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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How I Implement Tasks in the Mathematics Classroom (With Classroom Video)

Over the past few months I have featured the tasks of many mathematics experts on my blog. I credit these individuals for supplying my students with a premium experience for nothing. It is amazing to think about all the money that schools put into curricular materials when the best materials are usually free.

If you've found some of these tasks, then as a math teacher you have conquered half the battle. To get all the way there, it really depends on how effectively you use these tasks. This can be difficult because you must have a classroom culture where discussion and inquiry are the norm. The culture must also include students who are not afraid to falter (because they will falter). Transforming your classroom into this type of environment won't happen overnight. It takes days and weeks of modeling and discussion. I wrote a blog post for NCTM's MTMS Blogarithm on how to transform your classroom that can be found here (part one) and here (part two).

Implementation of these tasks differs slightly depending on the teacher...but the goal is the same. Here is @ddmeyer's approach...and I took a lot of cues from this because I use a lot of his tasks and believe in his philosophy. Here is what I do...adapt as you see fit.

1. Students walk into my room and everything is ready to start. There is a timer set to know when class starts (we don't use bells), but the students always start before timer because they want to get started...they enjoy seeing what the task will be for the week. This particular week it happened to be about cookies...and who doesn't like cookies?

2. I have a big television in my room. All of the information for the students is front and center on the television so as soon as the students walk in, they know what is happening. The info would look like this minus the person who made the task and the standard numbers. My students all have their own laptops, and since my Google Doc they see on the television is already shared with them, they can go to their computers and have access to all the links and a closer look if they cannot see. I house all of these pages on my classroom website towards the bottom. If your students do not have computers or tablets, you would just show this information to the whole class (like the informational video), but I like it this way because the students can go back at their own pace and view.

3. Some student like to be grouped together, some students like to stay by themselves, but either way I don't select the groups or who is by themselves. Some of these arrangements change from task to task and some stay the same. The students who are by themselves still talk with the other groups and me so they still have a large amount of communication happening.

4. I basically work the room for the whole period...walk around and listen to conversations, trying to help out without helping too much. I am good at walking away from students when my intention is to make sure they think about the situation for awhile. Middle school students are great at throwing out responses that have not been analyzed...and this helps. My 6th graders thought I was just rude at the beginning of the year but they figured it out. Students are going to struggle, but that is part of the process. When you first implement these tasks, students will struggle A LOT...especially if they have only been exposed to the traditional math class where discussion and collaboration can be lacking. Most of the discussion happens between groups or with me, but we will stop as a whole group if someone has discovered something noteworthy or if I can see everyone is struggling on the same idea and we need a classroom discussion.

5. Once a group or individual has finished a task, I will look it over. I may have also heard enough from the group that I just have them turn it in and I will look it over that night. What I am looking for from each student is a unique explanation so it is clear to me that they aren't just writing what a group member has, but that they actually understand. I will often hand back work and ask more clarifying questions to be able to gauge further if everything was understood. Ultimately I give the students an hour in class and then a week to finish the task before it is due. This fits nicely with my self-paced philosophy because some of these students need more think time than the hour.

I have included a link to a video of my 7th grade students participating in a task. The link will take you to a Google Doc with some information setting the stage, and the video is broken into four sections. Hopefully this post along with the video will give you ideas on how you can implement these tasks into your classroom.

Problem-Solving Task Video

Other Posts with Tasks Containing Student Work

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Wednesday, March 11, 2015

Shower Versus Bath Task

Last week's 6th grade task was courtesy of @ddmeyer and featured the price difference between taking a shower and taking a bath. This is a ratio heavy task and truthfully we have just started discussing ratios and proportions, so it was interesting to see how the students used what they already knew to come up with solutions.

Here is the modified task I displayed on my television before class for the students. As you will figure out from the student work, I changed the cost per gallon of water to 1/5 of a cent instead of the $0.19 I was using. I should have done some fact checking...

http://bit.ly/1A5Zcb7

Many of my students got off to a good start, and there are many paths to get to a reasonable response, but about 1/4 of my students made the mistake in some way of not realizing that the times displayed were minutes and seconds. I should rephrase that...I think they knew the time was minutes and seconds, but since the time per gallon was in seconds, answers for total gallons were off which made for a good discussion piece. Some students tried to divide the time (2:23) by the 26 or 27 seconds for the gallon in the shower, which wasn't correct because 2:23 isn't 223 seconds. I also had students count up or count down by seconds in a chart type fashion which would have been fine, but some of those students did not realize that minutes are not out of 100 but 60. I also had to have discussions on how to change minutes and seconds into seconds...which should give you an idea of the various levels of students that coexist in my classroom (and I am sure all of yours).

While not explicitly discussed, I like the estimation aspect to these tasks. Many students realized quickly that the bath is going to use more water due to the combination of longer length and a shorter amount of time to use a gallon of water making more gallons. This seems pretty trivial, but I am excited that my students take the time to think about these idea ahead of time. Most of my students have a good idea of the outcome before they arrive at the solution which is an important skill to have in my book.

If you are a 6th grade teacher and have not started discussing ratios, this is a great way to get started. Seeing the simplicity of 10 seconds being 1 gallon and trying to arrive at an ending time provides a nice visual to get the students primed.

Below are the standards I felt this task involved, along with student work and my discussion sheet I planned out prior to the task.

7.RP.A.3














My Help Sheet I Prepared Prior to Task


Previous Posts with Student Work



In-N-Out Burger

Dr. Clayton M. Edwards
Ed. D. Curriculum and Instruction (UNI)
Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014
MA Middle Level Mathematics (UNI)
Middle School Mathematics Instructor
Grundy Center Middle School
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