Illuminations: Fun with Fractions

Fun with Fractions

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Lesson 6

Another Look at Fractions of a Set

This lesson gives students another opportunity to explore fractions using the set model. This lesson is integrated with other areas of the math curriculum including data analysis and statistics.

Learning Objectives

Students will:

demonstrate understanding that a fraction can be represented as part of a set
identify fractions when the whole (set) and part of the set is given
describe a set of objects based on its fractional components
identify fraction relationships associated with the set
identify equivalent fractions
identify relationships inherent in equivalent fractions
reduce fractions to their lowest terms

Materials

One package of colored candies (such as M&Ms® or Skittles®) for each student
Create a Graph Web Tool
Circle Grapher

Instructional Plan

In this culminating activity, students examine the set model using colored candies. Give students an individual bag of colored candies, e.g., M&M's^® or Skittles^®. Have students open their bag of candies and sort by color. Have students count the number of each color in their set and record those data on notebook paper. Have students record the fraction of each color represented in their individual packet. All fractions should be reduced to lowest form.

Have students log on to the Create a Graph Tool from the National Center for Education Statistics. Students should choose the type of graph they want to create by using the pulldown menu. Once students have created their graph, they should label the data in fractional parts and reduce all fractions to lowest terms.

As a class, create a line plot of the number of candies in each bag. An example is shown below:

Have students determine the fractional representation for each number of candies. For example, for the graph shown above there were:

2 students with 22 candies (2/16 or 1/8),
4 students had 23 candies (4/16 or 1/4),
5 students had 24 candies (5/16),
3 students had 25 candies (3/16), and
2 students had 26 candies (2/16 or 1/8).

Next, have students log on to the Circle Grapher to create a circle graph for the class data.

Circle Grapher

Fractional representations should be labeled. Ask students to share their circle graphs with a neighbor. Discuss how a circle graph is useful for showing fractions of a set. Some students may also recognize that percents are also used in circle graphs. This discussion would be a nice tie-in to percents, specifically fractions out of 100.

Questions for Students

Which type of graph did you create when you went to the Create a Graph Tool from the National Center for Education Statistics? Why did you select this type of graph?

[Student responses may vary. They should give a valid justification for their graph selection.]

How does a line plot show the number of candies in each bag?

[Each "X" represents one piece of candy. For example, two Xs above the number 22 indicates two students whose bags contained 22 pieces of candy.]

Why is a circle graph an appropriate graph to use for fractions of a set?

[A circle graph is a good representation of fractions. The pieces of the circle graph represent a certain fraction (or percent.)]

Assessment Options

Since this is the culminating activity for the unit, it is important to use this activity as a summative assessment opportunity. You may wish to examine students' graphs, and have them write a few sentences summarizing each of the graphs.

Teacher Reflection

Do students understand that a fraction can be represented as part of a set?
Can students identify fractions when the whole (set) and part of the set is given?
Can students articulate relationships between fractions?
Do students understand the relationships inherent when comparing equivalent fractions?
Can students reduce fractions to lowest terms?
Are there other models of fractions that I could use with these students to extend their repertoire of fraction representations?
What other experiences can I introduce to students to help them better understand relationships among fractions?
How can I ensure that students have a solid conceptual understanding of fractions?
How can I help students relate the concepts in this unit to other areas of mathematics?
How can I help students relate the concepts in this unit to other areas of the curriculum?

NCTM Standards and Expectations

Data Analysis & Probability 3-5

Collect data using observations, surveys, and experiments.
Represent data using tables and graphs such as line plots, bar graphs, and line graphs.

Number & Operations 3-5

Recognize equivalent representations for the same number and generate them by decomposing and composing numbers.
Use models, benchmarks, and equivalent forms to judge the size of fractions.
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.
Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

This lesson prepared by Tracy Y. Hargrove.