Fun with Pattern Block Fractions

• 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

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.]

1. 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
2. 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.

1. 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.)
2. 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?

• 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?

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