Illuminations: Fun with Fractions

Fun with Fractions

Virtual Pattern Blocks

Students use virtual pattern blocks to problem solve and reason with fractions. They investigate relationships between parts and wholes using another representation of a region model, virtual fractions. Students use conversation to explain their understandings in order to extend and clarify their mathematical content knowledge.

Learning Objectives
 
Students will:
  • demonstrate understanding that a fraction is part of a whole
  • identify fraction relationships

Materials
 
Region Relationships 1 Activity Sheet (new, blank copy for each student)
Virtual Pattern Blocks, such as Pattern Blocks Program or National Library of Virtual Manipulatives: Pattern Blocks

Instructional Plan

Explain to students that they will use virtual fraction tools to model part-whole relationships. The directions for using the Web site should be reviewed prior to this lesson. They should be directed to log on to the Pattern Blocks program. A link to the instructions can be found at the bottom of the Web page. The students may 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 one to compare the area of the region. (Alternatively, students may use the National Library of Virtual Manipulatives: Pattern Blocks.

Have students work in pairs using the Web-based pattern blocks to explore relationships among the four shapes. Use the same Guiding Questions found in Lesson One. This will facilitate exploration with a new tool, help the students focus on the mathematical concepts demonstrated with this region model, and reinforce the content of the previous lesson, Investigating with Pattern Blocks.

The students should use the virtual pattern blocks to answer the questions. Provide students with a new, blank copy of the Region Relationships 1 activity sheet and ask them to complete it.

Region Relationships 1 Activity Sheet Region Relationships 1 Activity Sheet

Encourage students to discuss various options with their partner. This allows students to articulate their understandings, making them available for discussion, clarification, and extension.

Questions for Students
 

Is there a way to represent the red trapezoid using blue and green pattern blocks? Can you cover the red trapezoid using only one color? What does this tell us about the relationship between the blue rhombus and the green triangle?

[The trapezoid can be covered with one green triangle and one blue rhombus, or it can be covered with three green triangles. Consequently, there are two green triangles in one blue rhombus.]

Are there other ways to represent various pattern blocks (for example, the yellow hexagon) using more than one color pattern block?

[The students should be lead in a discussion of the relationships inherent in these representations.]

Assessment Options
 
  1. At this stage of the unit, it is important to know whether the students can do the following:

    • understand that a fraction is part of a whole
    • state the relationship between the pattern block shapes [e.g., that there are three triangles in one red trapezoid]
  2. 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 understand that a fraction is part of a whole? What activities are appropriate for those students who have not yet developed this understanding?
  • Which students/groups can articulate the relationship between the pattern block shapes? What activities are appropriate for those 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
  1. 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.
  2. Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
  3. Use models, benchmarks, and equivalent forms to judge the size of fractions.
This lesson prepared by Tracy Y. Hargrove.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

Web Sites
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