Word (.docx)
Acrobat (.pdf)
Examples
because 
is greater than 
and is greater than 
.
Clarifications
Clarification 1: When comparing fractions, instruction includes using an appropriately scaled number line and using reasoning about their size.Clarification 2: Instruction includes using benchmark quantities, such as 0, , , 
and 1, to compare fractions.
Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.
Clarification 4: Within this benchmark, the expectation is to use 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 to understand the relative size of fractions. Students will plot fractions on the appropriate scaled number line, compare fractions using relational symbols, and order fractions from greatest to least or least to greatest. Work builds on conceptual understanding of the size of fractions from grade 3 (MA.3.FR.2.1) where students learned to compare fractions with common numerators or common denominators.- Instruction may include helping students extend understanding by generating equivalent fractions with common numerators or common denominators to compare and order fractions.
- Instruction may include number lines, which will make a connection to using inch rulers 1 to measure to the nearest of one inch.
- Instruction may include using benchmark fractions and estimates to reason about the size of fractions when comparing them. Students can compare to by recognizing that 3 (in the numerator) is more than half of 5 (the denominator) so they can reason that > .
- Instruction includes fractions equal to and greater than one.
Common Misconceptions or Errors
- The student may mistake the fraction with the larger numerator and denominator as the larger fraction. The student may not pay attention to the relationship between the numerator and denominator when estimating.
- The student incorrectly judges that a mixed number like 1 is always greater than an improper fraction like because of the whole number in front.
Strategies to Support Tiered Instruction
- Instruction includes models that represent different numerators and denominators.
- For example, students think about fractions by reasoning about the size of the parts related to the numerator or denominator. Students compare to by
recognizing that 1 (in the numerator) is less than half of 4 (the denominator) so they can reason that < .
- This can also be shown with a model so that students can see the difference in the sizes of pieces when related to the whole.
- For example, students think about fractions by reasoning about the size of the parts related to the numerator or denominator. Students compare to by
recognizing that 1 (in the numerator) is less than half of 4 (the denominator) so they can reason that < .
- Instruction includes models and examples where fractions greater than one whole are represented in a mixed number and as an improper fraction.
- For example, students might think that is greater 1 than because of the whole number being represented. Instruction includes models to represent fractions that build conceptual understanding of fractions greater than 1.
Instructional Tasks
Instructional Task 1 (MTR.6.1)
- Use benchmark fractions and the number line below to compare the fractions and 2 . In the space below the number line, record the results of the comparison using the <, > or = symbol.
Instructional Items
Instructional Item 1
Four soccer players started a game with the exact same amount of water in their water bottles. The table shows how much water each soccer player has left at the end of the game. Who has the least amount of water remaining?
- a. Jackie
- b. Laura
- c. Terri
- d. Amanda
*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
Educational Games
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Tutorial
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will compare fractions with different denominators and add money using decimal notation to decide a procedure for ranking which cupcake a bakery should add to their menu.
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 MEA, students will decide which entertainer an owner of an entertainment company should hire. They will base their decisions on information provided on resumes. Students will calculate the cost of hiring the entertainer (multiplication of whole numbers) as well as compare the statistics of their talent competitions and attendance turn-out (comparing fractions). Students will write letters to the owner of the entertainment company ranking the entertainers and providing explanation and justification of their strategy for doing so.
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 work in groups to determine a procedure for ranking playground equipment to help a school purchase new equipment for their playground. Students will compare fractions with like and unlike denominators and numerators, make decisions based on information given in a data table, and write a letter to the school providing evidence for their decisions.
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
This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.
This lesson asks students to recommend which cookie the owners of The Cookie Jar should add to their menu. Before they make their decision, the students have to convert fractions so they have like denominators. Once they have converted the fractions they will be able to see exactly how many people voted for each cookie and they can factor in that information along with additional cookie facts to make their final recommendation.
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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.
MFAS Formative Assessments
Students are given three sets of fractions to compare and are asked to record the comparisons using the less than, greater than, or equal to symbols.
Students consider the correctness of a model for comparing four-fifths to three-fourths.
Students compare two fractions using benchmark fractions on a number line and record the comparison using the less than or greater than symbol.
Students compare two fractions with unlike denominators in the context of a word problem and record the comparison using an inequality symbol.
Original Student Tutorials Mathematics - Grades K-5
Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials
This is Part 2 in a two-part series. Click to open Part 1, “Mama’s Pizza, Butterflies, & Comparing Fractions.”
Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.
Student Resources
Original Student Tutorials
Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials
This is Part 2 in a two-part series. Click to open Part 1, “Mama’s Pizza, Butterflies, & Comparing Fractions.”
Type: Original Student Tutorial
Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.
Type: Original Student Tutorial
Educational Games
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!
Type: Educational Game
Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.
Type: Educational Game
Problem-Solving Tasks
The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.
Type: Problem-Solving Task
The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together. This task is best suited for instruction. Students can practice explaining their reasoning to each other in pairs or as part of a whole group discussion.
Type: Problem-Solving Task
The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size.
Type: Problem-Solving Task
This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.
Type: Problem-Solving Task
The purpose of this task is for students to identify which fraction is closest to the whole number 1.
Type: Problem-Solving Task
Tutorial
This tutorial for student audiences will assist learners with a further understanding that fractions are a way of showing part of a whole. Yet some fractions are larger than others. So this tutorial will help to refresh the understanding for the comparison of fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.
Type: Problem-Solving Task
The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together. This task is best suited for instruction. Students can practice explaining their reasoning to each other in pairs or as part of a whole group discussion.
Type: Problem-Solving Task
The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size.
Type: Problem-Solving Task
This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.
Type: Problem-Solving Task
The purpose of this task is for students to identify which fraction is closest to the whole number 1.
Type: Problem-Solving Task
Tutorial
This tutorial for student audiences will assist learners with a further understanding that fractions are a way of showing part of a whole. Yet some fractions are larger than others. So this tutorial will help to refresh the understanding for the comparison of fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.
Type: Tutorial
