Illuminations: Fun with Pattern Block Fractions

# Fun with Pattern Block Fractions

## Exploring the Value of the Whole

 This lesson focuses on the relationship between parts and the whole. These relationships were developed earlier and require the students to consider the size or value of the same fraction when different "wholes" are compared (i.e., the value of x is relative to the whole; x of a small pie is not equivalent to x of a large pie). This lesson promotes problem solving and reasoning as the students compare similar fractions with different "wholes." Students develop communication skills as they work in pairs and share their understanding about the relationship between the value of a fraction and the whole.

### Learning Objectives

 Students will: 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) demonstrate an understanding that the area of equivalent fractions is relative to the whole

### Materials

 Pattern Blocks Region Relationships 4 Activity Sheet

### Instructional Plan

Have students work in pairs or small groups [depending upon the best working arrangement for your students]. The students may have noticed that the same fraction (1/2, for example) is not always equivalent (or the regions are not always congruent). For example, have the students compare the answer to the following questions:

 The green triangle is what fraction of the blue rhombus ? [1/2] The red trapezoid is what fraction of the yellow hexagon ? [1/2] How can and both be equivalent to ______? (Query the students until they are able to articulate that the meaning or value of _____ relative to the whole.)

These and other questions are presented on the Region Relationships 4 activity sheet. Working in pairs, allow students to complete these questions.

On the activity sheet, students will explore other fraction relationships in which the fraction is the same but actually refers to two different wholes. For example,

 The blue rhombus is what fraction of the yellow hexagon ? [1/3] The green triangle is what fraction of the red trapezoid ? [1/3] How can and both be equivalent to 1/3? (Probe students until they are able to articulate that the meaning or value of 1/3 is relative to the whole.)

Have the students make similar comparisons using two yellow hexagons as the whole. Continue investigating relationships with other wholes (e.g., three or more yellow hexagons). You may choose to have them record the relationships in a math journal to which they may refer later. Each group should record relationships on chart paper to share with the whole class. As each group shares, have students add to their journal any relationships that they did not discover on their own.

### Questions for Students

 The green triangle is what fraction of the blue rhombus? [1/2] The red trapezoid is what fraction of the yellow hexagon? [1/2] How can both be equivalent to 1/2? The blue rhombus is what fraction of the yellow hexagon? [1/3] The green triangle is what fraction of the red trapezoid? [1/3] How can both be equivalent to 1/3? The green triangle is what fraction of the yellow hexagon? [1/6] What pattern block represents 1/6 when two yellow hexagons are used as the whole? [The blue rhombus] Do all parts representing 1/6 have equal size? Explain. [Student responses may vary.]

### Assessment Options

 At this stage of the unit, it is important to know whether the students can do the following: 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) demonstrate understanding that the area of equivalent fractions is relative to the whole The students' recordings can be used to make instructional decisions about their understanding of fraction relationships and the notion that the value of the fraction is relative to the whole. 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.

### Extensions

 Have students repeat the activity using virtual pattern blocks on the computer. They should be directed to the Pattern Blocks Program. (Alternatively, students may use the National Library of Virtual Manipulatives: Pattern Blocks.) Another good demonstration of the relationship of the part to the whole is to take two candy bars of the same brand, one bar that is miniature in size and one that is extra large. Ask the students: If you could have one-half of one of the two candy bars, which one-half would you prefer?

### Teacher Reflection

 Which students can identify the fractions represented by various pattern blocks when "whole" is defined in different ways? What activities are appropriate for students who have not yet developed this understanding? Which students demonstrate understanding that the area of equivalent fractions is relative to the whole? What activities are appropriate for the students who have not yet developed this understanding? Which pairs worked well together? Which groupings need to be changed for future lessons? If groups were not successful working together, what was the source of the problem? (i.e., were the problems behavior-related or were academic levels not matched appropriately in the groups?) What parts of the lesson went smoothly? What parts should be modified for the future?

### NCTM Standards and Expectations

 Number & Operations 3-5Develop 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

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