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 10

Numeration

The student demonstrates conceptual understanding of real numbers.

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 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

Fifth Grade

Number and Operations in Base Ten

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

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.

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.

Third Grade

Number and Operations-Fractions

Develop understanding of fractions as numbers.

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.

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.

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.

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

3.05a 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.

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.

4th Grade

Number and Number Sense

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.

4.2.b

4.3

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.

8th Grade

Number and Number Sense

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

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.

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

Lesson Outline

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.

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.

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.

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.

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.

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.