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

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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
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 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.

 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.

 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")