Paging Doctor Math: February 2015

Wednesday, February 25, 2015

Jenga Task

I always like to make sure my students get as many quality tasks as possible, so when I came across the idea of this task, which is arguably more at a 6th grade level, I still wanted my 7th grade students to have the experience since we did not do this last year in 6th grade. You cannot have enough problem solving experiences in your classroom! I also gave this task to my current 6th grade students.

Here is the original task courtesy of @daneehlert.

Here is my modified version of the task as the students viewed it...

http://bit.ly/19eFrJg

While not a huge difference in question three, I decided to use the fraction 6 1/2 with the 6th grade students and 6 5/8 with my 7th graders. 6 5/8 is easier for my 7th grade because they are more fluid with fractions and decimals at this point. My 6th graders could have used 6 5/8, but I think the length of time the computation would have taken is not as important the problem-solving outcomes I am looking for.

We had a problem starting this task because all I gave them was the information on the modified task link. The students weren't sure how to read the label for the board that was $2.72. We stopped and had a discussion of what 2 by 4 by 96 meant. Once the students understood that the boards purchased at the store were 96 inches in length, they were able to begin.

I am all for calculator use as long as students explain their understanding, but I think the calculator actually became a hinderance for this problem...especially on question 3. When the students got 14.4 when they divided 96 by 6 5/8 or 14.7 when they divided 96 by 6 1/2, many thought this was the leftover inches but it was really how much of the extra board was left. This problem was personified from question 1 when students did 96/10 and got 9.6. Not only is .6 end up being 6/10 of a board which is 6 inches, but it is also the leftover amount of inches. This is one of those math occurrences where it just happens to work out that way. Students who draw a picture were much more successful, at least in the short term.

Question 2 was either very brief or fairly time consuming depending on how the students thought about it. Many students figured out that if you are using all 96 inches, you have 480 inches available which exactly matches the length of the boards in the life-size Jenga tower. Others took a more systematic approach, buying a board and saving the leftover until they could create another piece of the tower.

Finally, the terminology I used was fairly confusing from the standpoint of the 96 inch board and the 10 inch board. I needed to have a different word than "board" for both of these items to alleviate confusion.

Here are the standards I attached to this task, along with student work and the set-up page I created for the task. Overall, this was an enjoyable task and the students liked the concept of taking something like the Jenga game and the plausibility of actually making it life size.

7.NS.A.3

6.NS.A.1

6.NS.B.2

My discussion notes on my iPad as I circulate the room talking with groups/individuals...

More discussion notes...

Even more discussion notes...

Thursday, February 19, 2015

Shrinking Dollar Task

I find using these task very valuable as an assessment piece to make sure students can apply what they are doing within a unit, but even more worthwhile when the task comes much later than the unit was presented. If students can apply the information later down the road and can explain thinking in detail, chances are what you went through the first time around stuck. I also like using tasks to introduce new concepts, but that wasn't the case this time around.

For this week's 7th grade task, I found a @ddmeyer task from his spreadsheet of tasks and added a few questions. I also took the answer video and put that at the beginning. The answer video did not have any numbers, but I thought it showed the students an excellent graphic of what this shrinking process would look like.

Here is what I presented to my students:

Modified Task

I think the biggest struggle for my students was the difference between percent growth/percent decrease, and the percentage remaining. To attempt to alleviate this problem, I emphasized that the growth or reduction should not include the original amount. We drew a few pictures to show this concept. I also related this to their own heights. We discussed what taking off an extra 100% would mean in this process as well. This wasn't prevalent with all my students, but it was the biggest problem.

I also had a few students confused with the wording of question six. If you can think of a better way to state that questions, please leave it in the comments. My goal was for them to see that while the sides decreased by 25%, the area actually decreased by 43% to 44% each time the dollar was shrunk on the copier.

As you will notice from the student work, most of my students use a ratio table method to work with all percent problems. I decided to present this as an option a few years ago because this method works for any proportion or percent situation, and the students understand what everything means. In the past I had student who would have to ask if they multiplied or divided in a percent scenario, but using this type of visual has alleviated that problem. Eventually, I have some students move on to other easier method that they figure out based on the ratio tables. In this task, I noticed a few students multiplied by .75 to find the 25% reduction. Other students spammed the divide 4 and multiply by 3 buttons on the calculator to simulate changing the whole to 25% and then 75% making the calculations quicker.

Here are the standards that I felt the task involved. I have also included the student work. One of the students commented that they saw a Despicable Me where they scanned their butt on the copy machine and could we try that next? I think we will stick with the dollar bills!

7.RP.A.3

7.EE.A.2

7.EE.B.3

My prep work I carry around on my iPad to help discussion with various groups and individuals...

I thought I would add this picture...a 7th grader trying to draw 5 millimeters with a meter stick...genius! This is why I love teaching middle school students...

Previous Posts with Student Work

Tile Floor Task

Penny Cube Task

Are the Thunder Playoff Bound?

Toothpick Task

Man Versus Squirrel

In-N-Out Burger

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

cedwards@spartanpride.net

@Doctor_Math (Twitter)

About Dr. Edwards

Dr. Edwards' Publications

Dr. Edwards' Curriculum Vita

Dr. Edwards' Math Website

Dr. Edwards' YouTube Channel

Dr. Edwards' 1:1 Math Philosophy

Dr. Edwards' Blog

Saturday, February 7, 2015

Tile Floor Task

I'd like to start this post with two disclaimers:

1. I don't pretend to know anything about laying tiles or carpentry of any sort. If anything in this problem is inaccurate to how it would be done in real life, feel free to let me know and I will update it...

2. I normally give credit to the creators of these tasks in all of my posts. I appreciate everything these math professionals do to make my job easier and my students' education better. That being said, I have used this task for a few years and I do not know where it came from. I know I modified it in some way, but I don't know its origin. Please fill me in if you know where this came from.

Back to business...of laying tiles. The idea of this task is for students to come up with an answer that would serve as an approximation for how much it would cost to tile the basement in the diagram provided. Here is what the students received at the start of class...

Tile Floor Task Info

I did this task a few times previously where I did not provide a floor map that students could draw on...I just gave them the picture on the computer. I learned that many of my students had trouble accurately drawing the diagram for use (as would I), so I made a few copies for each student. This task for the most part has one answer, but the variation comes in when the students try to decipher the square footage. There are multiple ways to divide up the floor, and students exhausted every possibility.

We had not yet discussed how to find the area of a triangle or trapezoid, so it was interesting to see how the students maneuvered around the roadblock at the bottom of the basement diagram. Some students took one of the triangles and placed it on the opposite side forming a rectangle. Others put the two triangles together to make a square. I enjoyed the creative aspect of something I haven't explicitly taught that can still be accomplished. Many math teachers have the debate as to whether these tasks should introduce new concepts or stick with applying previous knowledge...I say both.

One interesting misconception that I see common in 6th graders was on full display in this task..."should I multiply or divide?" This seems so easy to me that it's almost hard to explain to the students...

Example where you should multiply: 176 tiles multiplied by $17.50 per tiles to get the total price of the tiles. My advice to students...1 tile is 17.50, 2 tiles are $35.00, 3 tiles are $52.50 and so on...

Example where you should divide: 176 tiles divided by 22 tiles per hour to get the number of hours worked by the guy laying the tiles. My advice...start with 176 and see how many group of 22 are available (some students used repeated subtraction for this)...

Both of these methods take forever...but I felt most students came away with which of the two operations should be used before they had to completely finish the longer method.

Another aspect of these tasks that is probably overlooked from a teaching perspective is the amount of preparation the teacher must make to be ready to discuss all of the possibilities (correct or incorrect) a student may present. I like to hope that every student comes up with the correct path on attempt one, but that is rarely the case. I probably have 1000 different conversations during the hour given during class for these tasks, and all the conversations are a little different. As a teacher, you really have to be a flexible and quick thinker to keep up. This gets easier with experience! Here is what I did to plan for this lesson to make things easier...you'll never think of everything but it certainly helps (I do this for all my tasks and store the pics on my iPad Mini which I carry around during class):

Note: Ignore the bottom of the first picture. I accidentally wrote that the 396 was the tiles instead of the square feet, and I noticed my mistake mid-task and had to quickly get a replacement page ready on the go...

Finally, here are the Common Core standards this task focused on along with student work. Notice none of the standards list learning extensive knowledge of the carpentry profession :-)

6.RP.A.1

6.RP.A.3.D

6.G.A.1