Tuesday, January 14, 2014

Multiplying and Dividing Fractions Plans

You might recall that going into this quarter, I figured out a planning routine for differentiation that I think is AWESOME applesauce! I take all of the materials I have (task cards, worksheets, etc) and place them on a continuum of difficulty. (If I need to fill in holes for lower levels or higher levels, I begin searching for resources or create my own). In addition, I outlined the quarter with FOCUS CONCEPTS (new material) and REVIEW CONCEPTS (1 day/wk).

I outlined my fractions unit {loosely} before the quarter began, and of course, things have already changed a bit. Mainly, I realized that it would be okay to push a few things to next quarter (like coordinate planes) and spend an extra week on multiplying and dividing fractions. {Keep in mind that I do not suggest only teaching fractions for 4 weeks. We already spent a large chunk of 2nd quarter on fractions--adding, subtracting, and a little intro to multiplying. Can you tell I could literally spend ALL year on fractions and be in MATH~nerd~HEAVEN?}.

I thought I was differentiated to the max already, but as I began to teach my three classes, I understood that what I had considered lower-level needed to be even more straightforward or scaffolded for one of my classes (for this group, I have went back to my old math workbooks). Now, don't get me wrong, these kiddos that I have to drop back to the worksheet for CAN get it and have done so, but I found that they need a more straightforward approach first and then they move into the task card sets. With a worksheet, they seem to get more accomplished and grow more in their confidence that they CAN solve the problems--and they know they will be moving on to task cards, which they have a positive attitude about.

Here's my fraction outline in a continuum format. The first icon will be the easiest/basic entry level, with the activities/practice work moving into increasing levels of difficulty. Also, it is important to note that some of the individual sets of task cards (like the Chili Math Multiplying Fractions) already include questions in increasing level of difficulty. This pack of task cards has 60 cards that I broke into sets. Some of the first questions are straightforward multiplying fractions problems, while some of the later task cards make students think backwards to figure out the factors that were multiplied instead of just the product. Needless to say, these cards have kept us busy busy for a week (with whole group minilessons also included at the beginning of each math class). The extension column includes materials for those students who finish the tasks above and beyond and are ready to move on to other concepts or look at the focus concept in a new way.
Based on my routine math schedule that I brainstormed before the quarter began: 

Mon-Wed: Practice with Focus Concepts (new material we are trying to master, students work through the continuum)
Thurs: 1/2 time Data Day (charting our exit slips performance and assessing on an OLD skill); 1/2 time: Algebraic Thinking Day
Friday: 1/2 time remediation on old skill (based loosely on assessment performance) and 1/2 time continued work on Focus Concept (some students may be working on extensions while others are 'secretly' being remediated, and others are completing work from the week that they understand but just need more time to work on). Some students may also use mobymax.com as a differentiated spiral review/to fill in some unmastered skills.

I will say that in getting the quarter started last week and getting to know my new students, I decided not to implement the Thursday/Friday schedule until our second week back. We will definitely have assessment/data/algebra on Thursday and Remediation/Review on Friday this week.

By the time I teach math for the third hour, I am burned out...and worried that I can't fix everyone's issues and misunderstandings. But, after having a little lunch and getting to my planning time to further differentiate and plan for the next day, I get really excited and LOVE the ability to focus on only a few subjects (I'm also teaching reading/social studies integrated into an hour and 20 minute block).
I hope your teaching life is happy, and please comment with questions as I am hoping that I am able to explain what I am doing clearly, but I am not always sure it is!

Sunday, January 12, 2014

Pre-Assessment: Multiplying and Dividing Fractions

This past week, our run at departmentalizing our grade level began. If you have been checking in to the blog, you know that I was lucky enough to be the one who gets to teach math! I see the other two classes first, then my class returns to me for math. I was initially worried about behavior, routines, etc. but I really think behavior has improved dramatically because I am a new teacher to these kiddos and they get the impression that I am not going to put up with any mess. I love math and my main goals are to help them feel confident, learn to persevere, and to teach them what they need to know. I recently shared my math outline for the quarter which {of course!} changed a little once this week began.

Since I'm teaching two groups of students that I don't know, it was important to me to get to know them as math students as quickly as possible and to be ready to differentiate for them immediately. To prepare, I had each teacher group students into the following descriptors:
* Needs extra support
* Understands/Average
* Quickly Understands (Above Average)
* First to Finish (will always need something more)

These groups were recorded in a chart in google docs and I printed off multiple copies of it to help me learn student names, know how to group them for lessons, and to take notes on how they were doing with concepts during the week.

Since classes are at different levels and each of us got to different points in teaching multiplying and dividing fractions, I started on Monday with a low-pressure assessment that was also leveled in depth of knowledge demonstration. My students who easily know how to solve fraction equations had to write steps for solving the problem and then explain why they did certain steps. Why do we multiply fractions straight across and not have to find common denominators? :)
This assessment was more interesting than I expected and truly did what a pre-assessment is supposed to do. With the first class, many students completed the first problem by multiplying the numerators and keeping the denominators the same. Then for the second problem, some students began trying to find a common denominator. It was interesting (and nice) to be able to tell them that they were remembering how to add and subtract fractions and I was very proud of them for that. I explained that it is important to have a common denominator when adding/subtracting fractions, but you don't have to have one when multiplying. I tried to convince them that they would love multiplying fractions more because you don't have to have common denominators...they had already learned the harder concept last quarter! For students who knew how to multiply, I was able to see if they would simplify the final answers and turn improper fractions into mixed numbers. 

I hope this assessment was able to help students feel confident, rather than like they didn't have any idea what to do. (I was afraid some of them would shut down and not try anything, so I know I'm repeating myself, but I was really glad to be able to say "This is what you do know! I'm so glad you remembered that.")

I also have the same type of worksheet ready for dividing fractions, although I may use it differently with different classes. I haven't talked to my students about dividing fractions yet, so we may use this together to think about WHY flipping the second fraction makes sense. (If you want these, click on the images. I have put the file in my google drive for sharing with you.)
In my next post, I'm going to share with you how my plans {really} worked out and the modifications/change in pace that I already made this past week. 

You can catch up on other posts from my Departmentalizing Math Journey by clicking the icon below!
Happy Sunday Funday :) I hope you are looking forward to the workweek ahead!


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