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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 =).
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Cardinality Principle
- 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.- 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.
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 Items
Instructional Item 1
Use the number line below to plot the numbers 234, 247, 205.
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
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
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
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
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
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
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.
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.
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
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
MFAS Formative Assessments
Students are asked to compare numbers and then use the greater than, less than, or equal to symbols to complete inequality statements.
Students are asked to compare numbers with missing digits and explain their reasoning.
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.
Students are asked to compare two numbers used in a word problem and to write an inequality statement showing the relationship between the numbers.
Original Student Tutorials Mathematics - Grades K-5
Learn how to compare three-digit numbers using place value models, number lines and place value charts in this interactive tutorial.
Student Resources
Original Student Tutorial
Learn how to compare three-digit numbers using place value models, number lines and place value charts in this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
The purpose of this task if for students to gain a better understanding of <,=,> with the help of number sentences.
</,=,>
Type: Problem-Solving Task
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).
Type: Problem-Solving Task
The purpose of this task is for students to gain a better understanding of 3-digit numbers and their place value.
Type: Problem-Solving Task
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
Parent Resources
Problem-Solving Tasks
The purpose of this task if for students to gain a better understanding of <,=,> with the help of number sentences.
</,=,>
Type: Problem-Solving Task
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).
Type: Problem-Solving Task
The purpose of this task is for students to gain a better understanding of 3-digit numbers and their place value.
Type: Problem-Solving Task
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
