Standard #: MA.2.NSO.1.3


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Plot, order and compare whole numbers up to 1,000.


Examples


The numbers 424, 178 and 475 can be arranged in ascending order as 178, 424 and 475.

Clarifications


Clarification 1: When comparing numbers, instruction includes using a number line and using place values of the hundreds, tens and ones digits.

Clarification 2: Within this benchmark, the expectation is to use terms (e.g., less than, greater than, between or equal to) and symbols (<, > or =).



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

  • Number line 
  • Natural Number

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

 

Purpose and Instructional Strategies

The purpose of this benchmark is to extend the place value work of plot, order and compare from grade 1 by increasing the number set to 1,000. In grade 1, students ordered numbers in ascending order only. 
  • Instruction includes the use of numbers presented in multiple ways and different forms. 
  • Instruction includes the understanding that the value of a digit is impacted by its position in a number. 
  • Instruction includes the use of place value charts, place value cards, place value disks, place value chips and base ten blocks (MTR.2.1). 
  • Instruction includes the use of number lines using benchmark numbers to support comparing. 
  • Instruction includes the understanding that numbers can be reordered in both ascending and descending order.

 

Common Misconceptions or Errors

  • Students may incorrectly plot a three-digit numbers in a number line.
  • Students may not understand that a representation of a smaller portion of a number line (200 − 220) may have the same physical size as a representation of a larger number line (0 − 1,000). 
  • Students may have difficulty comparing two numbers that have the same digits in a different order (i.e., 852 and 582).

 

Strategies to Support Tiered Instruction

  • Instruction includes the use of a hundreds chart and base ten blocks. Teacher shares two numbers that have the same digits, but the numbers are in different places. 
    • For example, using numbers like 852 and 582, the students build the two numbers on place value charts. Teacher has students write the number under each of the base ten blocks representation. With the visual representation of the numbers available, ask which number is greater and which number has fewer of each of the base ten blocks. If students identify the incorrect number, teacher points out that there is a greater number of hundreds/flats in 852 than in 582.

blocks

  • Instruction includes the use of number lines with benchmark numbers to aid in placement of 3-digit numbers. May use multiple number lines with different end numbers to show the need to focus on the portion where the numbers lie.
    • For example, teachers begin with having students label a number line with end benchmarks 0 and 1,000. Then, have students determine what number is located in the middle (500). Students can then further label all of the 100 multiples on the line from 0 to 1,000. Next, show students three numbers (i.e. 435, 442, and 427) Teacher can then show a second number line and discuss that the end numbers can now change to get closer to these three numbers and label the ends with 400 and 450. Work with students to label the multiples of 10s that exist on this line. Then, have students determine where these three numbers are located.

graph

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

Provide students with five numerals (i.e., 1, 8, 5, 4 and 0). 
  • Part A. Create four different three-digit numbers that have a 4 in the hundreds place. 
  • Part B. Arrange the numbers created in order from greatest to least. Explain why which number is the greatest. 
  • Part C. Using two of the numbers created from Part A, write a statement using > or < to compare.

Instructional Task 2 (MTR.1.1, MTR.2.1, MTR.4.1, MTR.5.1)

Class Plotting on an Open Number Line
Materials: 4 Clothespins, 4 index cards, 4 feet of string or rope,
Teacher: Hang a piece of string in the classroom.

1. Ask a student to think of a three-digit number that has 3 tens in it and a 1 in the hundreds place. Write that number on an index card. Ask another student to place the number anywhere on the piece of string (open number line) using a clothespin.
2. Ask a student to think of a three-digit number that has 1 hundred in it. Write that number on an index card. Ask another student to place the number on the piece of string (open number line) using a clothespin. Ask the class if it should be placed to the right or the left of the first number. Ask “Is this number more or less than our first number?”
3. Ask a student to think of a three-digit number that has 1 hundred in it that would come after the 3 tens number. Write that number on an index card. Ask another student to place the number on the piece of string using a clothespin. Ask the class if it is greater than, less than, or equal to the first number on the number line. Ask the class if adjustments are needed to make room for the new number on the open number line (string). Make adjustments as needed.

4. Ask a student to think of a number that would come between the first and second number. Write that number on an index card. Ask the class “Should this number be placed closer to the first number or second number? How do you know?” Ask the class if adjustments are needed to the number line more accurate now that they have all the numbers placed. Make adjustments as needed.
5. Ask students to independently come up with at least three different true statements from the numbers on the class number line using >, < or = symbols. After giving students time to come up with statements, call on students and write their findings. Ask students to evaluate if they are in fact true statements. Remind students to come up with both greater than and less than statements.

Sample Class Number Line:

number line

Instructional Task 3 (MTR.1.1, MTR.2.1 , MTR.4.1, MTR.5.1)

Teacher provides 6 to 10 numbers on cards in either standard form, expanded form, word form or pictural form. Ask students to place them in ascending order. If any numbers are equal, they can be placed on top of each other to show that they are located at the same spot because they represent the same number. Ask students to come up with at least five different true statements from the numbers using the <,>, or = symbols.

Instructional Items

 

Instructional Item 1 

Use the number line below to plot the numbers 234, 247, 205. 

line

Instruction Item 2 

Use <, > or = to make the comparison statement 567 __ 576 true. 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012040: Grade Two Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 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 - 2024, 2024 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.2.NSO.1.AP.3 Plot, order and compare whole numbers up to 100.


Related Resources

Formative Assessments

Name Description
Using Digits

Students randomly pull five cards from a set of digit cards and use them to make the greatest and least three-digit numbers possible. They are also asked to use the greater than or less than symbols to compare the two numbers.

Who Has More?

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

Inequalities Using Symbols

Students are asked to compare numbers and then use the greater than, less than, or equal to symbols to complete inequality statements.

Missing Digits

Students are asked to compare numbers with missing digits and explain their reasoning.

Lesson Plans

Name Description
Comparing Three-Digit Numbers Using Symbols

In this lesson, students will use base ten blocks to model two and three-digit numbers and compare two-digit numbers to three-digit numbers and three-digit numbers to three-digit numbers using < and >.

Pop, Pop, Pop!

Students will research the effects of sugary drinks on their health.  They will interpret data on a variety of beverages presented in the form of bar graphs and decide which beverages should be included in school vending machines to ensure students have healthy drink options.

Less Than, Equal to, or Greater Than?

In this lesson, students move from comparing three-digit numbers built with base ten blocks to comparing three-digit numbers based on their place value. Students will use the greater than, less than, or equal sign to compare their values.

Water Parks Galore!

In this Model Eliciting Activity, MEA, students will devise a procedure, and justify it, in order to determine the best features of a water park. Students will use problem-solving skills and data sets presented in a bar graph and table. In a “twist,” students will be given new information and asked to determine whether their procedure still works. Students will create a bar graph representing the new data.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Class Pets

In this Model Eliciting Activity, MEA, students will devise a plan for ranking, and justify it, in order to choose the best class pet. Students will use problem-solving skills, interpret data presented in tables, add two-digit numbers, compare two and three-digit numbers, and create bar graphs.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Crazy Crayons!

In teams, students will make a decision on how to select the best crayons for a school supply store based on various crayon characteristics such as cost, transfer to paper, vibrancy of color, color residue, and breakage.

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.

Cellular Satisfaction

In this Model Eliciting Activity, MEA, a client is searching for the best cell phone carrier. Students will determine a procedure for ranking the companies based on votes for the favorite company and fees. The data is given in a scaled bar graph and a table. In a “twist,” the client provides more data, presented in a scaled pictograph, for the students to consider.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Restaurant Rankings: Which meal would you want to add to your cafeteria menu?

In this Model Eliciting Activity, MEA, students have been selected by the cafeteria manager to help rank healthy meal options that have been proposed to be added to the school cafeteria. The students will use information about the food and drink included in the meal, total calories, sodium content, calories from saturated fat, and calories from sugar to come up with a procedure for ranking the meal options. Then students will have to use or adapt their original procedures to include two more meal options in the rankings.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Chocolate Delight

In this Model Eliciting Activity, MEA, Chocolate Delight, a chocolate bar company, wants to improve its sales to elementary students by creating a healthy chocolate bar. They have tested 5 new recipes and need to determine which candy bar is best for children. The students will determine a procedure for ranking the recipes from best to worst based on the following criteria: healthiness, taste, and nut allergies and make a recommendation of the healthiest recipe to Chocolate Delight.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Best Classroom Pet

In this Model Eliciting Activity, MEA, the students will work in teams to use data to determine which classroom pet teachers should get for their classrooms based on several characteristics.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Symbol Spin

This lesson puts a spin on comparing three-digit numbers! The students will work cooperatively to compare two three-digit numbers based on the hundreds, tens, and ones place values. The students are encouraged to verbally explain their logic during the game. This is a lesson that will engage your students and can last all week long!

Less Could Be More!

This lesson helps teachers introduce the concept of comparing two numbers up to 1,000 using the terms Greater than, Less than, Equal to, and the symbols >, <, =.

How Can You Compare Two 3-Digit Numbers?

Students will use base-ten blocks, drawings, or place value charts to compare two 3-digit numbers Students will use the <,>, = symbols correctly when comparing numbers.

Comparing Two 3-Digit Numbers

This whole-class lesson will reinforce the concept of comparing two 3-digit numbers as well as provide practice for students to become comparing experts. Students will use playing cards to practice their skills.

Comparing Three-Digit Numbers

The students use place value to compare two three-digit numbers and write the appropriate symbol >, =, <.

How Many Inches, Feet, and Yards?

Students will measure the length of given objects using various measuring tools. The students will record their measurements using different units including inches, feet, and yards to the nearest whole unit. Students will also estimate and measure the lengths of objects, then compare their estimations to their measurements to find the difference.

 

Number Chompers

In this lesson, students will compare whole numbers up to 1,000, use the appropriate symbol, and read the comparison correctly.

Original Student Tutorial

Name Description
Tale of the Tallest Skyscraper

Learn how to compare three-digit numbers using place value models, number lines and place value charts in this interactive tutorial.

Problem-Solving Tasks

Name Description
Comparisons 2

The purpose of this task if for students to gain a better understanding of <,=,> with the help of number sentences.

</,=,>

Digits 2-5-7

Students who are struggling to build an understanding of the relationship between digit placement and the value of the number may still need concrete manipulatives such as grid paper and Base Ten Blocks. As a classroom extension, after students have worked independently or in small groups to solve the problem, the teacher can ask students to share their numbers, until all six possibilities are listed. Then, independently or as a whole group, students can order the six numbers from smallest to largest (or largest to smallest).

Ordering 3-digit numbers

The purpose of this task is for students to gain a better understanding of 3-digit numbers and their place value.

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.

Student Center Activities

Name Description
Place Value Sprint

In this game, students build the greatest or least possible number based on instructions by strategically placing digits as a team. They strengthen place value understanding while incorporating physical activity and teamwork.

FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Place Value Slide

In this game, students slide numbered caps strategically onto a place value chart to create the greatest or least number as they practice building and reading numbers to reinforce place value understanding.

FCR-STEM's Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Place Value Puzzler

In this game, students use clues about correct digits and their placement to determine a secret number while they develop number sense through logical deduction, strategic reasoning, and place value discussions.

FCR-STEM: Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Worksheet

Name Description
Open Number Line

Open Number Line

Student Resources

Original Student Tutorial

Name Description
Tale of the Tallest Skyscraper:

Learn how to compare three-digit numbers using place value models, number lines and place value charts in this interactive tutorial.

Problem-Solving Tasks

Name Description
Comparisons 2:

The purpose of this task if for students to gain a better understanding of <,=,> with the help of number sentences.

</,=,>

Digits 2-5-7:

Students who are struggling to build an understanding of the relationship between digit placement and the value of the number may still need concrete manipulatives such as grid paper and Base Ten Blocks. As a classroom extension, after students have worked independently or in small groups to solve the problem, the teacher can ask students to share their numbers, until all six possibilities are listed. Then, independently or as a whole group, students can order the six numbers from smallest to largest (or largest to smallest).

Ordering 3-digit numbers:

The purpose of this task is for students to gain a better understanding of 3-digit numbers and their place value.

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.

Worksheet

Name Description
Open Number Line:

Open Number Line



Parent Resources

Problem-Solving Tasks

Name Description
Comparisons 2:

The purpose of this task if for students to gain a better understanding of <,=,> with the help of number sentences.

</,=,>

Digits 2-5-7:

Students who are struggling to build an understanding of the relationship between digit placement and the value of the number may still need concrete manipulatives such as grid paper and Base Ten Blocks. As a classroom extension, after students have worked independently or in small groups to solve the problem, the teacher can ask students to share their numbers, until all six possibilities are listed. Then, independently or as a whole group, students can order the six numbers from smallest to largest (or largest to smallest).

Ordering 3-digit numbers:

The purpose of this task is for students to gain a better understanding of 3-digit numbers and their place value.

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.

Student Center Activities

Name Description
Place Value Sprint:

In this game, students build the greatest or least possible number based on instructions by strategically placing digits as a team. They strengthen place value understanding while incorporating physical activity and teamwork.

FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Place Value Slide:

In this game, students slide numbered caps strategically onto a place value chart to create the greatest or least number as they practice building and reading numbers to reinforce place value understanding.

FCR-STEM's Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Place Value Puzzler:

In this game, students use clues about correct digits and their placement to determine a secret number while they develop number sense through logical deduction, strategic reasoning, and place value discussions.

FCR-STEM: Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Worksheet

Name Description
Open Number Line:

Open Number Line



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