Thursday, December 10, 2015

Thursday Tool School: Understanding Fractions- Decomposing Fractions

Building a strong foundation for fractions in the early grades provides long-term support for the development of fraction operations in the upper grades. This understanding of operations of fractions begins around fourth grade. According to the Common Core State Standards for Math, students begin fraction operations by decomposing fractions into fractions with the same denominator in the fourth grade. 

Specifically, the related Common Core State Standard for Math states: 
4.NB.B.3.- Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 

4.NF.B.3.A.- Understand addition and subtraction of fractions as joining and separating parts referring to the same whole

4.NF.B.3.B- Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g. by using a visual fraction model. 

Understanding how to decompose fractions supports the following essential understandings: 
  • understand the meaning and purpose of the numerator, denominator, and unit (or whole)
  • addition of fractions is an extension of whole number addition and involves joining or combining disconnected parts
  • addition sequences can represent different problem situations
  • the interpretation of an problem situation can lead to different representations
  • the denominators of the addends remain the same and are not added together
  • addition and subtraction of fractions refer to the same unit, or whole
The activity I want to highlight today involves multiple ways to decompose fractions, using an 8-part spinner labeled with fractional quantities. Students spin the spinner and write a number sentence showing the decomposition of the fraction using fractions with the same denominator.

After spinning for the initial fraction and showing one decomposition (with an equation), students complete the following:
  • show the decomposition another way
  • justify the decomposition with a visual model
  • write a story to match the equation
Consider having students make a poster like the one below to demonstrate their understanding. 

Make it a cooperative task! Assign each task a number and have students rotate their roles. 
  1. Spin the spinner. Show how to decompose the fraction using an equation.
  2. Show how to decompose the fraction another way.
  3. Justify the decomposition with a visual model.
  4. Write a story to match your problem. 
Note: My cooperative learning mats would be a great addition to this activity and would help students identify their roles. The mat can be rotated clockwise or counter-clockwise to complete each new fraction set. Check it out here or by clicking on the picture to the right. 

Sound Off! How do you use math tools to teach fractions in the classroom?


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