Rates and Ratios Intro

Happy New Year!  I had all of these great plans to write lots of posts over winter break, but that obviously didn't happen (as I bet most of you would have figured).  It was very restful and much needed - especially the trip back to the States to be with family for the holidays. (Not to mention I got to go shopping in stores where the clothes fit! Japan is full of petite women, and at 5'9" I just don't fit that category.) 

Anyways, I managed to time it this year so we finished a chapter right before break and started a new chapter yesterday (our first day back) - Ratios and Rates.  I came up with a really cute idea for our intro to this (or at least I think it's cute) for our math notebooks. 

We cut out three similar ovals from different colored paper (I preprinted the ovals onto the paper) and then glued them down into our notebook so they were on top of each other.  On the largest oval we wrote ratios, the definition, how you can represent it and some examples.  Then, on the next oval we wrote rates (since a rate is a type of ratio it fits within the first oval), the definitition and an example.  On the third oval we wrote unit rates (since that is a type of rate and therefore ratio, it fits within the other two ovals), the definition and an example. 

This was a really quick, easy and colorful addition to our notebooks that gives students a visual representation of how the three relate to each other.  Last year I had a lot of students who thought rates and ratios were two completely different things - so I'm hoping this will help clear up that misconception.

Does anyone else have any cool ideas they want to share about ratios and rates?

~Brittany~

Problem Solving

We have officially entered September, and the second week of school.  The first week went very well, and I am SO excited about my students this year.  They all seem to be very sweet, and I am really looking forward to getting to know them better this year.  My schedule is also awesome - I am very happy with how that worked out for this year.  I am super excited about how my math notebooks are working out (although I still have a few kiddos without one - and at this point it's going to be tricky since most of the stores are sold out), but they are coming along well.  And, to top it off, I found out I am going to be department chair this year!  Yay!  One of my professional goals has been to take on more of a leadership role at school, and so I think this will be an excellent opportunity to do that.

I am starting out the year with a strong focus on the problem solving process.  Problem solving is one of our school's CSI (continuous school improvement) goals, and it was decided to use graphic organizers as our intervention.  Basically, it means we need to teach the students how to problem solve (which we do anyways), and introduce a graphic organizer as a strategy for problem solving.  So, that being said, I decided to make our first 'real' notebook entry the steps for problem solving.

I drew up and copied the feet (get it - steps?) for everyone, and had them cut them out and paste them in their notebooks.  We filled in the four steps that the math department decided on last year (understand, plan, solve and check), and then wrote an explanation of each step underneath.  The kids were amused by all of my references to writing on their feet, and turn to the page with their feet, and so on - I thought they were pretty cute, and much more engaging than traditional notes.  I borrowed the idea for the feet from... someone, but I can't remember who - and after looking through my pins and favorite blogs for about 30 minutes trying to give credit where it is due, I still can't find it.  So, let me know if it's your idea!

 

After we completed our steps, we put it into practice with our graphic organizer.  This is one of the graphic organizers that the faculty voted on last year, and that the math department modified to meet our needs.  The four corners have the four steps, and the center diamond is where students write the final answer.  We pasted the problem above the graphic organizer, and then I modeled how to use the graphic organizer.  We did another one together, and then two independently. 

 

One thing I love about the four step plan that we use is that you really do all of these steps every time you're problem solving - it's usually just internal.  Something I focus on in my classroom is being able to communicate about math and the process used to solve a problem.  This graphic organizer is a great tool to help them externalize their thinking.  It takes some practice - and I don't expect that the students have this much information on their graphic organizers to start with, but we continue to use them throughout the year and they do get better at it.  I tell them over and over that it is one thing to be able to get the right answer, and another to be able to explain how you got there.  My goal is that they are able to do both by the end of the year.

 

How does everyone else approach problem solving?  Anyone else have ideas on how to get students to communicate their thinking?