MA.2.NSO.1.2

loading spinner
Export Print
Compose and decompose three-digit numbers in multiple ways using hundreds, tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

Examples

The number 241 can be expressed as 2 hundreds + 4 tens + 1 one or as 24 tens + 1 one or as 241 ones.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 2
Strand: Number Sense and Operations
Standard: Understand the place value of three-digit numbers.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Expression 
  • Equation

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

 

Purpose and Instructional Strategies

The purpose of this benchmark is to extend the understanding of place value from grade 1 to include three-digit numbers and help students to identify ways numbers can be renamed flexibly using composition and decomposition (MTR.2.1). 
  • Instruction includes the use of base ten manipulatives and place value disks. 
  • Instruction includes the understanding that 100 can be thought of as a bundle of ten tens – called a “hundred.” 
  • Instruction includes the idea that the equal sign means “same as” and is used to balance equations.

 

Common Misconceptions or Errors

  • Students may think that because the grouping of the digits changes the value also changes.
    • For example, 879 is the same as 87 tens + 9 ones or 8 hundreds+ 79 ones.

 

Strategies to Support Tiered Instruction

  • Instruction includes opportunities to use base ten blocks and a place value chart with a 3- digit number (e.g., 326). Teacher asks students to exchange one ten and ones.
    • For example, teacher asks students to represent the value using a drawing. Students are asked to explain what they now have and how it is similar and different from the original representation of the number. Repeat this process with exchanging hundreds and tens. Teacher has students share the different representations with the group and again compare the similarities and differences. Students are asked to name/identify the different ways to name the values (grouping the hundreds into tens and the tens into the ones, e.g., 32 tens and 6 ones or 3 hundreds and 26 ones, etc.) 

  • Instruction includes opportunities to use base ten blocks to practice exchanging tens for ones and hundreds for tens. With each exchange, teacher has students represent using both the original representation and the new representation in a drawing on a place value chart. At every opportunity teacher asks students to name/identify the values they are using in the numbers. 
    • Example: 

tens and hundreds

 

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

The number 317 can be expressed as 3 hundreds + 1 ten + 7 ones or as 31 tens + 7 ones. Explain using objects or drawings how both expressions equal 317. 

 

Instructional Task 2 

Use a place value model to show how the number 134 can be represented as 13 tens and 4 ones.

 

Instructional Items

Instructional Item 1 

Express the number 783 using only hundreds and ones. 

 

Instructional Item 2 

Express the number 783 in multiple ways using only tens and ones. 

 

*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.
5012040: Mathematics - Grade Two (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712030: Access Mathematics Grade 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.2.NSO.1.AP.2: Compose and decompose two-digit numbers using tens and ones. Demonstrate each composition or decomposition with objects, drawings, expressions or equations.

Related Resources

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

Formative Assessments

Modeling Numbers with Base Ten Blocks:

Students use base ten blocks to model each of four numbers and then describe the number of hundreds, tens, and ones in each number.

Type: Formative Assessment

How Many Hundreds, Tens, and Ones?:

Students are asked to describe the number of hundreds, tens, and ones in four different three-digit numbers.

Type: Formative Assessment

Can You Write the Number?:

Students are asked to write numbers given descriptions of the number of hundreds, tens, and ones each contains.

Type: Formative Assessment

Showing One Hundred Equals Ten Tens:

Students are asked to compare ten tens to one hundred and justify their comparisons.

Type: Formative Assessment

Lesson Plans

Hundreds, and Tens, and Ones! Oh, My!:

The students will extend their base-ten understanding to hundreds and represent 3-digit numbers in a variety of ways, using 3-digits, words, base-ten blocks, drawings, and equations.

Type: Lesson Plan

Reading and Writing Numbers and Number Names:

Students will demonstrate their understanding of how to read and write numbers to 1000 using base-ten blocks and word form. Students will compose and decompose three-digit numbers in multiple ways using hundreds, tens, and ones.

Type: Lesson Plan

Place Value Representations:

This lesson encompasses several activities for learning the place value of three-digit numbers. Students match cards with other students' various representations of the same number. Pairs of students use playing cards and determine the digits' place values. Students find a partner to query about place value after a musical interlude.

Type: Lesson Plan

Shipping Hundreds, Tens, and Ones:

In this lesson students use a toy factory scenario to better understand three-digit numbers.

Type: Lesson Plan

Different Ways to Represent 3-Digit Numbers:

In this lesson, students will demonstrate their understanding of how to read and write numbers to 1000 using base-ten blocks and expanded form. Students will also explore decomposing 3-digit numbers in multiple ways.

Type: Lesson Plan

Bundles and Combos:

This lesson will help students learn that a 3-digit number can be composed of different combinations of hundreds, tens and ones.

Type: Lesson Plan

Odds and Evens:

This resource helps students identify numbers as odd or even using a variety of methods including creating pairs, skip counting by two’s, using number lines, and arrays. It also leads them to understand that all even numbers can be written as a sum of equal addends and odds can be written as the sum of equal addends plus one.

This resource can be conducted as one lesson or can be spread over multiple mini sessions if needed as noted within this resource as Lesson 1 and Lesson 2.

 

Type: Lesson Plan

Place Value - 3 Digit Numbers:

Students will decompose numbers by place value and represent them using concrete and pictorial models.

Type: Lesson Plan

Sweet Number Places:

This lesson is a continuation of the Sweet Values CPALMS lesson Resource 46493 and is a different way of teaching place value, with a story that you can continue to use to also teach addition and subtraction to your second graders. In this lesson students will learn to numerically represent numbers in different ways and understand that the three digits in a three-digit number represent amounts of hundreds, tens, and ones.

Type: Lesson Plan

Sweet Values:

This lesson is a different way of teaching place value, with a story that you can continue to use to also teach addition and subtraction to your second graders. In this lesson students will learn to represent numbers in different ways and understand that the three digits in a three-digit number represent amounts of hundreds, tens, and ones.

Type: Lesson Plan

Original Student Tutorial

Bianca's Place Value Bubble Gum Factory - Part 1:

Explore the Base 10 place value system with 3-digit numbers in Bianca's Bubble Gum Factory with this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

Decomposing Numbers into Tens and Ones:

After you try this knockout lesson idea, math misconceptions will be down for the count!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Three composing/decomposing problems:

The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.

Type: Problem-Solving Task

Ten $10s make $100:

The purpose of this task is for students to use currency to help better understand place value.

Type: Problem-Solving Task

Boxes and Cartons of Pencils:

This tasks uses school supplies in a problem to help students gain a better understanding of place value.

Type: Problem-Solving Task

Regrouping:

This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.

Type: Problem-Solving Task

Party Favors:

The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred. Second graders should have been given opportunities to work with objects and pictures that represent the grouping structure of the base-ten number system, which would help prepare them for doing this task.

Type: Problem-Solving Task

Bundling and Unbundling:

Students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Student must, in some cases, decompose hundreds to tens and tens to ones. The order of the summands does not always correspond to the place value, making these problems less routine than they might seem at first glance.

Type: Problem-Solving Task

Comparisons 1:

This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.

Type: Problem-Solving Task

Counting Stamps:

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.

Type: Problem-Solving Task

MFAS Formative Assessments

Can You Write the Number?:

Students are asked to write numbers given descriptions of the number of hundreds, tens, and ones each contains.

How Many Hundreds, Tens, and Ones?:

Students are asked to describe the number of hundreds, tens, and ones in four different three-digit numbers.

Modeling Numbers with Base Ten Blocks:

Students use base ten blocks to model each of four numbers and then describe the number of hundreds, tens, and ones in each number.

Showing One Hundred Equals Ten Tens:

Students are asked to compare ten tens to one hundred and justify their comparisons.

Original Student Tutorials Mathematics - Grades K-5

Bianca's Place Value Bubble Gum Factory - Part 1:

Explore the Base 10 place value system with 3-digit numbers in Bianca's Bubble Gum Factory with this interactive tutorial.

Student Resources

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

Original Student Tutorial

Bianca's Place Value Bubble Gum Factory - Part 1:

Explore the Base 10 place value system with 3-digit numbers in Bianca's Bubble Gum Factory with this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Three composing/decomposing problems:

The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.

Type: Problem-Solving Task

Ten $10s make $100:

The purpose of this task is for students to use currency to help better understand place value.

Type: Problem-Solving Task

Boxes and Cartons of Pencils:

This tasks uses school supplies in a problem to help students gain a better understanding of place value.

Type: Problem-Solving Task

Regrouping:

This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.

Type: Problem-Solving Task

Party Favors:

The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred. Second graders should have been given opportunities to work with objects and pictures that represent the grouping structure of the base-ten number system, which would help prepare them for doing this task.

Type: Problem-Solving Task

Bundling and Unbundling:

Students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Student must, in some cases, decompose hundreds to tens and tens to ones. The order of the summands does not always correspond to the place value, making these problems less routine than they might seem at first glance.

Type: Problem-Solving Task

Comparisons 1:

This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.

Type: Problem-Solving Task

Counting Stamps:

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.

Type: Problem-Solving Task

Parent Resources

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

Problem-Solving Tasks

Three composing/decomposing problems:

The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.

Type: Problem-Solving Task

Ten $10s make $100:

The purpose of this task is for students to use currency to help better understand place value.

Type: Problem-Solving Task

Boxes and Cartons of Pencils:

This tasks uses school supplies in a problem to help students gain a better understanding of place value.

Type: Problem-Solving Task

Regrouping:

This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.

Type: Problem-Solving Task

Party Favors:

The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred. Second graders should have been given opportunities to work with objects and pictures that represent the grouping structure of the base-ten number system, which would help prepare them for doing this task.

Type: Problem-Solving Task

Bundling and Unbundling:

Students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Student must, in some cases, decompose hundreds to tens and tens to ones. The order of the summands does not always correspond to the place value, making these problems less routine than they might seem at first glance.

Type: Problem-Solving Task

Comparisons 1:

This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.

Type: Problem-Solving Task

Counting Stamps:

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.

Type: Problem-Solving Task