Thursday, November 5, 2015

Thursday Tool School: Understanding Fractions- Parts and Wholes

Fractions. A single word that deflates the confidence of our most competent students and adults alike. In fact, I am sure that many readers are reliving their own fraction experiences as they read this post-- good or bad! I can't say that I myself don't have certain feelings about my own experiences with learning fractions, but over the years, I have developed a deeper understanding of fraction concepts through my experience as a teacher, a mathematics education graduate student, and now as a math coach-- which brings me to this month's series.

This month, I will share some of the understandings that I have developed over the years (and am still developing) with all of you. The really great news I want to share with you about fractions is that there are so many math tools you can use to reinforce these essential skills. With that in mind, each week in November, I will share a resource highlighting a fraction tool that can be used to address a specific Common Core Math Standard. 

Today's resource addresses the following Common Core State Standard for Math:
3.NF.A.1- Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a quantity a/b as the quantity formed by a parts as size 1/b.

I mentioned in an earlier post that I love to use pattern blocks to teach fractions. The yellow hexagon, red trapezoid, blue rhombus, and green triangle shapes fit together perfectly to model fractional relationships. The CCSSM standard above requires students to understand how to relate an individual piece to the whole using the formal fraction notation. 

The activity I created for this skill requires students to look at the fraction assigned to a specific piece and
a.) name the whole
b.) explain that the fraction's name is 1/b because it takes b parts to equal, make, or cover one whole.  

See the example below: 

I used pattern block for this initial activity, but many tools could and should be used to help students make the connection between the size of the part, named fraction, and the number of parts that make up the whole. For example, Cuisenaire rods can also be used to make this connection. It is important to note that it is essential for students to see the same size piece represent several different fractions based on the number of parts in the whole.  

See the example below: 

This activity would be great to use as a "record of learning" for an interactive notebook because it provides an example of a part, how and why it is named as 1/b, and references the relation to the whole. A blank copy of this resource is included below for you to add your own shapes and fractions. Students would then supply the picture of the whole and the explanation. 

Extension: As an additional challenge, try giving students the whole and the fraction and then allow them to determine the part. 

Blank Recording Sheet
Free Resource Alert! Click here for a free copy of the blank recording sheet. 

Note: While this activity does not emphasize using sets, it is important for students to complete the same process with sets of objects. Students tend to misunderstand fractions when presented as a set, so exposure to seeing fractions as parts of sets is important to fully understanding this skill. See the example below. 

Looking for more? Click here to check out a post I wrote in September about using pattern blocks to emphasize critical thinking with fractions. The post includes a freebie!

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


  1. This is a fantastic resource. Visuals are so helpful. Thanks for sharing.