Decomposing Fraction Fun!

Whether you teach from the Common Core or other sets of rigorous standards, the ability to decompose or “break apart” fractions and mixed numbers is key to strong “fraction sense” and the ability to successfully add and subtract fractions and mixed numbers.  I wanted to find a fun and challenging way for my students to practice the THINKING required to be efficient with this!

You may have heard of “number bonds” in the primary grades.  This activity taps into that concept to use fractions instead!  Students gain valuable practice in breaking apart fractions and putting them back together—all in a cooperative, “puzzle-like” activity!  Students work cooperatively to find the combinations of cards that can "compose" to be the large card.  We especially focus on "what makes one whole" in this process.

For each set, I had students lay out the larger number cards and the smaller fraction cards.  Cooperatively, they work to find the “decomposed” parts that add up to make the “total” number.  To keep my sets organized ( I made four at different levels so I could differentiate my groups), I copied my small cards on card stock of the same color as the border of the larger cards.  That way I know sets won’t get mixed up! 

Before they begin, I told the students a few things:

1.  Remember to use “like” denominators.  This activity does NOT ask students to change denominators.
2.  There are several ways to make some of the numbers.  You may not pick the correct one first and may need to “trade” cards to make the puzzle work.
3.  Use scratch paper or the recording sheet to keep track of your “tries” if it helps you stay organized. 
4.  Be patient with each other and persevere!

It was very interesting to watch my students work.  Some were very strategic and methodical while others were very random and struggled to keep track of what they had already tried.  This can lead to some good “coaching” moments for you!

I created the sets in the following order of sophistication...I was hoping to find a way for ALL my students to enjoy the rigor of the task--but at a "just right" level.  Some students worked through several sets today as part of our "review" day in math workshop.  One rotation was this decomposing activity, we did large number multiplication at another, and students worked to solve fraction word problems at a third--the three "big ideas" from this math unit.
So easy...just make some little cards with problems...have the students solve them on their own and check with a calculator!  We worked on organization of our work, accuracy, and EFFICIENCY today!  
As they worked on the decomposing card station, students did a lot of mental math as they looked for numbers to join together to make “the big number”.  Often, they needed several attempts.  On some of the sets, there are multiple ways to make numbers, and some students got a little frustrated.  I used some guiding questions to help.

Are you checking to make sure your denominators are the same?
If your “big number” is in eighths, what do you know about the smaller numbers?
Would there be another way to make ____?
What numbers might work to make the smallest/largest number first?

My students LOVED it…and want me to make some even more challenging ones!  Want to take a peek?  I did "pretty it up" and put it in my store.  Click the cover below if you want to check it out.

More fractions? YES!

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  1. I didn't take a look in the store yet, but OMG! This looks awesome! We are using Everyday Math and beginning Unit 5 this week. Lesson one is Decomposition of Fractions. My kiddos seemed to do fine with it over the last 2 days, but reviewing and extending using this will be great! Unit 4 covered "big number multiplication", so that review activity idea is awesome too. This is just what the doctor ordered, so I'm heading over to the store to pick one up soon. Thanks SOO much for all your hard work! Your work is always so great.

  2. Do you have a pacing guide to your math instruction? I have a lot of your products!