# Open-Ended Math

I’ve been using a blog for math since December. I’m finding it pretty successful on many levels and wasn’t aure that it would be this successful. With my background in Responsive Classroom I like to incorporate academic choice and challenge by choice. I try to make it a point that the children have a choice in how they solve the problem and where they enter the problem at. Does that sound tricky, making a math problem do those things while also ensuring that they are working cooperatively?

I spend time introducing math materials to my students. Base-ten blocks, counters, fraction rods, rulers, etc. Anything they need to use in math I make sure we take the time to learn how to use and care for it. I find this important to do because I want my students to use them if they need them. As new materials are introduced, they are added to their math tool kits. I also make sure that we have plenty of grid paper handy of various sizes in case it is needed. Having the materials out and handy makes a big difference when it comes time to solve problems.

When I first started to create open-ended math problems I began simply. At the time I began we were learning multiplication and division. A post looked something like this:
My four friends came over for lunch the other day. One of them brought brownies for our
dessert. When she cut the brownies, there was enough for each of us to have the same
amount. How many brownies could each of us have and how many did she cut? Explain how
you found your answer.
This was one of many problems we used for the children to learn the fives facts.

By this time the children had identified a strategy that worked for them: equal groups, repeated addition, arrays, or skip counting. They also identified the materials that worked best for them: dry-erase boards, counters, or graph paper. These two choices building Academic Choice because the children were able to choose the how.

As you can see from the problem, it is designed to be Open-ended, allowing the children to choose how to challenge themselves. For some of my students, discovering that we each had two, 2×5=10, was challenging for them. Whereas for others, discovering that we each ate 12, 5×12=60, was challenging. And all of them took the time to find multiple solutions to the problem.

Now that we are working with money, I have made the posts much more complex. I still want the children to practice their multiplication facts, paticularly the 6,7,8, and 9’s while at the same time subtracting money amounts. One of the posts the children will be doing in the next couple of days requires them to choose a number of friends (over 5) to take to the movies. They then have to choose which movie they will see (Pirates of the Carribbean or Kung Fu Panda) ANd how they will see it (2-D, 3-D, or IMAX). Then they have to determine which snacks they will buy, all while staying under a \$100 budget. This problem still builds in all of the choices of the earlier problems, but are now learning some ways to organize a lot of information using graphics.

And all the while the children are required to work cooperatively, with a partner to solve the problem. They post their solution together, and if they have time they provide feedback to their classmates on their response. And of course, we come back together to talk strategy. I think we all enjoy this because the children have the opportunity to share their expertise. It may sound like something like this will take a lot of time, but it takes anywhere from 45-60 minutes a day. On most days, the children have ample time to hop on an online game that allows them to practice math skills. Every mow and then we spend a couple of days on a problem, but that’s usually to provide the children with an opportunity to find a new solution to the problem.

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# Infographics In Math

Blogging is a norm in my classroom to learn and practice mathematical concepts.  I find that engaging my students in realistic stories helps them construct their own meaning of third grade math.  Lately, the stories have become more complex.  About a week ago we worked on a problem around my co-teacher’s recent wedding reception.  The children had no problem applying the mathematics, but it was difficult for them to keep track of all of the information.  I thought that infographics could be one tool they could use.
Throughout the year, I show my students how to break apart complex mathematical stories.  Using a strategy from Comprehending Math, I show them how to read the problem and determine what they know (K), what the want to know (W), and what conditions there are (C).  Over the years I have used a KWC chart, and have also shown the children how to underline what they know, circle what they want to know and highlight/box the conditions.  This typically works when what they want to know and/or the conditions are limited to one thing.
Back to the wedding favor post…
As I conferred with my students I noticed they were not struggling with the math at all.  I was confident in their abilities to solve the entire problem.  Yet, as I was looking back at their comments on the blog I realized that they when they went to respond they were missing chunks of their answers.  I decided that infographics would be a good way to meet a variety of their needs.  That night I took the post, broke it apart and created an infographic to model the process for them.
Using the picture from the blog post, I highlighted the condition with a green arrow to show that we had to spend less than \$500.  Next, I created the table that would be helpful in solving one part of the problem.  I highlighted how much it would cost to make one favor and added a note next to it explaining what I was showing.  Then I highlighted how much money would be spent in all and how many favors would be bought in all.  Again, I included a note explaining what that was showing.  Another part of the problem requested to know how the favors would be paid for in exact cash.  I included the money and a speech bubble explaining what it was showing.  In the end, I included a post-it note on the picture to pull all of that together in a few sentences, explaining the entire infographic
The end result?  Some of them were really jazzed about the idea, while others not so much.  Some of them tried this with the next problem about baseball gear.  My baseball fanatics were happy because they drew a baseball field.  Quite creatively, they decided that they would label the position with the corresponding dollar amount.  For example the item that cost \$4 would go on second base and the item that cost \$8 went in center field.  They used one dugout to hold the conditions and then another to host the table that would help them calculate.  A couple of them swore that they would never do an infographic again, but they would now start using a table instead.  All good, because I really just want them to find a tool that works for them and use it!

# Infographics

I have become obsessed with infographics.  I have seen them popping up more and more frequently on Twitter, blogs, and articles.  Last week, I tried to create an infographic for my end-of-year review.  I had tons of information on it, and probably too much on there.  For our summative review we need to include data, student work, and reflection.
Kinda pretty, in an elementary way, isn’t it?  But honestly, I didn’t know what I was doing.  I was more concerned about meeting all of the criteria for my summative review.  Which this does, but not in a format that will be accepted.  Yes … I had to do it over in Word format.
Despite being told I had to do all of my work over, I decided to give infographics another go.  Because I’m really not a data girl, I decided to create another one based on the data I had to collect.  Which, in the long run was a good thing, because it helped me get re-focused on what I had said my goal was this year.  Yes … I went through the motions of the summative review process.
So over the foggy weekend, I hunkered down with my iPad and started searching for more info on infographics.  It wasn’t until searching through Cool Infographics, Wild Apricot, and Six Revisions (along with a few others) that I realized an infographic is truly no different than those full page elaborate diagrams in a magazine or informational text.  Infographics typically include a visual representation of numerical information like timelines or graphs, and your conclusion of that information (Spyre Studios).
I sketched out what I wanted to include in my infographic and went from there.  My sketch and my final result really look nothing alike.  As I was creating my infographic I remembered that my professional goal was related to 21st Century Skills.  In remembering, I realized that I had not included anything in any of my review about 21st Century Skills.  So, I started to go through my blogs, and classroom Twitter feeds to gather more data.   As you can see, I have much more data on this infographic accompanied by a couple of conclusions.
There are all kinds of Web2.0 tools that you can use to create charts, timelines and maps.  But really, all I used was Excel.  If I were to include a timeline, I certainly would use a Web2.0 tool.  To create the graphic itself, I used Microsoft Publisher.  I happen to enjoy Publisher, but for this particular medium, it has its limitations.  However, Glogster, LinoIt, Prezi, and even a website or blog host could probably allow you to do the same.  Now that I feel more confident in creating infographics, I look forward to using them in the classroom.  Particularly, now that it is the end of the year it would be a great way for my visual-spatial kiddoes to reflect upon their school year or even tell their fourth grade teacher about themselves.