Relevent Math Tasks

  Today at the session on cultural context in Math and performance tasks, one of the presenters talked about creating performance tasks that are relevant to students.  She took time to show how to create the tasks that students will understand.

Many places in Alaska heat their houses or saunas with wood.  So she started with a picture of a cord of wood showing it is 4 x 4 x 8.  Surrounding it were four more pictures, each showing a load of wood but in a different mode of transport such as a boat, a pickup truck, a 4 wheeler with a trailer and a snow machine with a sled. The idea is you include enough information so students can find out that not all cords are the same.

Then she showed us a picture of a water tank from one of the villages she'd visited. There were enough items such as a truck that students can make educated guesses as to the measurements of the tank so the students can calculate the volume. 

The discussion made me realized I did a performance task years ago when the high school created a cross curricular unit.

Step one: I had students read an account of the battle of Dunkirk.  I had them note the number of men moved from France back to the UK. 

Step two:  Determine the number of boats they could use from the village and decide how many people each boat could carry.

Step three: Calculate the total number of people who could be carried by all the boats in one round trip.

Step four:  Calculate the time it would take for a round trip, including 20 min to stop, load, and turn around.

Step five: Calculate how many trips would it take to move all the soldiers from the next village over to our village. 

Step six:  Compare the time it would take for the village to move that many people with the time it took originally.

This performance task used a situation they were familiar with so they could picture the operation mounted back in 1940. It turns a historical event into something students could relate to and understand.

Now I know what to do to turn photos, or historical events into performance tasks.

Performance Tasks

Yesterday, I was privileged to sit through a great session performance tasks.  It was awesome.  The presenter started with the handshake problem.  Its based on the idea of if you have a certain number of people in the room and everyone shakes each other's hands, how many handshakes happened?

Once everyone had an answer, people wrote their answers up on the board.  Rather than say who was correct, she had us stand up and recreate it while writing the information in a T-chart on the board.  By the time she got to the end, everyone understood what was going on and who had the answer.

She defined performance tasks as tasks with either multiple answers or multiple ways to get single answers.  It was also cool because she shared with us student work so we could see their thinking.  As a final step in the process, she had us take our textbooks and find a problem in the section we are teaching to rewrite into performance tasks.

Before we rewrote anything, she showed us how to take a simple coin problem which had one answer and change it into a performance task.  We also talked about ways of grading the task using a rubric.  This is important for me because the state is going to put performance tasks on the next state test in April so my students need to know how to do them.

I have the perfect place to put them.  Wednesdays I usually have the students do word problems from the NCTM magazines.  I think I"ll start performance tasks on Wednesdays.  A performance task is a specialized word problem so we will be moving from problems with one answer to problems with either multiple answers or multiple ways to solve. 

I am thrilled to have had this lesson. The leader is a retired math teacher who now works as a coach.  It is so refreshing. I get tired of going to professional development only to get someone who has no idea how to apply their material to Math.  This was totally awesome and the lady is due back in January at our next in-service.  Yeah!!!!

another view of mathematical tasks.

I took the class on mathematical tasks and learned a few more things.  In addition to ones like you have dogs and chickens.  There is a total of 40 heads and 96 feet.  How many dogs are there?  This one is actually on the internet.  I know because the reading teacher who helps out wanted to try it and found it on the internet.  I am glad to know this because one of my students found it on the internet and copied everything down word for word.  I would have known by the language in the explanation, even if I had not known it was on the internet.  I think if I use this again, I will change the animals so they won't find it on the internet.
The presenter also offered some short tasks that can be given during class and shouldn't take more than 5 mins.  You have a 3 x 5 card and three dice.  You fold the 3 by 5 card in half like a hamburger bun.  You line the three dice up so that all the 7 exposed surfaces add up to 23.  This can take some time and it helps develop both problem solving skills and mathematical vocabulary when you write up how you came up with the answer. 
Some of the places recommended for having good tasks like these include:
School improvement network
Inside Mathematics
NCTM
Illustrative Mathematics
NCSM
NRich.
I plan to check each of these sites out for tasks.

QV lite

I had several of my classes today try the QV lite.  The QV is short for quantitative vocabulary and has the two sections. I had most of my ELL students try the grade 3 quantitative  and most of my students did ok but didn't get 100%. These ELL students are in 9 to 12th grades, so it didn't really surprise me.  The higher performing students in grades 11 and 12 tried the 9th grade tests and they struggled.  I suspect they would have even more trouble with the vocabulary part.
I know that I have to use different methods due to the majority of students being ELL.  I just bought a book called "The trouble with Math is English."  It addresses the issue of teaching math to ELL students and after a quick glance it looks like it will provide me with some really awesome ways to help my students.  I plan to read it and choose one or two methods to integrate into teaching.
I have decided to change my homework assignments.  Instead of more practice from the book, I am looking up complex tasks or performance tasks to assign. Research is indicating that having students do such problems will help improve their understanding of math.  I will hand out the homework assignments and post a digital copy in either Showbie, Schoology, Edmodo or the wiki but I think our school wiki is having issues.  I figure if a student has a digital device, they can download the appropriate app, do the work on the app and then submit it back to me.  Even with digital devices I have a few students who will loose both digital and hard copies.