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!

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!

3rd Quarter 5th Grade Common Core Math Outline

I'm ready to share my outline for math for 3rd quarter. These plans show the standards we will learn each week, the review standards I will focus on on Fridays, and the materials that I have to work with so far. Some of the weeks may seem a little slim, but I'm still working on planning out the specifics of those. I also plan to do a Week-By-Week "Peek at My Week" for math where I will outline the gist of my daily plans. Hopefully, this will help me plan better and you can enjoy the specifics. Did you already read about my math routine?                                                              
These plans are in a PDF with clickable links. Click on the image to go to the PDF. Poke around and see what you find. I have linked a few freebies that go straight to google doc files, so you might find something useful and free.

Modeling Multiplication of Fractions

It sure feels like I have been writing about fractions like CRAZY~CRAZY, but we spend almost all of 2nd quarter and part of 3rd quarter learning fraction concepts. Are you looking for a way to launch your unit on multiplying fractions (read-elicit some prior knowledge and a reality check on where students are in their fraction understanding?) I created these task cards to do just that with my students. I wanted to focus on representing situations/word problems with models and equations. I also incorporated the opposite--representing models and creating word problems. It was interesting to see my students try to color the fraction models to represent the word problems.

Did I mention that these cards grew from the fact that I was pretty sure that many of my high-achieving students could solve the equations for multiplying fractions, but I was not sure that they truly understood what they were doing or why you would multiply a fraction by a fraction or a fraction by a whole number. With these cards, students were exposed to examples, had to represent what it meant on a picture, and had to create their own situations/word problems.

I included 16 task cards each for multiplying fractions times a whole number and fractions times a fraction. 8 of the cards in each set focus on modeling a word problem and 8 of the cards focus on writing a word problem and equation to represent a model.

The student answer sheets for these task cards include all parts students are to complete (IE-models, equations, written word problems, etc).

I also made a version of the task cards that are one to a page so that you can show them on the smart board. This is actually how I used the problems to launch the lesson (students had their recording sheets and I displayed the cards on the board so that we could "math talk" about what we were thinking and share our representations.) After day 1, students worked on the task cards independently. These task cards fit 4th and 5th grade Common Core standards for fractions.

Have you checked out my other recent math posts? Here's a run-down: 

Fractions Fractions Fractions  (differentiation strategies and subtracting fractions with regrouping)

Adding and Subtracting Fractions w Unlike Denominators

Division with Fractional Parts (Multistep and CHALLENGING!)

Multiplying and Dividing Fractions with a Focus on Area Word Problem Task Cards (House Plans Themed)

Multiplying and Dividing Fractions Word Problem Task Cards (cupcake theme)

You can check out all of my fractions products HERE @ TPT

Oh yeah, I also made an "Everything Fractions" pinterest board, if you want to follow along. I've already pinned some goodies, especially websites for integrating technology in math, but I will keep pinning every time I see a great fraction idea.

I'm cooking up one more idea for an interactive fraction lesson that I hope I can make work...

Thanks for stopping by!

Cyber Monday and Tuesday~SAVE 28% on TPT and FLASH Fractions FREEBIE!

Cute clip art from Ink n Little Things 

Time for a sitewide TPT sale! These only happen a few times a year! You can grab everything in my store for 28% off by using the code CYBER!

I just uploaded a new Fractions Skills product~Methods for Comparing and Ordering Fractions. This is a freebie through the CYBER Monday/Tuesday sale, so grab it now! It goes up to 2.25 on Wednesday!

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.)

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!)