Blog Archives

Math 3 File Sharing

11/17/2014

Have you ever found a great resource on the web that you would like to use to teach your students but ended up spending hours turning it into something you could use because the file was in PDF or some other non-adjustable format? Are you the type of teacher who likes sharing lesson content ideas with other professionals? Would you like to have easy access to lesson materials in their original file format so that you can customize them to your teaching style in the format that you have chosen? Then the Weber School District (WSD) Math-3 (honors) Professional Learning Community (PLC) file sharing site is for you.

I created the WSD Math3H PLC file sharing site as my Math for America (MfA) Master Teacher project. My vision for the file sharing site is an outgrowth of the The Weber School District file sharing site called "Weber Tube" which allows Weber School District teachers to upload their teaching files that they can then embed into their blogs. Unfortunately, the files on WeberTube all end up being PDF and are not customizable.

The WeberTube file sharing site gets quite a bit of traffic. In fact, my files have been viewed over 197,000 times!

I wanted access to original content and felt that sharing my own materials was an "even trade." I have created my own file sharing site for uploading files in their original file format as a means of bringing together member lesson ideas so that everyone can benefit. The link to my site is: http://math3h.pbworks.com/ which takes you to the FrontPage.

The file organization format follows a schedule of topics that was developed based upon the Weber School District Math-3 Scope and Sequence Document (a suggested order of topics created by a team of Weber School District teachers). Each PLC member takes the lead responsibility for a given week on an alternating basis. The lead person selects in advance the lesson they are responsible for and other members provide inputs to that lesson. Lesson inputs can be used by the lead lesson preparer but are not required to be used. The goal is having original content available. For the first iteration of this process, one finalized lesson per week is the goal.

Members upload files and put them into the folder corresponding to the week that topic is listed on the schedule.

If you do not teach Math-3 (honors), I envision the project expanding to include Math-2 and Math-1. If you would like to be involved in the project by uploading content for your own use and sharing your own materials, go to the file sharing site: math3h.pbworks.com and click on the link requesting to join. If that does not work, please send a request to jelong@wsd.net (subject: math3h.pbworks.com).

We can all benefit from a file sharing site like this. Please consider joining.

About the author: Jeff Long teaches math at Roy High School in the Weber School District. He coordinates the Weber School District Math-3 (honors) Professional learning community whose file sharing site is math3h.pbworks.com. His school bog is at http://blog.wsd.net/jelong/ .

Are you a Utah math teacher? Do you have a favorite task you'd like to share? Please email MaryAnn Moore at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.

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Mathematical Modeling Continuum

11/1/2014

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Last weekend I attended the Math for America Utah Fall Conference. The topic of the conference was Mathematical Modeling and the presenter was Kara Imm, Co-Director of Math in the City. My mind is still spinning a little from some of the ideas I received, but I wanted to share one or two in particular that have already had an impact on my teaching practice.

Less is More

Original from Ellen Whitesides Adapted by Kara Imm

Dan Meyer has been talking recently about how "You can always add. You can't subtract." Usually a mediocre math task or even a good math task can be made much better by removing some of the information. For example, in this task called Styrofoam Cups by Andrew Stadel, rather than presenting students will all of the information they need to solve the problem (how many cups will stack to reach the height of the door), Andrew Stadel asks students "What information would be useful to know here and how would you get it?" Since we're not in Andrew's classroom and can't actually measure the height of the door and the height of the cup, he provides us with links to pictures of that information which can be given to students when they request it. By leaving that information off to begin with, students are given the opportunity to think about the problem and why that information would be useful.

I find that sometimes when students are given a problem that gives them every piece of information they need, they have a hard time then knowing how to process the information. In contrast, when I allow students to think about and request information, they have a much better idea of what to do with it because they've thought about why the information would be important and how it relates to the situation.

Processing the Information

Original from Ellen Whitesides Adapted by Kara Imm

As students ask me for information, I ask them "Why do you think that would be important to know?" After that student gives their reasoning, I like to ask a few other students if there is any other reason they would want to know that information. I don't tell them how to use the information they request. They tell me!

Choosing the Model

Original from Ellen Whitesides Adapted by Kara Imm

Let the students choose the model! That is one of my biggest take-aways from Kara Imm's presentation last weekend. During first term, I always focus on connecting multiple representations of functions (picture, words, equation, graph, table). When I presented the Styrofoam Cups task to my three honors classes two weeks ago, I gave them this multiple representations form that I created (see document at right) to use in solving the problem. I was so concerned about their fluency in determining independent/dependent variables, slope, y-intercept and creating multiple representations, that I took away their opportunity to choose the model that made the most sense to them. I didn't let them choose a model - I made them use all of them! Coming back to the classroom this week, I could hear Kara Imm telling me "Less is More" and Dan Meyer telling me "You can always add. You can't always subtract." So that's what I did. I broke this lesson into two days for my accelerated class. On the first day, after we discussed all the important information, I had them choose any strategy they wanted to solve the problem and record their strategy in their math journal. On the second day, I asked them to describe their thinking and wrote them out on the board. The strategies ranged from guess and check, to writing an equation, to drawing a diagram. After we had discussed all of their strategies, I gave them the multiple representations form. This seemed like a good compromise between letting my students begin by choosing their own model and then later making certain that they are able to move fluently between models.

Moving Along the Modeling Continuum

Each of these ideas about mathematical modeling (Collecting and Selecting Information, Processing the Information, and Selecting the Model) can be represented along continuum. Some tasks are high in one area and low in another. Sometimes all a task needs is a small tweak to make it fall a little higher on the modeling continuum.

A Final Thought

In the four classes that have done the Styrofoam Cups task, my students were able to determine the information that they needed rather quickly. However, all of those classes were honors classes. This has me wondering if I perhaps ought to make some changes before I run this with my regular ed classes next week. One thing that really got me thinking was this blog post by Joe Schwartz from Exit10A. Joe talks about working on his own to solve this swingwraps task, also written by Andrew Stadel. What fascinated me most about Joe's thinking was this image that he shared:

To help him think about how many times a swing would wrap around a pole, he grabbed a poster tube and a chain, and wrapped the chain around the tube. What a beautifully simple model! I would have never thought of doing that!

At our MfA conference, Kara Imm suggested providing students with a Tool Table. For the task we did at the conference, the tool table held paper (lined and graph), rulers, string, markers, tape, scissors. There were also pieces of tape on the wall to use as 'measuring stations'. We had each been instructed to bring a graphing calculator to the conference. Kara later told us that she wished this hadn't happened, because it limited the types of models that we constructed. She mentioned that she sometimes puts a limited number of graphing calculators on the tool table - but not enough for all students/groups to have one. Students are given full access to all the tools at the tool table, but are not told how to use them.

My students have tool baskets at their tables, in which I vary the tools that are available depending on the activity. When I run the Styrofoam Cups lesson with my regular ed math classes in a week or two, I'm going to include some cups of varying sizes. If students struggle to identify the information that they need to solve the problem, I will give them some time to experiment with stacking the cups in their tool baskets, if they choose to do so. Just another testament to the power of online collaboration and the #MTBoS! Thanks Mr. Schwartz! I would have never thought of that without you!

About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.

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Math 3 File Sharing

Mathematical Modeling Continuum

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