Property
• Factor

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to be able to state (recall) their multiplication and division facts in an effortless manner. This work builds on prior multiplication and related division fact strategy work from grade 3 (MA.3.NSO.2.4). Students also understand that multiplication is commutative and that the Distributive Property can be used to break more complex facts into easier ones.
• To help reach the automaticity of multiplication and related division facts, the related concepts should be considered to be foundational. These concepts may be addressed during the exploration or procedural reliability stage (MA.3.NSO.2.4) of the benchmark progression.
• Multiplication by zeroes and ones
• Doubles (2s facts)
• Double and Double Again (4s)
• Doubling three times (8s)
• Tens facts (relating to place value, 5 × 10 is 5 tens or 50)
• Five facts (half of tens or connect to the analog clock)
• Skip counting (counting groups of __ and knowing how many groups have been counted)
• Square numbers (the physical and visual representation of these facts make a square; e.g., 3 × 3)
• Nines (10 groups less 1 group; e.g., 9 × 3 is 10 groups of 3 minus 1 group of 3 so 30– 3 = 27)
• Decomposing into known facts (6 × 7 is a double - 6 × 6 - plus one more group of 6)
• Elevens (10 groups and 1 group more; e.g., 11 × 5 is 10 groups of 5 plus 1 group of 5 so 50 + 5 = 55)
• Decomposing using the Distributive property (12 × 6 = (10 × 6) + (2 × 6) = (60) + (12) = 72)
• Throughout K-5 instruction, it is not recommended to use timed fact fluency assessments to learn and practice facts.

### Common Misconceptions or Errors

• Many students have difficulty with multiplication and related division facts when teachers rely solely on memorization of facts. It is important that strategy work and conceptual understanding is the foundation of instruction for multiplication and division facts.

### Strategies to Support Tiered Instruction

• Instruction includes building strategies and conceptual understanding to recall facts to find unknown multiplication facts by using known facts.
• For example, if students do not know the product for 9 × 12 have them use a known fact such as 10 × 12. The known fact of 10 × 12 = 120 can be used to find the product of 9 × 12 by subtracting one more group of 12 from the product of 120 to find the product of 108.
• For example, if students do not know the product for 6 × 7 have them use a known fact such as 5 × 7. The known fact of 5 × 7 = 35 can used to find the product of 6 × 7 by adding one more group of 7 to the product of 35 to find the product of 42.
• Instruction includes building strategies and conceptual understanding to recall facts to find unknown division facts by using known multiplication facts.
• For example, if students do not know the quotient for 121 ÷ 11 have them think about how many groups of 11 equal 121. Have students write the problem as a missing factor problem __ × 11 = 121 to help use multiplication facts to find the quotient. Students can also use known multiplication facts to solve: 10 groups of 11 is 110 and one more group of 11 equals 121 so 121 ÷ 11 equals 11.
• For example, if students do not know the quotient for 45 ÷ 5 have them think about how many groups of 5 equal 45. Have students write the problem as a missing factor problem ___ × 5 = 45 to help use known multiplication facts to find the quotient.

• Explain how the 2s facts, 4s facts, and 8s facts for multiplication are related.

### Instructional Items

Instructional Item 1

Select all the true equations.
• a. 11=132÷11
• b. 7×12=84
• c. 56=7×7
• d. 49÷7=7
• e. 6×11=66

*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.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (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.4.NSO.2.AP.1: Recall multiplication facts of one-digit whole numbers multiplied by 1, 2, 5 and 10.

## Related Resources

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

## Educational Games

Arithmetic Workout:

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

Type: Educational Game

Ice Ice Maybe: An Operations Estimation Game:

This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

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

## Lesson Plans

Making Sense of Multiplication to Build Fluency of 6's, 7's, 8's, and 9's:

This lesson will help students multiply numbers with factors of 6, 7, 8, or 9 through decomposing numbers in an array and applying the distributive property. Many times, these factors are difficult for students to recall from memory. Teaching students how to use an array can give them a visual representation of the final product. This visual can also help students to make the connection that multiplying whole numbers is a sum of equal groups. Decomposing the numbers and using the distributive property is a strategy for students to use who are having trouble solving these higher factor multiplication facts.

Type: Lesson Plan

Factor Word Challenges:

Students will apply multiplication, division and factor knowledge to word problems.

Type: Lesson Plan

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

Type: Lesson Plan

Fun with Factors:

This is an introductory lesson addressing factors for number 1-20. Factoring will lead students to discover differences and similarities between prime and composite numbers. Students will also discuss five claims about factors, prime, and composite numbers and create support from examples and non-examples to determine whether these claims are valid or invalid.

Type: Lesson Plan

## Perspectives Video: Experts

Fluency vs. Automaticity:

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: 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

What is Automaticity?:

What does automaticity look like? What is the role of automaticity in mathematics? Dr. Lawrence Gray explores what it means for students to have automaticity with basic mathematics facts in this Expert Perspectives video.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Idea

The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Type: Perspectives Video: Teaching Idea

Bowling for Numbers:

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.

## Teaching Idea

A Square of Numbers (problem to solve using addition, subtraction, multiplication, division):

A problem for students to solve using students' understanding of the operations of addition, subtraction, multiplication, and division. The problem presents an opportunity for students to appreciate the value of approaching a solution in a systematic way using what they know about the structure of operations.

Type: Teaching Idea

## STEM Lessons - Model Eliciting Activity

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

## Student Resources

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

## Educational Games

Arithmetic Workout:

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

Type: Educational Game

Ice Ice Maybe: An Operations Estimation Game:

This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

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.