Saturday, February 9, 2013

Fractions Day 7: When a "whole" isn't a "whole"!

I promised another entry in FractionFest 2013 (though a Twitter follower renamed it "Fractionpalooza" which I L-O-V-E!) so here goes . . .
fractions
It is super important to remember that fractions come in all shapes and sizes, so I keep bringing my students back to the idea that--like decimals--fractions are numbers that let us talk about pieces of numbers!  Next week we will be really digging into number lines, but we spent a few days this week digging in to fractions of sets.  We started with this question:

Which is bigger--1/2 of 12 cubes or 1/3 of 18 cubes?

I had the students glue the prompt into their notebooks and to decide on an answer and try to "prove it" with words, pictures, or by modeling.
fractions

I walked around to snoop, and I was a little surprised at what I saw.  About 1/2 my kids (1/2 of 22 for those who are really in the fraction zone) got it instantly in their heads.  The other 1/2 didn't even seem to know where to start.  I asked the students to self-select groups--if they wanted help, they should join me up front in the room and if they were confident, I asked them to pair up and to try to write this type of problem for each other.  

When I had my group, I poured out the cubes in a pile and we spent some time modeling this problem and talking through it.  We reviewed key concepts and terms from the past few days and then worked for a while "telling stories" along this same line.  "Which would be more--1/2 of 16 M&M's or 1/4 of 20?" and so on.  Gradually, through modeling, more and more students left the group to go work with a partner to try more.

After a while, it was time to move on--it was Friday after all--so I decided to treat them to some edible manipulatives!
fractions
Math is always better when it is filled with artificial colors and flavors, right?
fractions of sets
Notice the  "What fraction of your Skittles are brown?"  This REALLY tripped them up!  Even my first-ones-dones struggled with what the answer to that would be.  Some even tried to count the purple ones as browns!
fractions
As the problems got trickier, a few students needed to pull out cubes or other counters to model.
We are definitely in a better place with our fractional understanding--but a few students are still really struggling with the idea that if 1/4 of 20 is 5, 3/4 of 20 is 15 so next week we will do some more work with that.  I did introduce a "drawing model" to some students--next week I will expand on that.  I do think we are clear that a "whole" can be a "thing"--like a pizza, a pan of brownies, or a piece of paper but that a "whole" can also be a "whole bunch" or a set.  More next week!

I did include the Skittles fraction sheet if you are interested. . . 




***UPDATE***
This blog post is now a part of my comprehensive fraction unit available by clicking the image below.  Hundreds of teachers have now used it to change the way they teach fractions!  



12 comments:

  1. That Skittle Fraction Freebie looks great! I am just starting fractions with my fourth graders, so this will be perfect. We used skittles for mean, median, and mode and they went nuts. They are going to be so excited! Thank you!

    Amy
    Eclectic Educating

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    1. You can't go wrong with candy, in my mind! :) We can't be serious ALL the time!

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  2. Thanks so much for the fraction freebie - it looks fantastic. My class loves when we use food as manipulatives!

    Looking From Third to Fourth

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    1. I, PERSONALLY, love it when we use food as manipulatives! I always have to buy TWO bags to make sure there are enough...and then--of course--there are leftovers!

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  3. I've used skittles before too :) Also froot loops and we've made fraction bracelets with beads - you get a neat bracelet at the end of the lesson to take home to mom :)
    Lynn

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    1. Sounds like a blog post in the making, Lynn... ;)

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  4. Nice activities! I'm featuring this post on Bagels and Blogs tomorrow. :)

    Donna
    Math Coach’s Corner

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    1. Thanks, Donna! I just marked your post from today...next week is number lines for us! I am hoping you got to see some of my posts from earlier this week--further evidence of what real problem solving is! Thanks for stopping by!

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  5. I teach 5th grade, but this post was amazing and I think I can do most of what you described, even if it will be a review for a lot of my kiddos. I am so glad I found another upper elementary blog. I am your newest follower here, on facebook and at your TPT store!!

    Julie
    My Journey to 5th Grade

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    1. That's great, Julie! I'm so glad you found me! I think a lot of things I do can easily be tailored for 5th grade...and, to be honest, I tend to "teach high" and support those who struggle. We should never underestimate our students!

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  6. Thank you for this freebie! I'm doing fractions now, and "fraction of a set" will be after February vacation!

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    1. February vacation? NICE! Glad you like the freebie! My students had a ball!

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