Illuminations: Fun with Fractions

Fun with Fractions

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Expanding Our Pattern Block Fraction Repertoire

In this lesson, the students expand the number of fractions they can represent with pattern blocks by increasing the whole. Instead of representing the whole with one yellow hexagon, the students explore fractional relationships when two, three, and four yellow hexagons constitute the whole.

Learning Objectives

Students will:

identify fractions when the whole (region) and a part of the region are given
represent the fractional relationship between the pattern block shapes using a standard form of the written notation (e.g., the green triangle is x of the blue rhombus)
identify the fractions represented by various pattern blocks when "whole" is defined in different ways (e.g., 1 whole = 1 yellow hexagon; 1 whole = 2 or more yellow hexagons)

Materials

Pattern Blocks
Chart Paper
Markers
Region Relationships 3 Activity Sheet
Virtual Pattern Blocks, such as Virtual Pattern Blocks Program or National Library of Virtual Manipulatives: Pattern Blocks

Instructional Plan

Tell the students that they are going to work with a different whole, two hexagons. This is the first set of questions on the Region Relationships 3 activity sheet.

Region Relationships 3 Activity Sheet

Arrange students in pairs or small groups (depending upon the best working arrangement for your class) and have them explore each of the four pattern blocks to determine what fraction of the new whole (two hexagons) is being represented. For example,

The yellow hexagon is what fraction of the whole? [1/2]
The red trapezoid is what fraction of the whole? [1/4]
The blue rhombus is what fraction of the whole? [1/6]
The green triangle is what fraction of the whole? [1/12]

Have the students find the value in fractional form for each pattern block when three hexagons represent the whole.

Have the students find the value in fractional form for each pattern block when four hexagons represent the whole.

Each group should record relationships on chart paper to share with the whole class. Individual students should record all the fraction relationships they know. This may be done in a math journal to which they refer later. As each group shares, have students amend their journal entries to include any relationships they may have missed.

Allow students to repeat the activity using the Virtual Pattern Blocks applet. The directions for using this applet should be reviewed prior to the lesson. A link to the instructions can be found at the bottom of the Web page. The students need to be guided in how to drag the pattern blocks to the work area. When making comparisons, the students can drag one pattern block on top of another to compare the area of the region. (Alternatively, students may use the National Library of Virtual Manipulatives: Pattern Blocks.)

Questions for Students

How would your fractions change if you used three yellow hexagons as the whole?

[The students should discover that the hexagon now represents 1/3; the trapezoid, 1/6; the rhombus, 1/9; and the triangle, 1/18.]

How would your fractions change if you used four yellow hexagons as the whole? Five yellow hexagons as a whole? Can you extend this investigation to other wholes? What fractions do each of the pattern blocks represent with this new whole?

Assessment Options

At this stage of the unit, it is important to know whether the students can do the following:
- identify fractions when the whole (region) and a part of the region is given
- represent the fractional relationship between the pattern block shapes using standard form of the written notation (e.g., the green triangle is x of the blue rhombus)
- Identify the fractions represented by various pattern blocks when "whole" is defined in different ways (e.g., 1 whole = 1 yellow hexagon; 1 whole = 2 or more yellow hexagons)
The students' recordings can be used to make instructional decisions about their understanding of fraction relationships. Because this entire unit deals with relationships, areas needing additional work can be developed during subsequent lessons. You may choose to use the Class Notes recording sheet to make anecdotal notes about the students' understanding and use those notes to guide your instructional planning.

Teacher Reflection

Which students can identify fractions when the whole (region) and a part of the region are given? What activities are appropriate for the students who have not yet developed this understanding?
Which students can represent the fractional relationship between the pattern block shapes using a standard form of the written notation (e.g., the green triangle is x of the blue rhombus). What activities are appropriate for the students who have not yet developed this understanding?
Which students can identify the fractions represented by various pattern blocks when "whole" is defined in different ways (e.g., 1 whole = 1 yellow hexagon; 1 whole = 2 or more yellow hexagons). What activities are appropriate for the 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

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 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.

This lesson prepared by Tracy Y. Hargrove.

1 period

NCTM Resources

Making Sense of Fractions, Ratios, and Proportions

Web Sites


More and Better Mathematics for All Students