Tuesday, February 26, 2013

Fractions Day 14: Composing and Decomposing

Today was a math rotations day in grade 4 . . . I started the day with a minilesson and then we broke up into three math groups to rotate around the following centers:

--“teacher time”
--problem solving
--</>/= activity

Today’s minilesson focused on “composing” and “decomposing”  using unit fractions, and I was hopeful that it would go smoothly.  I was fairly confident based on the work we have done over the last few weeks that the students would easily manage this concept, and my students did not disappoint me.

We reviewed the idea of “unit fraction” and used the fraction bars in Kidspiration to model different ways to build fractions.  We talked about how you can build or “compose” new fractions with unit fractions (which I also call counting fractions…just like we count WHOLE numbers, we can count FRACTIONS too!). 

We then tied the fraction bars to a more traditional adding and subtracting notation—we modeled by counting unit fraction groups to add and by crossing out fractions to subtract.  Students seemed to be really understanding, so I felt ready to send them off to do our math rotations.

Here is our rotation board:

(I’ve flipped the top cards backward to hide the names).  Today’s groups were picked based on needs—I knew that I wanted to differentiate the “teacher time” rotation.  Some days my groups are mixed ability--it all depends on what I am trying to accomplish.  For most of the investigations we have done during this unit, my groups are entirely mixed by gender, ability, and so on.

So here were our rotations in  nutshell!

1.  The "teacher time" rotation was with me.  We worked on reviewing the material taught in the mini lesson by having students try different combinations of addition and subtraction in their notebooks.  For my strugglers, we started really slow and brought the Smartboard back up with the fraction bars so we could make the tie.  By the time they were finished, we had written all sorts of different equations with addition and subtraction with like denominators.  We drilled in the concept that we can only add and subtract fractions with equal parts--or else we need to do some extra work!  We showed how adding 1/2 and 1/4 cannot possibly be 2/6.  We worked to come up with many equations that equaled "5/8" such as ...
1/8 + 2/8 + 2/8 
7/8 - 2/8 
4/8 + 1/8 

and so on.  

The other two groups were ready to move beyond this.  I started by adding in both improper fractions and mixed numbers for them and things seemed to be moving pretty smoothly.  I asked them to find many equations with the solution 1 3/4 and they handled that as well.  I then decided to work on true/false problems with them so I threw out problems such as 

5/8 + 2/8 < 3 x 1/3  True or False?


4 1/4 - 3 3/4 > 1/2  True or False?

The students handled the multiplication with ease--they have such good number sense that they realize that three "1/3's" is a whole--no computation required!

We then started playing more with improper fractions and the students tried writing problems to stump each other--tons of fun and very developmentally appropriate for each group.  

2.  The second rotation was a free explore station with fraction cards and <, >, and = cards.  I gave the students a number of different ways to interact with the cards...

--they could flip two cards over and decide which symbol would go between them
--they could flip 5 cards and put them in order smallest to largest
--they could flip two cards over and find 2 more cards that would fit between them
--they could come up with their own sequencing practice

And practice they did!  Each time I asked this group to rotate, they MOANED!  Can you believe?  They MOANED that they had to stop sequencing fractions!  I heard some fantastic discussion and some very creative thinking.  One group even decided to try to take a larger fraction card and find smaller ones that they could "decompose" the larger one into.  Really?  So much fun!  For those of you who have purchased the fraction sequencing set, this is one of the activities in that resource.  I will include it in the unit as well.

3.  The final rotation was a problem solving station.  Because I felt the students have enough number sense and addition/subtraction skills now, I was ready to send them off to try to tackle some word problems with fractions.  I will include these problems in my unit, but for those of you who aren't interested in purchasing the big unit in a few weeks (I promise I will work as hard as I can to get it done in the next 1-2 weeks), the set of word problems IS available in my store now.  I will put the link at the bottom of this post.  I let the students buddy up if they wanted.  I was super pleased with what I saw!  I will save one example of some great teamwork for another post!

Here is the teaser for the next post!  This was the "a ha" problem for one of my students today!

So, I hope you get a taste for one way I organize my math time . . . many of my lessons have been very "investigation" oriented--today was a more "guided math" approach which allowed me to really dig in and see how far certain students can be pushed.  Tomorrow--more problem solving and small group pulling based on the 3 exit slips I have given this week.  I have a few petunias who need a little more work with equivalent fractions and comparing fractions--so while the class has rotations tomorrow, I will be pulling small groups instead of having a "teacher time" rotation.  

Thanks for stopping by!  Stay tuned . . .


  1. Thank you so much for blogging about your fraction journey! You are an inspirational teacher and I am loving your investigative/inquiry fraction lessons. I am a first year teacher, who just began teaching 4th grade in January. I aspire to be the type of teacher that you appear to be but am struggling to keep up right now. We are currently working on fractions in math right now and I have been following your blog daily, and have to admit, have borrowed quite a few of your lesson ideas. So I just thought I would let you know that I am very appreciative of your sharing and your hard work. It is making all the difference to this brand new teacher. I will stay tuned in, and will be among the first to purchase this unit. I will be done with fractions by then but the purchase will allow me to give back to you and I will be able to save it for next year. Thanks again!


    1. Oh Kristin...what a nice comment! Please remember that I have done this for 20 years--and even I feel overwhelmed lots of the time! Please let me know what I can do to help you in this first of MANY years! Fourth grade is the best...but you need to be patient with yourself!

  2. I tend to be an "all or nothing" thinker. I've done rotations for math, inquiry lessons, and more direct instruction. Depending on the group, I based most of my year's instruction on their needs. I've never even CONSIDERED changing the delivery based on the lesson, not the students.

    This is a huge light bulb moment for me. I'm nearing the end of my ninth year teaching, and love learning and growing. Thank you so much for helping me on this journey!

    My principal has the expectation that cooperative learning is a part of every. single. lesson. I am actively brainstorming ways to make sure that I meet his expectations while using the outstanding framework you've developed.

    P.S. I love to proofread and edit. If you'd like some help with that, please let me know. :) I still plan on purchasing the unit with multiple licenses to use with my grade level next year.

    1. That's so cool! Don't you love it when your brain suddenly goes "OOOHHHHHH!" I had one of those moments the other day when a fellow teacher was explaining how she was organizing her writing unit...so easy, but I just hadn't thought about it yet! (PS--I may take you up on the proofreading offer!)

  3. I've been glued to these fractions posts! I'm doing a similar unit with my third graders and it has been so amazing to see what your fourth graders are doing.

    Just curious, because I have been toying around with rotations in my class as well. How long are your math blocks? How long does each group get at each station? I'm feeling a bit rushed in my 45 minute period, and want to see what I can do to make things run a little more smoothly.

    Thanks for all the inspiration!

    1. Hi Julie! I have a little flexibility with my block--it averages 60-70 minutes per day. When I do rotations, I tend to do a 15 minute minilesson and 3 fifteen minute rotations. Have you considered doing rotations over 2 days? Maybe students get to 2 rotations each day? If you have 4 stations, you could do a "double" lesson...minilesson each day, then 2 15 minute rotations? Just a thought...


    2. That sounds like a great idea. Will give it a try!