Explore the MathTwitterBlogosphere Post #1

So I really need to get blogging more, so I am so grateful to see this happening. I’ve decided to answer the first question:

What is one of your favorite open-ended/rich problems?  How do you use it in your classroom? (If you have a problem you have been wanting to try, but haven’t had the courage or opportunity to try it out yet, write about how you would or will use the problem in your classroom.)

So I recently finished this problem, which I have been tweaking each year and still don’t think is perfect, but it’s gotten so much better. It’s called The Class Party Problem and involves having students explore the costs of various parties and determine which one would be best based on cost. The students model linear relationships using a table, graph, and equation, then answer some comprehension questions and make a convincing poster as their final product. They also reflect on their learning through blog posts and comment on each others work.

Here’s the task:
The Class Party Problem

Here’s the group work sheet I use:
Cooperative Group Responsibilities

Here’s the Blog Post Reflection:
Class Party Problem Reflection

What I like
This task really allows students of all abilities to shine. All my students are able to fill out the table to get started. Once they’ve done that, they discuss with their groups about the appropriate scaling on the axes to graph their data. My struggling students get stuck on writing the equations, but after talking to them about the patterns in the table, they are able to formulate the cost per person as the rate of change and the initial fee as the y-intercept.

I also like the products they create. (I’ll upload some pictures when I get back to school. I forgot to take some =P) The posters show the tables, graphs, and answers to comprehension questions. What’s nice is that’ I’ve already used the data from their tables to talk about rate of change directly from the table. We’ll be using the graphs to talk about systems of equations soon. Being able to reference back to this problem gives them some context they can see.

What I don’t like and what needs some work
So this is the first year where I’ve really slowed down and allowed them to dive into the concepts a lot more. The comprehension questions are still the ones I used my first year teaching and have to be changed majorly next year. They are too boring and I need to find a way to better surface the concepts that this problem reinforces.

I also think there should be a technology piece to this. Having them graph the lines on the computer and use them to find the intersections. I work at an Arts & Technology school, so infusing art and technology into these products is at the core of our school.

I also need to find ways to scaffold this task for my students with IEPs who struggle working in groups or working with concepts without someone there to help guide their thinking. I had 5 groups (out of 24) who really struggled to complete this task without my constant intervention and they really didn’t learn what most other groups learned.

A bit more
I’m transitioning my curriculum to be common core aligned and it’s taking a lot more work than I imagined. However, I’m seeing my students think more critically and this is a big improvement from my standard direct instruction aligned to California content standards and CST preparation. I’m also very excited that California has canceled CSTs for this school year. I have to say, it took a big weight off my shoulders and I feel like I can be a teacher who works hard to teach the students mathematics and not being forced to squeeze 9 months of content into 7 months.

I look forward to blogging more. Thanks to anyone who reads this! Please give critical feedback, I’m an every growing and learning teacher!

9 Thoughts

  1. I appreciate how in depth you presented the problem with a graphic organizer to organize the information for your students. I am interested to see the blog posts by your students and their discussion. I have tried a blog post with elementary age students and it doesn’t turn out the way that I would like. What tips do you have to support positive discourse through technology?

    1. Thanks for reading! So I built my own site to handle the interactivity in the classroom because what is out there just didn’t appeal to me. One thing I’ve worked on is showing excellent comments left by students. I also remind them that when I read their comments, I should know that they actually read the post, so they should make sure to show that in some way. I have 9th-11th grade students in my class, and it went from “Good Post” the first few times to: “it was really fun working with you on the project, and i must agree, the equation was pretty easy to figure out.”

      What I like about student blogging is that I can read them anywhere and don’t have to carry around papers. I can also comment on their posts and other teachers use the posts to get an idea of how a student is doing in my class.

      I’m planning to do a post here on my website soon, I think I’ll start with the blogging piece!

  2. I really like this activity! I struggle with letting my kids do group work but I think the jobs are very clear and that is what I need to work on. I love the fact that you have kids blogging. How do you make that happen in your classroom…do you have a set of computers they can all use?

    1. Thanks for reading. I too had struggled with group work. For the 9th graders on the back of the group sheet you will notice a table with 18 squares that says “Classwork Points”. While I’m circulating, I stamp this sheet and groups had to get 15 points after 3 days of work. If a group is off task, I pretend I’m about to stamp, then stop and say “I don’t think everyone is following the group work agreements” and walk away. It’s a nice subtle way to keep them on task.

      My school is testing 1-1 computers in all classrooms in the 9th grade this year. I was fortunate to have computers last year as well through a grant giving Chromebooks to Algebra 1 teachers. I’ll share some of my successes and failures in using computers in the classroom in a future post. It certainly takes some work to make them a useful tool and not a distraction.

  3. Great task- I like all of the different representations of the situation. Maybe you could have a set of “question” cards for certain parts that you know they are going to struggle with. On the card you could put an example that models what they might struggle with, and then a question which might lead them in the right direction? I’m thinking one for how to complete a table, one for how to graph ordered pairs, etc? You might be able to make them general enough that they could be used for different tasks…

    1. I love this idea! This sounds like a great way to differentiate, especially with students who have varied skill levels!

  4. Hey Brandon,

    Welcome to the MTBoS! I feel so lucky that you posted before me so I got to read your post! We are doing linear equations next and this activity is perfect. We are working on the activities in the Pattern and Function Connection by Fulton. I read about it here http://exponentialcurve.blogspot.com/2013/09/linear-patterns-in-algebra-1.html.
    The exercises in this book do an amazing job of helping kids see the equation from the table (starting with a pattern). My challenge has always been having students write the equation as well, but I think that going through this book has helped them so much!

    Thank you for including all of your documents with your project. They are amazing and very thorough! I would like to try this project with my students, and am curious to see if the Pattern book really helps them develop the equations. I will get back to you! I hope that you keep blogging, as this was a great project and I’d love to see more from you!
    Julie

    1. Thanks Julie! I love the way they connect the intercept and slope to the pattern. I’ve been working on this with my students, but don’t think they’ve all made this connection. I think I’m going to do this lesson sometime this week as we wrap up the unit! Let me know how it goes with your students!

    2. Julie! I totally did that activity this week and it was a hit with the students. They really got into finding the rate of change and y-intercept in each of the representations. It made graphing lines from slope-intercept form easier too because we have some common language to use when describing the process. Thanks again for tip!

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