Thursday, December 18, 2014

Are the Thunder Playoff Bound?

Playoffs?????

@mjfenton was able to take a rather unique storyline from this year's NBA season and turn it into an interesting mathematical task.

http://reasonandwonder.com/?page_id=2063

If you don't follow the NBA, the Oklahoma City Thunder have been an upper echelon franchise for the past 4 or 5 years. They have two of the associations biggest stars...Kevin Durant and Russell Westbrook. Both players missed the beginning of the season with injuries, but are back but behind the eight-ball. In their absence, the team got off to a putrid start. OKC fan/teacher @_levi_ assured me that the Thunder would make the playoffs, but I thought it might be better to let my 7th graders decide.

Here is what I gave the students with some slight altercations to the original...

http://bit.ly/137tfGi

Here are the base questions I proposed...

1) If you take the past seasons into account, how many wins do you think the Thunder can finish with this year given the 5 win and 12 loss start?

2) Given that 8 teams make the playoff in the Western Conference, do you think they can make the playoffs with such a bad start? If so, how high of seed would you expect them to get given the standings of the previous 5 years?


3) The all-time winningest season for the Thunder came when they were still the Seattle Supersonics. The Sonics won 64 games in 1995-1996. What percentage of the remaining games would the Thunder have to attain to break that record this season?

As far as standards go...

7.RP.A

Students used a variety of methods to find a way to compare current and previous data, whether it be through use of proportions and ratios/finding percentages...ultimately solving a problem

6.RP.A

Even though I used this with 7th graders, most of the calculations were a product of this 6th grade domain...

I don't think this entirely applies, but I think a case could be made that this task links with 7.SP.A.1 and 7.SP.A.2 as well. Students are using past samples of previous Thunder records and past Western Conference results to make predictions.

This task did not get off the ground smoothly. I knew we were in trouble when a student walked in, looked at the information on my television and said,"NBA, is that football?" One of the biggest problems I had was my students' lack of sports knowledge (and this is boys and girls). Many students didn't know what a record of 50-32 meant. This was a roadblock, but nothing insurmountable...

Students came up with many ways to make the first prediction of final total wins. Here are a few:

*Based on percentage of the previous year (most comparable to this season)

*Based on average of the last 2 or 5 years using both a percentage or proportion out of 65 (we had to discuss how the short year would mess with the average)

*Using the current record since both player's returns (6-1) and using that ratio the the rest of the season (a little higher than average but you could make the argument)

The second question was even more diverse:

*Looking at the last 5 seasons where the predicted wins would slot the Thunder, getting rid of an outlier seed number (2), and averaging the rest

*Using the current percentages of this season and the percentage of the predicted Thunder finish and slotting them accordingly

*Finding the average wins from the previous seasons for each seed

The third question was more of right or wrong answer when compared to the other two.

This task is different than a majority of tasks I have done in my class because there is much more variability with the answers. Frankly, this is because there are more variables to account for and students can pick and choose those variables. Another task I have done recently with many different solutions possible is @MathletePearce's Mowing the Lawn (one of my student's work appears at the bottom of the link). Most of the tasks have done (like most of the @ddmeyer tasks we have completed) have multiple entry points and multiple paths, but usually the solution is similar (this might be an overgeneralization, but I think it makes sense). I don't think either is better than the other...they are just different.

Overall, this was a successful task that I will use again next year. By the way @_levi_, you should be able to sleep at night...all of my 7th graders concluded the Thunder would make the playoffs...you just might be without the home court advantage.

Below is a sampling of student work...Enjoy!












Previous Posts to Tasks and Student Work:

Toothpick Task

Man Versus Squirrel 


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

Wednesday, December 10, 2014

Toothpick Task

This week my 6th grade worked on a modified version of a task dealing with a toothpick pyramid created by @ddmeyer.

http://threeacts.mrmeyer.com/toothpicks/

As you will notice, the primary standard for this task is from the high school set, so I changed some of the questions to fit my 6th graders while using the video. Here are the questions I asked my students to prove...


1) How many complete rows of toothpicks can you make?

2) Will there be any extra? How many?

3) How many more would you need to complete the next full row?

4) How many toothpicks would the container need to create 20 rows?

When focusing in on the standards, my questions align to the following:


6.RP.A.1


*The idea that row 1 has 3 toothpicks and row 2 has 6 toothpicks/row 1 has 1 triangle and row 2 has 2 triangles


6.RP.A.3


*Applying the above concept to an actual situation


6.EE.A.2


*Recognizing that each row is +3 for toothpicks or +1 for triangles

Even more important than the content standards are the Standards for Mathematical Practice. I have found that what any of my students have in knowledge of content coming to me from 5th grade to 6th grade, they are severely lacking in these process standards...and this includes your traditionally high achieving math students as well. I wrote a few NCTM Blogarithm post (part one and part two) on this topic and how hard you must work to ensure that these process standards are improving on a daily basis...and this task is just another opportunity.

Can your students make sense of the problem initially?

Can your students recognize patterns?

Can your students create an argument defending their solution?

Can your students prove a solution with some sort of mathematical model?

These are just a few of the questions I emphasis when doing a task like this. At this point in the year, my 6th graders are used to me listening to what they have to say, and then walking away to let them think a little more. At the beginning of the year they didn't understand why I would walk away when they were stuck or on the brink of a discovery. Now they smile when I walk away...because they are starting to get the point.

As far as student struggles go, one of the main culprits was thinking that the number in each row was the number of total toothpicks. I had a few poor students go to 83 rows because they thought that meant 249 total toothpicks. We had a good laugh when they realized they spent 20 minutes on that process for a minimal result. Those types of mistakes happen and can cause frustration, but all the mistakes can be turned into great teachable moments mathematically, which will ultimately help the student improve. 

After looking this over, what are other questions I could have asked my 6th grade students?

Here are varied levels of student work for this task:










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

Wednesday, December 3, 2014

Man Versus Squirrel

My 7th grade recently completed a variation of a task that I call Man Versus Squirrel. I found this task via this link courtesy of Geoff @emergentmath...

http://emergentmath.com/2014/01/22/guy-racing-another-guy-in-a-squirrel-costume-obviously-a-systems-problem/

Additions to the task were also made by Dane Ehlert as well @daneehlert

http://wmh3acts.weebly.com/squirrel-race-geoff-krall.html

Here are the questions I asked the students about this situation with the expectation to prove each response...

1) If the distance of the race is approximately 360 feet, and the guy gets a 4 second head start, who wins the race?


2) How long would the race have to be in order to have a tie if the guy only gets a 2 second head start?

3) Is Squirrel Man Faster than Usain Bolt?


I did give them an approximation of the length of the race since we have not explored the Pythagorean Theorem...

Through the conversations with my students, I found out that the trickiest parts was to simulate the head start. Many students were confused how to tack that onto and/or subtract it off from and who the addition or subtraction would go to. That is always the interesting part of doing these tasks...you can scour over the task for hours trying to anticipate pitfalls (which is a good idea by the way), but you will never catch them all.

Here are some work examples from my students for your viewing pleasure. I attempted to find different routes for each question so you can see the variability. I will also leave you with one of the greatest quote in the history of quotes (from the second video on this link) that middle school students really enjoy (if you work with middle school students...you can imagine the response).

"And here comes the squirrel...he smells nuts!"














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