# MAFS.4.NBT.2.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

### Clarifications

Examples of Opportunities for In-Depth Focus

When students work toward meeting this standard, they combine prior understanding of multiplication and division with deepening understanding of the base-ten system of units to find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors. This work will develop further in grade 5 and culminate in fluency with the standard algorithms in grade 6.
General Information
Subject Area: Mathematics
Domain-Subdomain: Number and Operations in Base Ten
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Items may not require finding a quotient within the factor pairs of 10 x 10
• Calculator :

No

• Context :

No context

Sample Test Items (2)

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.4.NBT.2.AP.6a: Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors, using two different strategies.

## Related Resources

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

## Assessments

Sample 4 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 3 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 2 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 1 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

## 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

Dividing Using an Area Model:

Students are asked to interpret a division problem with a one-digit divisor that has been completed using an area model. If the student is successful, he or she is asked to complete a division problem with a one-digit divisor using an area model.

Type: Formative Assessment

Book Drive:

Students are asked to solve a division problem using a strategy based on place value.

Type: Formative Assessment

Interpreting Division:

Students are asked to analyze and explain another student’s division work in terms of a partial quotients strategy and to apply this strategy to another division problem.

Type: Formative Assessment

Dividing Using Place Value:

Students are asked to complete a division problem using place value.

Type: Formative Assessment

## Lesson Plans

"Life's a Breeze!":

In this Engineering Design Challenge, students must design a vessel that will carry passengers safely and quickly across a body of water by harnessing the power of the wind. Students will be given the opportunity to test and improve their vessels as they apply various math and science skills.

Type: Lesson Plan

Heating Up the Neighborhood:

This Engineering Design Challenge is intended to help students apply the concepts of heat insulators as they build a model house and test different materials to use as insulators, stopping the warm air from escaping and keeping the cool air out. Students will also have an opportunity to use technology in their exploration of heat energy.

Type: Lesson Plan

Set Sail with STEM: Exploring Wind and Water Movement as Energy with Sailboats:

Come sail away with this STEM activity! Students will use hands-on inquiry to find out more about wind and its effect on sails. Through trial and error and based on data collected, students will design, build, and race their own vessel or "sailboat" across the boundless waters of a kiddie pool. Students should gain a better understanding of how moving water and air are sources of energy and can propel objects forward at varying rates of speed.

Type: Lesson Plan

Dividing for Equal Groups:

This lesson is meant to help solidify division understanding before teaching the standard algorithm.  Given a situational story, students will use base 10 blocks to model division in order to solve problems. It may be used for 4th or 5th grade depending on the size of the divisor.

Type: Lesson Plan

I Love Leftovers!:

In this lesson, students will explore situational problems that address the different ways to interpret the remainder.

Type: Lesson Plan

I See! Division with the Distributive Property:

In this lesson, students will use visual models to represent division using the distributive property as a strategy. Students will have an understanding of how to decompose numbers in the context of division problems using an area model.

Type: Lesson Plan

Aaron and Anya's Quilt Challenge: Problem Solving and Interpreting Remainders:

In this situational story, Aaron and Anya find a large piece of brightly colored fabric. They decide to cut it into squares to make a quilt. Students will find the area of the fabric by multiplying two digits by two digits. They will explore factors as they figure out the largest quilt square that can be cut for 25 students. There will be fabric left over; students will have to determine and justify remainders based on several different scenarios. Finally, students will create their own quilt square using grid paper.

Type: Lesson Plan

Share and Share Alike:

This lesson is an introduction to division and does not include a procedural recording for division. The student will be able to physically model the division of 2-, 3-, and 4-digit dividends with 1-digit divisors using objects and base ten blocks and explain the meaning of a remainder.

Type: Lesson Plan

## Original Student Tutorials

CPALMS Aquarium: Part 3 Division with Larger Numbers:

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

Type: Original Student Tutorial

CPALMS Aquarium Part 2: Division Strategies:

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

Type: Original Student Tutorial

CPALMS Aquarium: Connecting Multiplication and Division: Part 1:

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.

This is part 1 of a two-part series. Click to open Part 2, Division Strategies.

Type: Original Student Tutorial

## Teaching Idea

Hand Spans, A Lesson for Third and Fourth Graders (Division and Measurement):

A measurement activity to give students experience with the grouping model of division and practice with rulers and tape measures.

Type: Teaching Idea

## Tutorials

Division: The importance of place value:

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

## MFAS Formative Assessments

Book Drive:

Students are asked to solve a division problem using a strategy based on place value.

Dividing Using an Area Model:

Students are asked to interpret a division problem with a one-digit divisor that has been completed using an area model. If the student is successful, he or she is asked to complete a division problem with a one-digit divisor using an area model.

Dividing Using Place Value:

Students are asked to complete a division problem using place value.

Interpreting Division:

Students are asked to analyze and explain another student’s division work in terms of a partial quotients strategy and to apply this strategy to another division problem.

## Original Student Tutorials Mathematics - Grades K-5

CPALMS Aquarium Part 2: Division Strategies:

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

CPALMS Aquarium: Connecting Multiplication and Division: Part 1:

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.

This is part 1 of a two-part series. Click to open Part 2, Division Strategies.

CPALMS Aquarium: Part 3 Division with Larger Numbers:

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

## Student Resources

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

## Original Student Tutorials

CPALMS Aquarium: Part 3 Division with Larger Numbers:

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

Type: Original Student Tutorial

CPALMS Aquarium Part 2: Division Strategies:

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

Type: Original Student Tutorial

CPALMS Aquarium: Connecting Multiplication and Division: Part 1:

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.

This is part 1 of a two-part series. Click to open Part 2, Division Strategies.

Type: Original Student Tutorial

## 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

## Tutorials

Division: The importance of place value:

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

## Parent Resources

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

## Tutorials

Division: The importance of place value:

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial