Standard 1 : Use place value understanding and properties of operations to perform multi-digit arithmetic. (Additional Cluster) (Archived)



This document was generated on CPALMS - www.cpalms.org


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.

General Information

Number: MAFS.3.NBT.1
Title: Use place value understanding and properties of operations to perform multi-digit arithmetic. (Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 3
Domain-Subdomain: Number and Operations in Base Ten

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.3.NBT.1.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
MAFS.3.NBT.1.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Clarifications:

Students fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (Although 3.OA.3.7 and 3.NBT.1.2 are both fluency standards, these two standards do not represent equal investments of time in grade 3. Note that students in grade 2 were already adding and subtracting within 1000, just not fluently.
That makes 3.NBT.1.2 a relatively small and incremental expectation. By contrast, multiplication and division are new in grade 3, and meeting the multiplication and division fluency standard 3.OA.3.7 with understanding is a major portion of students’ work in grade 3.)

MAFS.3.NBT.1.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.3.NBT.1.AP.1a: Use place value to round to the nearest 10 or 100.
MAFS.3.NBT.1.AP.2a: Use the relationships between addition and subtraction to solve problems.
MAFS.3.NBT.1.AP.2b: Solve multi-step addition and subtraction problems up to 100.
MAFS.3.NBT.1.AP.3a: Multiply one-digit numbers by 10, 20, and 50.


Related Resources

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

Original Student Tutorials

Name Description
Rounding Whole Numbers Part 2: To the Nearest Hundred:

Help Barkley learn to round numbers to the nearest hundred and bury delicious bones in this dog-themed, interactive tutorial.

Click HERE to open "Rounding Whole Numbers Part 1: To the Nearest Ten" 

Rounding Whole Numbers Part 1: To the Nearest Ten:

Help Barkley learn how to round numbers to the nearest ten with this interactive tutorial.

Multiplying By Multiples of Ten: Part 2 :

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Multiply By Multiples of Ten: Part 1 :

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

Speedy Sam:

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial. 

Rounding Party:

Learn how to round two-, three-, and four-digit numbers to the nearest 10 or 100 in this party-themed, interactive tutorial.

Educational Games

Name Description
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.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

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.

Estimator Four:

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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.

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. 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.

Educational Software / Tools

Name Description
Hundreds Chart:

A printable hundreds chart featuring a 10x10 table numbered 1 to 100. (found on Illuminations website under "Trading for Quarters")

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
Packages of 50:

Students consider the solution to a multiplication problem and explain their thinking.

Multiplying by Multiples of Ten:

Students are asked to explain how the knowing the product of nine and three can help in finding the product of nine and 30.

Explaining Multiplication Using Multiples of Ten:

Students are asked to explain why, when multiplying by a power of 10, the product has a zero in the ones place.

How Are These Two Problems Related?:

Students are asked to consider how using an easier, known fact could help them solve a related multiplication problem with a multiple of 10.

Rounding to the Nearest 10:

Students round one- to four-digit numbers to the nearest 10.

The Smallest and Largest Numbers Possible:

Student are asked to find the smallest and largest possible numbers that will round to given values.

Rounding to the Nearest Hundred:

Students round two-, three-, and four-digit numbers to the nearest hundred.

Mystery Number Rounding Problem:

The student determines the value of a number which when rounded to the nearest 10 and to the nearest 100 is 300.

Wanda's Method:

The student is encouraged to use compensation to efficiently add multi-digit numbers.

Subtraction Within 1000:

Students are asked to complete four subtraction problems (within 1000) using strategies of their own choosing.

Adding and Subtracting Using Properties:

Students are asked to complete addition and subtraction problems that can be done more easily by using properties.

Addition Within 1000:

Students are asked to add four different pairs of numbers (within 1000) using strategies of their own choosing.

Lesson Plans

Name Description
Terrarium:

In this lesson plan students are challenged with building a self-sufficient terrarium.

Zoom, Zoom, Vroom Vroom!:

In this lesson, students will explore forces, kinetic energy, and potential energy by engineering their own vehicles utilizing via the engineering design process.

Blowin' Around the House:

In this engineering design challenge, student teams will design a house that will withstand high winds.

DOLO - Dinosaurs Only Live Once?:

During this activity, students will create an incubator to save the last dinosaur eggs. Students will use their knowledge of energy to develop a strategy and choose which materials would be best for their dinosaur egg incubator.

Fishing for Multiples of 10:

This lesson introduces students to multiplying one-digit numbers by multiples of 10. It is a guided inquiry lesson where students will be building array's using base-ten blocks and the concepts of place-value.

Astounding Addition:

In this lesson, students will explore and demonstrate various addition strategies within 1000.

Tens, Tens, and More Tens:
In this lesson, students will practice using various strategies for multiplying one digit numbers by multiples of ten.
Party Planning: Using Multiplication:

As the end of the year approaches, and your students have already learned several multiplication strategies, this party planning activity can help put all of that hard work into action. Students will be asked to use a menu and catalog to purchase food, decorations and goody bag items for an upcoming party. (I use this right before our end of the year 3rd Grade Luau Party, and have students purchase items that correlate with that theme. However, it can be used to plan an ideal birthday party, 4th of July Celebration, family reunion, etc.) After working together as a whole group, children will work with a partner and, ultimately independently, to solve one and two-digit multiplication and addition problems. Your students will get a chance to be creative and apply multiplication strategies to real world scenarios.

Ten, Ten, We All Win!!!!!:

In this lesson, students should be able to grasp the concept of multiplying one-digit numbers by 10 in the range of 10-90 using strategies based on place value and properties of operations.

I'm Hot He's Not:

In this lesson, students will demonstrate knowledge of Place Value to round whole numbers to the nearest 10 and 100 using the following strategies: Number line, number strip, Counting on and back. Students will be given three problems to demonstrate the relationship of nearness on a number line in three of the four strategies learned to round whole number to the nearest 10 or 100.

Food Delivery to Grandma's House:

Through playing a game, the students use the number line as a model to help them integrate the use of place value to round numbers to the nearest tens.

Rockin' Road Trip MEA:

In this model-eliciting activity (MEA), students will work together to determine the best bus for a class trip.  Students will be able to decide between several buses with varying capabilities and costs while practicing their application of multiplying one-digit whole numbers by a multiple of ten.

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. Click here to learn more about MEAs and how they can transform your classroom.

Reading is Fun!:

In this MEA, students will work in groups to rank books using the following criteria: price, genre, number of pages, reading level and a summary provided for each book. The students must calculate the price for a class set of each book by multiplying each price by 20 students. There is a budget of $100. Students are then given a new budget and a new criteria and asked to re-evaluate their decision.

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. Click here to learn more about MEAs and how they can transform your classroom.

Peace Love Baseball:

Batter Up!!! Help the Peace Love Baseball Championship find a home!!! In this interactive Model-Eliciting Activity (MEA), the students will successfully multiply one digit whole numbers by multiples of 10. The students will also work collaboratively to express their opinions, while considering those of their peers.

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. Click here to learn more about MEAs and how they can transform your classroom.

What Decade is It? - Rounding Whole Numbers to the Nearest 10:

In this lesson, students will tap prior knowledge of place value and dimes to round numbers to the nearest 10. Students will use number lines with tick marks in increments of 10 to visualize the closer decade and then progress to using the place value of numerals to round to the tens place. Pairs of students will participate in a rounding activity using a number line.

Rounding for Decades:

By using prior skip-counting knowledge, place value, and number lines, students will learn how to round to the nearest ten.

Perfect Pool Plans:

Students will help select the perfect pool construction company to build pools for a vacation housing development. They will have to look at several factors and come up with a plan to find a company that meets the needs of their client.

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. Click here to learn more about MEAs and how they can transform your classroom.

Multiply by Multiples of 10 with Number Cubes:

In this lesson students will use various strategies to multiply one-digit numbers by multiples of 10 within the range of 10-90. The strategies will encompass the Distributive, Commutative, and Associative properties, place value, number lines, base-ten blocks, diagrams, hundreds chart. Students will play a game with number cubes to practice this multiplication.

Dining Dilemma!:

The students will compare different nutritional content of chicken nuggets from many restaurants. They will factor in the calories, the total fat, saturated fat, and sodium levels in the nuggets to rank the nuggets from healthiest to least healthy.

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. Click here to learn more about MEAs and how they can transform your classroom.

Jumping Beans: Adding with Open Number Lines:

Students will use the open number line as a strategy to add within 1,000. The lesson begins with a formative assessment that evaluates students' strategies for efficiently solving addition sentences within 1,000. In order for students to have practice reinforcing the skill, students will complete the guided practice with open number lines, as well as playing the game, Jumping Beans. To conclude the lesson, students will evaluate a solution to an open number line problem.

Rounding Round and Round:

In this lesson, students will gain fluency with rounding numbers to the nearest 10s and 100s place. The lesson has number lines to help students understand rounding.

Round the Number Line:

The focus of this lesson is to find the halfway point and use it to round numbers.  The lesson rounds numbers 0 to 100 to the nearest ten and 0 to 1000 to the nearest ten and hundred. 

Decoding Decomposing {Adding two 3-digit Numbers}:

Students will add 3-digit numbers by decomposing them by place value.  It is a useful lesson to reinforce place value concepts when adding.

How Did the Baby Chick Cross the Road to Rounding?:

In this lesson, students will engage in tellling jokes and doing outside activities to discover rounding concepts. Students will use a vertical number line to round numbers from 0 to 1,000.

How Many Seeds in a Pumpkin?:

In this hands-on math exploration, students will use knowledge of estimation and multiplication to develop strategies for estimating how many seeds are in a medium-sized pumpkin.

Lunchroom Logistics:

The principal needs help planning the school lunch schedule!  Students will plan a lunch schedule to accommodate all of the students in the school.  However, there can only be 100 students in the cafeteria at a time and only 20 students can sit at a table.  Students will figure out how to arrange the lunch schedule so that every class eats together and so that certain grade levels are not together at the same time.

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. Click here to learn more about MEAs and how they can transform your classroom.

Rounding Relay:

This lesson uses a relay game  to provide students with practice for their rounding skills.

Lesson Study Resource Kit

Name Description
Number and Operations in Base Ten Lesson Study Resource Kit - Third Grade: This lesson study resource kit can be used to guide and support teams of third grade teachers as they engage in lesson study focused on the academic standards in the Number and Operations in Base Ten domain.

Problem-Solving Tasks

Name Description
Rounding to 50 or 500:

The purpose of this task is to answer multiple questions regarding rounding. There still may be students who laboriously list every number; the teacher should encourage a more thoughtful approach.

Classroom Supplies:

The purpose of this task is for students to "Solve problems involving the four operations" (3.OA.A) and "Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories" (3.MD.3).

Student Center Activity

Name Description
Edcite: Mathematics Grade 3:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Teaching Ideas

Name Description
More Place Value Activities:

This webpage contains instructions for several activities and games designed to develop students' understanding of place value while reinforcing addition and subtraction skills. Downloadable materials and suggestions for variations are included along with links to online games. This is the second of two pages of similar activities. The first, Place Value Activities, is cataloged separately.

Shamu Math-SeaWorld Classroom Activity: In this activity, the students demonstrate that numbers can be used to describe various quantities and relationships between quantities. Students gain experience adding, subtracting, multiplying, and dividing - building their understanding of how numbers are put together and taken apart. Students connect what they know to symbolic representation using number sentences.
Popcorn Math: This webpage features 8 popcorn-themed math activities that can be used at various grade levels. Topics covered include volume, estimating, graphing, measuring, and place value.

Tutorials

Name Description
Subtracting: regrouping twice:

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Examples rounding to the nearest 10 and 100:

In this Khan Academy video tutorial, see examples of how to round up to four-digit numbers to the nearest ten and hundred.

Rounding to the nearest 100:

In this Khan Academy video tutorial, use a number line to round three-digit numbers to the nearest hundred.

Rounding to the nearest 10:

In this Khan Academy video, use a number line to round two-digit numbers to the nearest ten.

Mental technique for subtraction without regrouping:

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Subtracting hundreds, tens, and ones:

In this Khan Academy video tutorial, learn how to subtract three-digit numbers by subtracting ones, tens, and hundreds represented with base ten blocks and the standard algorithm.

Subtracting ten or one hundred:

In this video tutorial from Khan Academy, learn how to subtract 1, 10, or 100 from a three-digit number while making a connection between the standard algorithm and a concrete representation using base ten blocks.

Adding hundreds, tens, and ones:

In this video tutorial from Khan Academy, learn how to add three-digit numbers by adding ones, tens, and hundreds by thinking about the connection between base ten block representation and the standard algorithm.

Adding ten or one hundred:

In this video tutorial from Khan Academy, learn how to add 10 or 100 to a number using base ten blocks.

Virtual Manipulative

Name Description
Quick Math: This interesting game requires the learners to think fast and click on the correct symbol to complete the equation as quickly as possible.


Student Resources

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

Original Student Tutorials

Title Description
Rounding Whole Numbers Part 2: To the Nearest Hundred:

Help Barkley learn to round numbers to the nearest hundred and bury delicious bones in this dog-themed, interactive tutorial.

Click HERE to open "Rounding Whole Numbers Part 1: To the Nearest Ten" 

Rounding Whole Numbers Part 1: To the Nearest Ten:

Help Barkley learn how to round numbers to the nearest ten with this interactive tutorial.

Multiplying By Multiples of Ten: Part 2 :

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Multiply By Multiples of Ten: Part 1 :

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

Speedy Sam:

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial. 

Rounding Party:

Learn how to round two-, three-, and four-digit numbers to the nearest 10 or 100 in this party-themed, interactive tutorial.

Educational Games

Title Description
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.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

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.

Estimator Four:

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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.

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. 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.

Educational Software / Tools

Title Description
Hundreds Chart:

A printable hundreds chart featuring a 10x10 table numbered 1 to 100. (found on Illuminations website under "Trading for Quarters")

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.

Problem-Solving Tasks

Title Description
Rounding to 50 or 500:

The purpose of this task is to answer multiple questions regarding rounding. There still may be students who laboriously list every number; the teacher should encourage a more thoughtful approach.

Classroom Supplies:

The purpose of this task is for students to "Solve problems involving the four operations" (3.OA.A) and "Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories" (3.MD.3).

Student Center Activity

Title Description
Edcite: Mathematics Grade 3:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Tutorials

Title Description
Subtracting: regrouping twice:

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Examples rounding to the nearest 10 and 100:

In this Khan Academy video tutorial, see examples of how to round up to four-digit numbers to the nearest ten and hundred.

Rounding to the nearest 100:

In this Khan Academy video tutorial, use a number line to round three-digit numbers to the nearest hundred.

Rounding to the nearest 10:

In this Khan Academy video, use a number line to round two-digit numbers to the nearest ten.

Mental technique for subtraction without regrouping:

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Subtracting hundreds, tens, and ones:

In this Khan Academy video tutorial, learn how to subtract three-digit numbers by subtracting ones, tens, and hundreds represented with base ten blocks and the standard algorithm.

Subtracting ten or one hundred:

In this video tutorial from Khan Academy, learn how to subtract 1, 10, or 100 from a three-digit number while making a connection between the standard algorithm and a concrete representation using base ten blocks.

Adding hundreds, tens, and ones:

In this video tutorial from Khan Academy, learn how to add three-digit numbers by adding ones, tens, and hundreds by thinking about the connection between base ten block representation and the standard algorithm.

Adding ten or one hundred:

In this video tutorial from Khan Academy, learn how to add 10 or 100 to a number using base ten blocks.



Parent Resources

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

Educational Software / Tool

Title Description
Hundreds Chart:

A printable hundreds chart featuring a 10x10 table numbered 1 to 100. (found on Illuminations website under "Trading for Quarters")

Problem-Solving Tasks

Title Description
Rounding to 50 or 500:

The purpose of this task is to answer multiple questions regarding rounding. There still may be students who laboriously list every number; the teacher should encourage a more thoughtful approach.

Classroom Supplies:

The purpose of this task is for students to "Solve problems involving the four operations" (3.OA.A) and "Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories" (3.MD.3).

Tutorials

Title Description
Subtracting: regrouping twice:

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Examples rounding to the nearest 10 and 100:

In this Khan Academy video tutorial, see examples of how to round up to four-digit numbers to the nearest ten and hundred.

Rounding to the nearest 100:

In this Khan Academy video tutorial, use a number line to round three-digit numbers to the nearest hundred.

Rounding to the nearest 10:

In this Khan Academy video, use a number line to round two-digit numbers to the nearest ten.

Mental technique for subtraction without regrouping:

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Subtracting hundreds, tens, and ones:

In this Khan Academy video tutorial, learn how to subtract three-digit numbers by subtracting ones, tens, and hundreds represented with base ten blocks and the standard algorithm.

Subtracting ten or one hundred:

In this video tutorial from Khan Academy, learn how to subtract 1, 10, or 100 from a three-digit number while making a connection between the standard algorithm and a concrete representation using base ten blocks.

Adding hundreds, tens, and ones:

In this video tutorial from Khan Academy, learn how to add three-digit numbers by adding ones, tens, and hundreds by thinking about the connection between base ten block representation and the standard algorithm.

Adding ten or one hundred:

In this video tutorial from Khan Academy, learn how to add 10 or 100 to a number using base ten blocks.

Virtual Manipulative

Title Description
Quick Math: This interesting game requires the learners to think fast and click on the correct symbol to complete the equation as quickly as possible.