Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.
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 =).
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
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.
- 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
Access Point Number |
Access Point Title |
MA.4.FR.1.AP.4a | Explore mixed numbers and fractions greater than one. |
MA.4.FR.1.AP.4b | Using visual models, compare fractions less than one with different numerators and different denominators. Denominators limited to 2, 3, 4, 6, 8 or 10. |
Related Resources
Educational Games
Name |
Description |
Flower Power: An Ordering of Rational Numbers Game | 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!
|
Fraction Quiz | 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. |
Formative Assessments
Name |
Description |
Corn Farms | Students compare two fractions with unlike denominators in the context of a word problem and record the comparison using an inequality symbol. |
Comparing Fractions Using Benchmark Fractions | Students compare two fractions using benchmark fractions on a number line and record the comparison using the less than or greater than symbol. |
Comparing Four-Fifths and Three-Fourths | Students consider the correctness of a model for comparing four-fifths to three-fourths. |
Compare Fractions | 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. |
Lesson Plans
Name |
Description |
Lessen the Litter | Students will calculate the total amount of trash at different locations in the community to determine which location has the most trash and explore ways a community can work together to prevent future trash buildup in this integrated lesson plan. |
Ocean Heroes | Students will learn ways to help keep the ocean clean by recycling and write letters to lobby government officials to support recycling programs. They will decide which materials are most important to recycle by looking at several characteristics of the materials including whether they are renewable or nonrenewable, if the material will decompose, and the amount of the materials currently being recycled in this MEA.
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. |
Majority Rules | Students will use the benchmark fraction ½ to estimate and compare fractions and make a connection to achieving a simple majority when voting during this integrated lesson. |
Slither Not in the Everglades! Python MEA | 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. |
Fractions: Let's Compare | The lesson is an application and extension of fraction comparison strategies, not an introduction. While the beginning of the lesson has a review, the situational stories require students to read and analyze carefully. |
Wondrous Water Parks | 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. |
Out of Order? | This lesson is a way for students to use benchmark fractions to get a conceptual understanding of comparing and ordering fractions. |
Fraction Line-up! | Students will model and compare fraction pairs by writing an inequality. |
Gettin' Fancy with Fractions | In this lesson, students engage in problem solving, a fraction sort activity and play the game "Fraction War" to practice and demonstrate understanding of using benchmark quantities when comparing fractions with different numerators and denominators. This lesson is not intended as initial instruction on using benchmark quantities to compare fractions. Instead, it may be useful for skill reinforcement, student engagement, and formative assessment of skill mastery. Parts of this lesson could be revisited periodically as students build comfort and mastery comparing fractions. |
Looking for Patterns in a Sequence of Fractions | Students generate and describe a numerical pattern using the multiplication and subtraction of fractions. |
Ordering Fractions | Students work in groups to arrange sets of fraction cards from least to greatest using multiple strategies. Fractions include those greater than one. |
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Name |
Description |
Listing fractions in increasing size | 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. |
Comparing two different pizzas | 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. |
Comparing Sums of Unit Fractions | 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. |
Using Benchmarks to Compare Fractions | 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. |
Which is Closer to 1? | The purpose of this task is for students to identify which fraction is closest to the whole number 1. |
Tutorial
Name |
Description |
Comparing Fractions | 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. |
Student Resources
Original Student Tutorials
Educational Games
Name |
Description |
Flower Power: An Ordering of Rational Numbers Game: | 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!
|
Fraction Quiz: | 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. |
Problem-Solving Tasks
Name |
Description |
Listing fractions in increasing size: | 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. |
Comparing two different pizzas: | 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. |
Comparing Sums of Unit Fractions: | 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. |
Using Benchmarks to Compare Fractions: | 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. |
Which is Closer to 1?: | The purpose of this task is for students to identify which fraction is closest to the whole number 1. |
Tutorial
Name |
Description |
Comparing Fractions: | 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. |
Parent Resources
Problem-Solving Tasks
Name |
Description |
Listing fractions in increasing size: | 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. |
Comparing two different pizzas: | 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. |
Comparing Sums of Unit Fractions: | 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. |
Using Benchmarks to Compare Fractions: | 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. |
Which is Closer to 1?: | The purpose of this task is for students to identify which fraction is closest to the whole number 1. |
Tutorial
Name |
Description |
Comparing Fractions: | 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. |