Word (.docx)
Acrobat (.pdf)
Examples
The numbers 72, 35 and 58 can be arranged in ascending order as 35, 58 and 72.Clarifications
Clarification 1: When comparing numbers, instruction includes using a number line and using place values of the 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
- NA
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to understand that the value of a digit is impacted by its position in a number. A three in the tens place has a value of 30 while a 3 in the ones place has a value of 3. In Kindergarten, students located, ordered and compared numbers from 0 to 20 using the same number line. Students fill in missing numbers on a number a line. Kindergarten students are not expected to use the relational symbols =, > or < when comparing numbers (MTR.5.1).- Instruction may include students modeling the numbers with manipulatives to compare given numbers prior to placing them on the number line or after placing them on a number line.
- Instruction may include students’ writing numbers in expanded form to compare given numbers.
- Instruction may include students plotting numbers on number lines to compare numbers.
Common Misconceptions or Errors
- Students may not recognize that a number’s value is directly related to its placement on a number line. In these cases, having students build a number using base ten manipulatives prior to plotting the number onto a number lines could be helpful.
Strategies to Support Tiered Instruction
- Teacher co-constructs a number line (string or painter’s tape), labeling the ends of the
number line (0-100). Students are asked to place 50 on the number line. Teacher
discusses the placement of the number and then repeat the process with the numbers 25
and 75. Teacher asks students to identify numbers that are greater than... and less than....
- Example: Teacher provides opportunities to use a number line and place value chart with base-ten blocks. Have students begin by placing the place value rods end to end along the number line (creating a number path). If students have difficulty with understanding that each rod represents a group of ten, use tiles or units to represent each whole number on the number line (number path).
- Teacher asks students to plot and represent a number on the number
line and on the place value chart. Then, the teacher asks students to identify a number that
is greater, also plotting this number on the number line and representing the number on
the place value chart. Repeat with a number that is less than.
- Example:
Instructional Tasks
Instructional Task 1 (MTR.1.1, MTR.4.1)
Class Plotting on an Open Number LineMaterials: 4 Clothespins, 4 index cards, 4 feet of string or rope
Teacher: Hang a piece of string in the front of the classroom.
- Ask a student to think of a two digit number that has 3 tens in it. 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.
- Ask a student to think of a two digit number that has 5 tens 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?”
- Ask a student to think of a two digit number that has 9 ones in it that would come after the 5 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.
- 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.
- 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 and 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:
Instructional Items
Instructional Item 1
Order the numbers 99, 79 and 89 from least to greatest. Plot the numbers on the number line.
Instructional Item 2
Using the numbers 99, 79 or 89, make three true statements.
Instructional Item 3
Write a true statement using the numbers 63 and 36.*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 Tutorials
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
In the story Arthur's Pet Business, Arthur shows his parents that he is responsible enough to deserve a pet dog and his mom gives him permission to get one. However, Arthur needs your help choosing the perfect dog. Help Arthur meet all the requirements needed to find the perfect pet for his family from the research he shares with you about the breeds they are considering, taking into consideration size, shedding, barking, friendliness, etc. Then write a justification to describe why you chose the perfect pet for Arthur and his family.
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.
Teams of students will use math to solve an open-ended, real-world problem to help their parent or caregiver choose the best babysitter. Students will apply mathematical skills of place value (two-digit number tens and ones) and counting to perform math calculations while analyzing data sets. This MEA will facilitate students demonstrating higher level critical thinking and problem solving during class discussions and in writing.
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.
Pete the Cat wants a new pair of shoes and needs the students' help selecting the right ones for him. Students will work with a team to select the best shoes for Pete. Students will use symbols to compare the costs of shoes within 100.
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.
In the story Curious George and the Pizza Party (by Rey, H.A., and Margret Rey), Curious George attends a pizza party for a friend. Now the man with the yellow hat wants to plan his own pizza party for Curious George, but he needs the students' help. Help the man with the yellow hat use the data about the different pizza companies in his area to rank the options from best to worst, considering the toppings offered, crust options, prices, and customer satisfaction ratings. Then the students will use the special promotions from each pizza company and their math skills to figure out which pizza place offers the best deals. Each team of students will write letters to the man with the yellow hat explaining how they ranked the companies and why they chose their rankings to help him choose the best pizza for George's party.
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.
MFAS Formative Assessments
Students find numbers given specific criteria and use inequality symbols to compare numbers.
Students count two sets of base ten blocks, write the number for each set, and then use symbols (inequality or equality) to compare the two numbers.
Students are asked to scale a number line and use it to draw a segment of length nine.
Students are asked to find a number that was represented by a length on an incomplete number line.
Students are asked to compare numbers by examining the digits in the tens and ones places and then use the greater than, less than, or equal to symbols to write an inequality statement.
Original Student Tutorials Mathematics - Grades K-5
Learn how to plot numbers on number lines using data from race cars in this interactive tutorial.
This is part 1 of 3 in a series of tutorials on plotting and comparing numbers. Click below to open the other tutorials in the series.
- Part 2 (Coming soon)
- Part 3 (Coming soon)
Learn how to order and compare numbers from least to greatest using number lines and place value with the students in Mr. Rivera’s class in this interactive tutorial.
This is Part 3 of 3 in the tutorial series. Click below to open parts 1 and 3.
- Part 1: Number Lines
- Part 2: Using Number Lines or Order Numbers
- Part 3: Comparing Statements
Learn how to order to compare numbers using >, <, and = symbols with Mr. Rivera’s class as they build and test racing cars in this interactive tutorial.
This is Part 3 of 3 in the tutorial series. Click below to open parts 1 and 2.
Student Resources
Original Student Tutorials
Learn how to order and compare numbers from least to greatest using number lines and place value with the students in Mr. Rivera’s class in this interactive tutorial.
This is Part 3 of 3 in the tutorial series. Click below to open parts 1 and 3.
- Part 1: Number Lines
- Part 2: Using Number Lines or Order Numbers
- Part 3: Comparing Statements
Type: Original Student Tutorial
Learn how to order to compare numbers using >, <, and = symbols with Mr. Rivera’s class as they build and test racing cars in this interactive tutorial.
This is Part 3 of 3 in the tutorial series. Click below to open parts 1 and 2.
Type: Original Student Tutorial
Learn how to plot numbers on number lines using data from race cars in this interactive tutorial.
This is part 1 of 3 in a series of tutorials on plotting and comparing numbers. Click below to open the other tutorials in the series.
- Part 2 (Coming soon)
- Part 3 (Coming soon)
Type: Original Student Tutorial
Problem-Solving Task
The purpose of this task is to give students an opportunity to compare numbers less than 100 to benchmark numbers. Even though a number line is not explicitly given in the task, it is useful for students to list the numbers in the order they would appear on the number line; this allows them to focus on the relative ordering without worrying about the exact placement on the number line.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
This activity is designed to be a short, repeatable activity to build student flexibility with the number sequence. Begin by randomly giving each student in the classroom one card from one of the sets you have made. Challenge the students to get themselves into order as quickly as they can.
Type: Problem-Solving Task
The purpose of this task is to give students an opportunity to compare numbers less than 100 to benchmark numbers. Even though a number line is not explicitly given in the task, it is useful for students to list the numbers in the order they would appear on the number line; this allows them to focus on the relative ordering without worrying about the exact placement on the number line.
Type: Problem-Solving Task
