Wednesday, November 27, 2013

Fractions, Fractions, Fractions! ~Differentiation at its Best!

Hi All,
This post is going to be about FRACTIONS! And, DIFFERENTIATION (don't you love it when it just works out?) We have been working on adding and subtracting fractions with unlike denominators in my class. I started with Jennifer Findley's Winter Themed Fraction Centers, specifically I used the snow globes addition and subtraction of fractions task cards. (These were simple problems with unlike denominators that were easy to make common, no word problems, just equations, so a good first step for practice).

Once students understand finding common denominators, I always move to subtracting fractions with unlike denominators where you must "borrow" or "regroup." I decided to make my own problems for this concept, breaking the different types of borrowing problems down instead of using my old worksheets that had everything all mixed up.

I came up with three types of problems:
* Whole Number Start
* Mixed Numbers with Like Denominators (provides a scaffolding/easier set of problems for students who have difficulty moving to multi-step problems; they can get the hang of borrowing without having to worry about finding like denominators, then move on to putting it all together with the next set of task cards).
* Mixed Numbers with Unlike Denominators

For whole number start, I taught students to use the "add up to start" strategy:
I hoped to develop some mental math skills, and students loved it because they found this method to be simple to understand.

Now, did I mention that part of this post was about "differentiation at its best?" Well, this set of task cards (and a few others that I have) allowed me to differentiate for the different needs in my classroom. I copied each of the three sets on different colored card stock. (The three types of subtraction problems come with 16 questions, with two of the sets having 8 equations and 8 word problems).

Most of my students were able to complete all of the "whole number start" problems on the day I introduced it. (I am not always concerned that students finish all of a set of task cards, but that they get enough practice, so often, a handful of students don't end up finishing them.)

On the following day, I explained to students how to borrow 1 whole and convert it to the fractional parts that they needed in order to be able to subtract. I then explained that I had two sets of cards (one with like denominators and one with unlike) and allowed them to choose where to start. I also told them that if they weren't sure which would be best for them to start on, just ask me! (I held my breath hoping that students who needed to start on the easier problems--like denominators--would choose to do so...and they did!) Students who started with the like denominator problems (orange cards) moved on to the unlike denominators (green cards) later in the week.
Once students completed the green set of cards, they worked on my Candy Shop Task Cards (a mix of adding and subtracting fractions with unlike denominators, including problems where students have to borrow.)

 Subtracting Fractions with Unlike denominators task cards word problems

 Adding Subtracting Fractions Unlike Denominators Task Cards Word Problems Models
This is our second year teaching the Common Core State Standards, and I believe that I am finally getting my resources for math stocked so that I can better differentiate for my kiddos. I have a group of about 7 students that always need reinforcement of a lesson and move a lot slower than the rest of my class. Most of the rest of my students are "gifted" and just catch on to math concepts very quickly. What to do, what to do with all of these different levels of math students? Often, I introduce something quickly and allow my gifted students to ask questions as they are working, instead of trying to hit all of the ways they might see the problem. I have also developed the strategy of explaining a common question that pops up to one or two students and then asking them to teach others when they come to me with questions. It works out pretty well for us!

My group that moves a little slower gets a reteaching lesson, perhaps explained in a different way, and some extra practice with me before they head to working on task cards. They worked at the kidney table this week and I sat with  them for the most part. This group also benefits from immediate reinforcement, so I am sure to check their work regularly during task card work. (This also helps me catch them before they make a pattern of mistakes too many times.)

You know what else helped my differentiation the past two weeks? I was able to fit TWO large carpets in my room! I have one in front of my reader's workshop white board and one in front of my smartboard. I also have a kidney table, so I was able to send students to different carpets to work on the different levels of task cards. When students finished one set and got their answers checked, they are able to move on to the next carpet and set of questions. It worked like a well-oiled machine!

Next, we move on to multiplying and dividing fractions, so I have to assess what materials I already have for this and get to work on anything new that I need. You can check out all of my fractions products HERE as I reorganized and labeled some of my TPT store this week!

After a successful week of differentiation in math, I feel like "Genius teacher"~said with sarcasm! Will I ever perfect this machine? Sometimes I find myself relearning lessons that I thought I learned years ago (with 8.5 years under my belt); sometimes I find it hard to carry what I thought I learned from one group of students to another group, but then they show me that they need the same basic structure!
PS~When differentiating with a number of different task cards, worksheets, or problem sets, PREPARED ANSWER KEYS are a MUST for my sanity! All of my task card sets come with answer keys and I fully appreciate it when I buy a product that has provided a key!!! (Often, I let my students check themselves...they don't cheat and help themselves confirm answers!)

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