Comparing Fractions

Abstract

The following discussions and activities are designed to give students practice in comparing fractions. The activities provide ample practice opportunities to reinforce the information from the discussions.

Objectives

Upon completion of this lesson, students will:

  • have had practice in simplifying fractions
  • gained experience comparing fractions and ordering them on a number line
  • worked on developing methods to estimate the values of fractions

Standards Addressed

Grade 3

  • Numeration

    • The student demonstrates conceptual understanding of simple fractions with denominators 2, 3, 4, or 10.

Grade 4

  • Numeration

    • The student demonstrates conceptual understanding of fractions with denominators 2 through 12.

Grade 5

  • Numeration

    • The student demonstrates conceptual understanding of positive fractions with denominators 1 through 12 and 100 with proper and mixed numbers and benchmark percents (10%, 25%, 50%, 75%, 100%).

Grade 6

  • Numeration

    • The student demonstrates conceptual understanding of fractions (proper or mixed numbers), decimals, percents (whole number), or integers.
    • The student demonstrates conceptual understanding of fractions, mixed numbers, or percents.

Grade 7

  • Numeration

    • The student demonstrates conceptual understanding of rational numbers (fractions, decimals, percents, or integers).
    • The student demonstrates conceptual understanding of positive fractions, decimals, or percents.

Grade 8

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.
    • The student demonstrates conceptual understanding of rational numbers (fractions, decimals, or percents including integers).

Grade 9

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.

Grade 10

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.

Grade 3

  • Number Sense

    • 3.0 Students understand the relationship between whole numbers, simple fractions, and decimals

Grade 6

  • Number Sense

    • 1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages

Third Grade

  • Number and Operations-Fractions

    • Develop understanding of fractions as numbers.

Fourth Grade

  • Number and Operations-Fractions

    • Extend understanding of fraction equivalence and ordering.
    • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Fifth Grade

  • Number and Operations in Base Ten

    • Perform operations with multi-digit whole numbers and with decimals to hundredths.

Sixth Grade

  • Ratios and Proportional Relationships

    • Understand ratio concepts and use ratio reasoning to solve problems.

  • The Number System

    • Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Grades 6-8

  • Numbers and Operations

    • Compute fluently and make reasonable estimates
    • Understand meanings of operations and how they relate to one another

Grade 4

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will read, write, model, and compute with non-negative rational numbers.

Grade 5

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will understand and compute with non-negative rational numbers.

Grade 6

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.

Grade 7

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will understand and compute with rational numbers.

3rd Grade

  • Number and Operations

    • The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.

5th Grade

  • Numbers and Operations

    • The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions.

5th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

6th Grade

  • Number and Operation

    • Content Standard 1.0 The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

7th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

8th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

3rd Grade

  • Numbers and Operations

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

4th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Grade 4

  • Number, Operation, and Quantitative Reasoning

    • 2. The student describes and compares fractional parts of whole objects or sets of objects.

3rd Grade

  • Number and Number Sense

    • 3.6 The student will compare the numerical value of two fractions having like and unlike denominators, using concrete or pictorial models involving areas/regions, lengths/measurements, and sets.
    • 3.05a The student will divide regions and sets to represent a fraction;
    • 3.05b The student will name and write the fractions represented by a given model (area/region, length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths.
    • 3.06 The student will compare the numerical value of two fractions having like and unlike denominators, using concrete or pictorial models involving areas/regions, lengths/measurements, and sets.

4th Grade

  • Number and Number Sense

    • 4.2.b
    • 4.3
    • 4.2.b The student will represent equivalent fractions;
    • 4.3 The student will compare the numerical value of fractions (with like and unlike denominators) having denominators of 12 or less, using concrete materials.

8th Grade

  • Number and Number Sense

    • 8.1c compare and order decimals, fractions, percents, and numbers written in scientific notation.

6th Grade

  • Number and Number Sense

    • 6.2 The student will describe and compare two sets of data, using ratios, and will use appropriate notations, such as a/b, a to b, and a:b.
    • 6.4 The student will compare and order whole numbers, fractions, and decimals, using concrete materials, drawings or pictures, and mathematical symbols.

Textbooks Aligned

Grade Six

  • Bits and Pieces I

    • Investigation Two: Comparing Fractions

6th

  • Module 5 - Creating Things

    • Section 1: Comparing Fractions
      • Reason for Alignment: The Comparing Fractions lesson is an introductory level and ties well to the book.

7th

  • Module 3 - Codes

    • Section 3: Fractions
      • Reason for Alignment: The lesson Comparing Fractions ties to a number of the fraction activities. This is a basic lesson, with possible discussions to be used with students.

Grade 5

  • Some of the Parts

    • Relationships between Fractions

Grade 6

  • Fraction Times

    • Fraction/Percent/Decimal/Ration Relationships

  • More or Less

    • Fraction/Decimal/Percent Relationships

Student Prerequisites

  • Arithmetic: Students must be able to:
    • work with simple fractions in lowest terms
    • simplify fractions
  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag.
    • use a browser for experimenting with the activities.

Teacher Preparation

  • Access to a browser
  • Pencil and paper

Key Terms

Lesson Outline

  1. Focus and Review

    Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

    • Ask students if they remember how to reduce a fraction, such as 8/12 or 6/60.
    • Lead a discussion about fractions to review basic terminology and understanding.

  2. Objectives

    Let the students know what it is they will be doing and learning today. Say something like this:

    • Today, class, we will be talking more about fractions, and how to compare them.
    • We are going to use the computers to learn about fractions, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about this activity first.

  3. Teacher Input

    • You may choose to lead the students in a short discussion about comparing fractions.
    • Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.
    • Open your browser to Fraction Finder in order to demonstrate this activity to the students.

  4. Guided Practice

    • You may want to have students take turns giving answers to the problems and work through one or two games as a class until students are ready to try it on their own.
    • If you choose to, you may also show students the Conversions tool, which converts fractions to decimals, and decimals to fractions.

  5. Independent Practice

    • Allow the students to work in groups of two. Monitor the room for questions and be sure that the students are on the correct web site.

  6. Closure

    • You may wish to bring the class back together to discuss any problems that were especially hard for students to solve. Once the students have been allowed to share what they found, summarize once more the main points of the lesson.

Alternate Outline

This lesson can be rearranged in several ways if there is only one available computer:

  • Have students complete paper worksheets of problems with fractions on a number line and use Fraction Finder as a reward for two students at a time who have shown proficiency in solving the problems on paper.
  • Alternatively, select students who need additional practice to use the game. Teams of one strong student and one who needs help work well with this activity.