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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
- Assessment Limits :
Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100. Fractions
may be fractions greater than 1 and students may not be guided to
put fractions in lowest terms or to simplify.
Two fractions being compared must have both different numerators and
different denominators. - Calculator :
No
- Context :
Allowable
- Test Item #: Sample Item 1
- Question:
Select >, <, or = to complete a true comparison for each pair of fractions.
- Difficulty: N/A
- Type: MI: Matching Item
Related Courses
Related Access Points
Related Resources
Educational Games
Formative Assessments
Image/Photograph
Lesson Plans
Original Student Tutorials
Problem-Solving Tasks
Virtual Manipulatives
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
This Model Eliciting Activity is written at a 4th grade level. In this open-ended problem, students must consider how to rank potting soil based on factors like fraction of ingredients, price, and eco-friendliness. In teams, students determine their procedures and write letters back to the client.
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
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
Virtual Manipulatives
Match shapes and numbers to earn stars in this fractions game.
- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns
Type: Virtual Manipulative
In this activity, you will graphically determine the value of two given fractions represented as points on a number line. You will then graphically find a fraction whose value is between the two given fractions and determine its value.
Type: Virtual Manipulative
Parent Resources
Image/Photograph
Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.
Type: Image/Photograph
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
Virtual Manipulative
Match shapes and numbers to earn stars in this fractions game.
- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns
Type: Virtual Manipulative
