Illuminations: Fun with Fractions

Fun with Fractions

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

More Fun with Fraction Strips

Students continue to work with fraction strips to compare and order fractions. This lesson builds on the work done with fraction relationships in the previous lesson. Students develop skills in problem solving and reasoning as they make connections between various fractions.

Learning Objectives

Students will:

demonstrate understanding that a fraction can be represented as part of a linear region
describe part of a linear region using fractions
compare fractions to determine if one fraction is greater than, less than, or equal to another fraction
order fractions from least to greatest or from greatest to least

Materials

Fraction strips from the previous lesson
Comparing and Ordering Fractions Activity Sheet

Instructional Plan

To assess prior knowledge, invite students to reflect on the previous lesson. Ask them to describe what they learned from creating fraction strips and ideas for using them in practical ways.

To begin the lesson, have students take out their fraction strips from the previous lesson. They will use them to compare fractions on the Comparing and Ordering Fractions Activity Sheet.

Comparing and Ordering Fractions Activity Sheet

Students should use their fraction strips to model each fraction being compared. Fraction strips representing each fraction should be lined up so that they can be compared directly.

For example, when comparing 1/2 and 2/4, the fractions should be modeled and lined up as follows:

Guide students through comparing another example or two from the Comparing and Ordering Fractions Activity Sheet. When students feel confident with the task, ask them to continue comparing fractions. Answers should be checked with a partner. Discuss answers, and have students correct any responses that were incorrect.

Next, have students order their fractions by lining up each set (1/2s, 1/3s, 1/4s, 1/6s, and 1/8s) with the “whole” strip. Place the "whole" strip at the top, then the 1/2s underneath the “whole,” then 1/3s, 1/4s, 1/6s, and 1/8s, respectively.

Have students record the order from greatest to least. Ask them if they notice any patterns as the fractions get smaller. Prompt students to notice that there is an inverse relationship between the size of the fraction and the denominator when the numerator is one.

Students might express this concept as follows: As the fractions get smaller, the denominator gets larger. Students should record this relationship.

Ask students if they believe this relationship always holds true. Have them investigate this question by using their fraction strips to order the fractions in Part II of the Comparing and Ordering Fractions Activity Sheet. This sheet includes a variety of fractions where the numerator is not always one.

Students should come to the conclusion that this pattern only consistently occurs when the numerator is constant. Discuss answers and have students correct any responses that were incorrect.

Questions for Students

What patterns do you notice when you compare fractions?

[If the numerator is the same for both fractions, the larger the denominator, the smaller the fraction. If the denominator is the same for both fractions, the larger the numerator, the larger the fraction.]

When you order the fraction strips from largest (the "whole") to smallest (1/8s), what do you notice about the relationship between the size of the fraction and the denominator?

[As the fractions get smaller, the denominator gets larger. There is an inverse relationship. Students should be reminded that in each case, the numerator is one.]

Do you think this relationship always holds true?

[Student responses may vary.]

Does a similar relationship hold true for fractions where the denominator is some constant number?

[There is an opposite relationship. That is, as the numerator increases, so does the size of the fraction.]

Assessment Options

At this stage of the unit, students should be able to do the following:
- demonstrate understanding that a fraction can be represented as part of a linear region
- describe part of a linear region using fractions
- compare fractions to determine if one fraction is greater than, less than, or equal to another fraction
- Order fractions from least to greatest or from greatest to least.
Examining students’ recordings about fraction relationships on the Comparing and Ordering Fractions Activity Sheet can be helpful in making instructional decisions about students’ understanding of the length model.

Teacher Reflection

Which students understand that a fraction can be represented as part of a linear region? What activities are appropriate for students who have not yet developed this understanding?
Which students can describe part of a linear region using fractions? What activities are appropriate for students who have not yet developed this understanding?
Which students can compare fractions using fraction strips? What activities are appropriate for students who have not yet developed this understanding?
Which students can order fractions from least to greatest or from greatest to least? What activities are appropriate for students who have not yet developed this understanding?
What parts of the lesson went smoothly? What parts should be modified for the future?

NCTM Standards and Expectations

Number & Operations 3-5

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

This lesson was developed by Tracy Y. Hargrove.