Friday, April 17, 2015

Doritos Roulette

This task is why I am such a proponent of Twitter. Living in a small district you may be the only game in town when it comes to middle level mathematics (or whatever your subject is). It's difficult to hear about new ideas unless you take your own initiative to seek out said ideas. Through following a select number of mathematical experts on Twitter, I am able to find tasks to ensure my students have the best experience possible. This particular possibility is courtesy of @mathletepearce. How else am I going to connect with a math professional from Canada without Twitter? We did a professional development dealing with Twitter the other day and while we have some outstanding teachers in our district, I was a little surprised that very few were taking advantage of Twitter as an educational tool. I was very pleased that out district is pushing this additional mode of personal professional development.

Here is the task with additional questions. This is what the students saw on my television and on their laptops when they walked in.

http://bit.ly/1F6zZ8X

I like to make this as real as possible, so I bought a bag of these chips off of Amazon. It cost a pretty penny, but the students really enjoyed actually eating all of the chips and keeping track so we had some real data. @mathletepearce has a video on his link with data if you don't want to buy the chips, but again, I like to use the data that is relevant to my students upping the excitement level.

As we were collecting data (we did this at the conclusion of a few class periods...and by collect data I mean eat chips), I noticed a few inconsistencies. First, we had a lot of broken chips in our bag so it was hard to get an accurate total chip count. We ended up with way more than was supposedly in the bag. In addition to the broken chips, I feel some of my students might be on the wimpy end of the spectrum when it comes to properly identifying a "hot chip." In a bag where the chips are mixed, one would assume that there is a small amount of cross contamination involved. I felt like any small hint of spice resulted in my students tallying a hot chip when in reality it might have been a regular. In the grand scheme of things it didn't really matter because it brought more discussion into the theoretical and experimental probabilities.

One thing I noticed about this task was that it was a little ho hum as far as student answers sans the last question (and I didn't really like that one either as far as answers go, but we did have a nice post discussion). One theory I had was that the questions were not as high level as normal. That may have been it, but I actually think my students are just getting better at solving these tasks...more specifically figuring out what needs to be done. Up to this point many of my students had to spend a lot of time planning out what they needed to do to solve a question. I feel that through the use of these tasks through 6th and now 7th grade (I've had them for back to back years), students are able to dissect the different pieces of information faster leading to a quicker result.

Here are the standards I associated with this task. I have also included student work at the bottom along with my guide to help me quickly discuss with individual students or groups.

7.RP.A.3





























My Discussion Sheet


What does a task look like in action?

Spreadsheet of Task I Have Used in the Classroom

Other Posts with Tasks Containing Student Work

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Tuesday, March 31, 2015

Elevator or Stairs Task


This week's 6th grade task is brought to you courtesy of @daneehlert and deals with one of life's greatest dilemmas...do I wait forever for the elevator or just suck it up and take the stairs? I've been in this situation many times and it seems like I always make the wrong choice for some reason (similar to when I choose the wrong line to check-out at in Target).

My class is self-paced for the most part, but at the current time most students are somewhere in our ratio unit. The task took longer for some students because they were at the very beginning of the unit and the task actually acted as both instruction and application. It was interesting to see the comparison between student's work who had already completed the ratio unit compared to those just starting. The only really difference was how long the task took...the learning was solid both ways.

Here is the original page for the task...

http://wmh3acts.weebly.com/elevator-or-stairs.html

Here is the modified version the students were presented with...

https://docs.google.com/document/d/17qJNU_qvDe1Tx3wV0DA6bROrCUZiRmoZVCJ6VcaIZDI/edit?usp=sharing

I actually predicted this in a Tweet prior to the start of this task (which is more of a reason for teachers to plan obsessively to try to predict anything your students may come up with or struggle with so you are prepared...you won't, but try), but my students had a hard time grasping how if you were on the 4th floor, you really only had 3 flights of stairs to the 1st floor (same goes for the elevator).

Even though I push like crazy for as many labels and explanations as I can get, this concept is not as automatic with my 6th grade as I would like for a few select students. I noticed the two different sets of labels on the ratios were getting a little confusing to some. Seconds and stairs versus seconds and feet...this problem was most prevalent with those not using labels, so make sure to encourage labels and a key point of mathematical understanding.

The differences in methods were also interesting. When providing instruction with ratios, I always start with the ratio table. I feel like this makes the most sense to students, and also provides the base understanding needed to eventually shift to a quicker method. In the student work you will notice many students using the table, but other students who graduated to something else. I do not explicitly teach any shortcuts with ratios. I have found that this only skews the learning and prevents long-term understanding. When students are ready for the shortcuts, they will intuitively discover them.

Question two ended up being one of the most difficult questions the 6th grade had to encounter this year task-wise. I think most of this was due to the sheer amount of information each student had to keep track of. Again, having everything labeled really helps with the confusion. Students who were probably the most successful quickly figured out how many seconds it took to traverse one floor with the dueling modes of transportation, essentially creating their own usable ratio. Many students opted for a large scale chart which worked well but was time consuming.

We addressed many interesting questions like how the speed going down the stairs might change if you had a large number of flights, and what if you had to stop on the elevator to pick someone up? All of these are the unforeseen variables of life. Math is normally presented a lot cleaner than life. That is why I like these tasks so much. You can really dive into the all the variables at play and decide how much each one would change the outcome. Below is our student work, standards, as well as my help sheet for the task. Hopefully now you will be better prepared for when math and life collide!



8.EE.C.8.C























My notes to help with the discussion


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Monday, March 16, 2015

Cookie Cutter Task

With Pi Day on the horizon (at the time), I decided to use a task that focused on the circle, which is a big introduction into the 7th grade curriculum. We started talking about circles about a month ago in more of a distributive practice fashion, measuring the diameter and circumference of various circles as well as a few other situations involving everyone's favorite horse Prickly Pete (apologies...low-quality video) tied to a rope (click on "problems" and yes I know it's a goat).

This task is courtesy of @mathletepearce. Here is the original situation...

https://tapintoteenminds.com/3act-math/cookie-cutter/

This task is actually also accompanied by a video of my classroom that I decided to tape as an extra bonus...

Classroom Video

Here is the information and questions I displayed for the students as they walked into the room...

http://bit.ly/1MhEopX

This task ends up being a fairly straightforward subtracting out an area situation but the circle information is so new to the students that it adds an extra layer of thinking as to what exactly needs to be subtracted out. As we went through the task, a lot of interesting student ideas or missteps occurred (in no particular order):

*Do I use the circumference or area?

*How do I find the distance or the sides of the original dough?

*What does the decimal mean at the end of the first question when I found out there were three extra cookies? This was particularly interesting because many students thought this was the leftover dough at first when it is actually how much of a cookie is left.

*Could I just ignore the twelve original cookies and not subtract them out, instead just finding how many cookies could fit into the area of the original dough?

*What's a way to find the leftover dough after the 15 cookies? Take the area left after 12 cookies and subtract off the area of 3 cookies!

*Does circumference and diameter serve any purpose other than finding the area (actually just the diameter)?

*Do the little spaces of dough in between the cookies make that much of a difference?

*If there was about 2% of the dough unused, what percentage of the dough is needed to make a cookie?

*If there is no decimal left for the dough, does that mean there isn't any dough left?

*Should I find how many of the square cookies fit into each side of the dough or figure out how much space each of those cookies are and how many would fit?

*1/4 is 25% so 1/8 would be half that much?

*Oops I figured the square cookie as a circle...

There were a lot of big x-outs on student work this time around. I was really glad we did this task when we did because I think it did force the students to think deep past just the simple circle calculations into what was actually important...and there nothing wrong with students struggling, that is just part of the process. Below are the standards, student work, and my help sheet. Happy late Pi Day!
7.RP.A.3





























My discussion help sheet

Other Posts with Tasks Containing Student Work
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