Standard 1 : Generalize place value understanding for multi-digit whole numbers. (Major 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.4.NBT.1
Title: Generalize place value understanding for multi-digit whole numbers. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 4
Domain-Subdomain: Number and Operations in Base Ten

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.4.NBT.1.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
MAFS.4.NBT.1.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
MAFS.4.NBT.1.3: Use place value understanding to round multi-digit whole numbers to any place.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.4.NBT.1.AP.1a: Compare the value of a digit when it is represented in a different place of two three-digit numbers (e.g., The digit 2 in 124 is ten times the digit 2 in 472).
MAFS.4.NBT.1.AP.2a: Compare multi-digit numbers.
MAFS.4.NBT.1.AP.2b: Write or select the expanded form for a multi-digit number.
MAFS.4.NBT.1.AP.3a: Use a hundreds chart or number line to round to any place (i.e., ones, tens, hundreds, thousands).
MAFS.4.NBT.1.AP.2c: Understand the role of commas to read and write numerals between 1,000 and 1,000,000.


Related Resources

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

Original Student Tutorials

Name Description
Rounding Larger Numbers with Endangered Animals:

Learn how to round larger whole numbers to any place value while exploring endangered species in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

Who's Top Dog, Now? Comparing Numbers:

Learn how to compare numbers using the greater than and less than symbols in this interactive tutorial that compares some pretty cool things!

Candy Engineer: Place Value:

Read and write multi-digit whole numbers using base-ten numerals and number names using the Base 10 place value system in this interactive tutorial.

Note: this tutorial exceeds the number limits of the benchmark.

Candy Sales Are Booming! Expanded Notation:

Learn how to write numbers using place value in different forms like standard, word, and expanded notation in this interactive tutorial.

The Treasure of Aryabhata: Place Value Comparison:

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student 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.

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Formative Assessments

Name Description
Comparing Amounts of Baseball Cards:

Students are asked to compare the value of the digit three in 35 baseball cards to the value of the digit three in 350 baseball cards.

Rounding To The Hundred Thousands Place:

Students are asked to round four numbers to the hundred thousands place and explain their reasoning.

Rounding To Ten Thousands Place:

Students are asked to round four numbers to the ten thousands place and explain their reasoning.

Base Ten Place Value:

Students are given opportunities to explain the relationship between place value and the power of ten in multiplying and dividing.

Reading Greater Numbers:

Students are asked to read aloud several numbers that are greater than one thousand.

Rounding Numbers:

Students are asked to round four numbers to different places and explain their reasoning.

Numbers In Expanded Form:

Students are asked to write numbers in both standard form (as base ten numerals) and expanded form.

Collections:

Students are asked to compare two numbers in the context of a word problem and write an inequality statement showing the relationship between the numbers.

Writing Number Names to a Million:

Students will write the number name (word form) of a number when given the base-ten numeral (standard form).

Seven Hundred Seventy Seven:

Students are asked to consider the number 777 and how each of the digits in the number are related.

Family Vacations:

Students are given three-digit numbers in the context of a word problem and are asked to tell how much greater the digit in the tens place is than the digit in the ones place.

Using Word and Expanded Form:

Students compare two numbers, one given in word form and the other given in expanded form.

Rounding to the Thousands Place:

Students are asked to round four numbers to the thousands place and explain their reasoning

Lesson Plans

Name Description
Just Right Goldilocks’ Café: Temperature & Turbidity:

This is lesson 3 of 3 in the Goldilocks’ Café Just Right unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” temperature and turbidity level. Students will use both the temperature probe and turbidity sensor and code using ScratchX during their investigation.

Just Right Goldilocks’ Café: Turbidity:

This is lesson 2 of 3 in the Just Right Goldilocks’ Café unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” level of turbidity. Students will use turbidity sensors and code using ScratchX during their investigation.

Just Right Goldilocks’ Café: Temperature:

This is lesson 1 of 3 in the Just Right Goldilocks’ Café unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” temperature. Students will use temperature probes and code using ScratchX during their investigation.

 

Lesson #2 - Moon Phase Unit:

This is lesson 2 of 3 in the Moon Phase unit. This lesson will help students design a flowchart model to find the phase of the Moon by making decisions based on certain conditions. This lesson also gives students insight into working with the design model made earlier and an opportunity to upload/draw costumes of different lunar phases in Scratch.

Lesson #1 - Moon Phase Unit :

This is lesson 1 of 3 in the Moon Phase Unit. This lesson introduces students to the eight Moon phases and their names in a counter-clockwise sequential order starting with the New Moon as phase 1. Students will also be introduced to how a flowchart can help make decisions, in this case whether or not the Moon is full.

10X Bigger!:

In this lesson students will move from constructing concrete models of what happens to a number when you multiply the number by 10 into drawing their own pictorial representations of the same process with numbers up to 1,000. They will develop an understanding of the rule 'a digit in one place represents ten times what it represents in the place to its right' and apply this rule to a variety of situations.

Round Me!:

This lesson uses benchmark numbers to help students round to the nearest 10, 100, 1000. This lesson incorporates visuals and the use of the number line in order to help students better understand the concept. Students play a game that reinforces the standard.

What's My Value?:

This lesson will allow students to deepen their knowledge in place value. The teacher will use modeling, guided math groups, and independent practice to help students understand that the digit in one place represents ten times what it represents in the place to its right. Students will use base 10 blocks to build numbers and make general observations about the values of numbers. Students will also draw and label models, to make understanding concrete. In groups of 4-5, students will work together and discuss (using discussion questions) to deepen their knowledge on the topic.

Terrific Tim’s Ten Tiny Toes:

Students will learn how a digit in one place represents ten times what it represents in the place to its right. Students will model and solve real-world problems on their own and with their friends using word problems, snacks, and their friends' toes!

My Digit is Bigger than Your Digit! Comparing Multi-digit Numbers:

In this lesson, the students will explore place value using manipulatives to help them compare multi-digit numbers in the context of the book A Million Dots by Andrew Clements.

Planet Hoppers, Inc: A Space Suit Design Company:

Students are asked to evaluate several space suit designs and select the best design based on given data. Students work in collaborative groups to develop a procedure for selecting the best design and share their ideas with the rest of the class. A twist is introduced and the groups are challenged to test the validity of their procedure.

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.

Kudos for Kicks - MEA:

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers and decimals by using different mathematical operations of addition, subtraction, and multiplication. The students will be asked to assist a discount shoe store owner, who is planning a one day sale promotion, to choose a famous brand sneaker to feature for the one day sale. Students will determine which one will bring in more customers, as well as provide the most profit. Students will need to read a data table, rank the famous brand sneakers from 1-6, calculate the total profit margin per pair, and the total sales potential profit margin determined by the number of sneakers in stock. A twist is added to the problem when additional stock items are added, plus one of the brands is removed and two new brands are added.

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.

We All Scream for ICE CREAM - MEA:

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers, fractions, decimals and percent by using different mathematical operations. The students will be asked to assist an ice cream shop owner, who is planning a promotional program "Flavor of the Month," to rank the ice cream flavors based on the data provided. Students will need to read a data table, rank the flavors, convert the fraction amount to a percent and decimal and per serving costs to a decimal as well. A twist is added to the problem when one of the flavors is too expensive to make because of seasonal availability but two new flavors are added to be calculated. An additional twist is given by adding an adult survey to the second data table. The students will need to recalculate the new percent and decimals for the additional flavors.

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.

The Right Rental:

In this MEA students will have to find the right rental for a client as they use their knowledge of numbers and some reasoning. Students will read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

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.

Which Bank is Consumer Friendly?:

This MEA is a student's exploration of banking. In the first task, they will create a model that will rank banks from most consumer friendly to least consumer friendly. In the second task, they will need to modify their models to address additional banks and additional criteria. Students can then test their models while researching real banks and determining their level of consumer friendliness.

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.

Help Me Build a Roller Coaster:

Students will evaluate different factors for building the right roller coaster. They will compare and contrast multi-digit numbers to determine coaster capacity, etc.

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.

Adventure Falls Bus Purchase:

The school district needs to purchase new buses to transport students. Students will be asked to rank the bus choices based on the data provided. The data provided is: price, year, new/used, and capacity (how many students the buses hold). In the twist, students will be given safety information and must decide how to change their procedure with the new information.

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.

Let's Make a Movie:

Students will add and subtract multi-digit whole numbers (through the millions) to compare and contrast movie genres.

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.

Best Baseball Player?:

In this 4th grade MEA, students will use data to compare which baseball player they think is the best hitter using actual stats.

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.

Cars for Sale MEA:

Students will compare multi-digit numbers to create a procedure for choosing the best car for Edward Easy to buy for his driving school. They will have to weigh quantitative and qualitative factors to determine the best car to purchase. Students will present their recommendations and the steps to the procedure they created in writing and orally.

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.

The Street Where Place Value Lives:

Students will apply their place value knowledge to connect place value to the millions by relating it to their communities. Students can discuss and write about place value, using their connections.

Oh Where, Oh Where, Should I Put You?:

This highly engaging game is played after the unit on place value has been taught. It is designed to allow the student to think about the placement of a number before writing it down, in order to write the largest and/or smallest number.

Just Hanging A-Round:

In this lesson, students will demonstrate knowledge of rounding up to the 10,000 place value with the aid of a number line.

Problem-Solving Task

Name Description
Ordering 4-digit numbers:

It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.

Tutorials

Name Description
Regrouping Numbers: 4,500 = 3 thousands + ? hundreds:

In this tutorial, you will look at regrouping a number by different place values.

How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.



Student Resources

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

Original Student Tutorials

Title Description
Rounding Larger Numbers with Endangered Animals:

Learn how to round larger whole numbers to any place value while exploring endangered species in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

Who's Top Dog, Now? Comparing Numbers:

Learn how to compare numbers using the greater than and less than symbols in this interactive tutorial that compares some pretty cool things!

Candy Engineer: Place Value:

Read and write multi-digit whole numbers using base-ten numerals and number names using the Base 10 place value system in this interactive tutorial.

Note: this tutorial exceeds the number limits of the benchmark.

Candy Sales Are Booming! Expanded Notation:

Learn how to write numbers using place value in different forms like standard, word, and expanded notation in this interactive tutorial.

The Treasure of Aryabhata: Place Value Comparison:

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student 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.

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Problem-Solving Task

Title Description
Ordering 4-digit numbers:

It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.

Tutorials

Title Description
Regrouping Numbers: 4,500 = 3 thousands + ? hundreds:

In this tutorial, you will look at regrouping a number by different place values.

How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.



Parent Resources

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

Problem-Solving Task

Title Description
Ordering 4-digit numbers:

It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.

Tutorial

Title Description
How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.