Math As A Teachable Moment: Problem Solving

This activity should really be called Problem Solving & Problem Posing because the students do both.
I generally post a problem on the board or on chart paper (if I'm really on the ball).  Students copy down the problem in their Problem Solving books and then try to answer the problem.  The problem is usually based on a concept we are currently working in math such as:  measurement (g, kg, ml, L, perimeter, area), number operations (+, —,  ÷, X ) or time.  Students get about 8-10 minutes to work on the problem.  When they have solved the problem, they write their own problem using the same format.

There's a lot of sharing out and class discussion about HOW we solved the problem (what strategies did you use?)  Students know that they have to show their thinking...not just write down the answer!

Here are some samples of a problem we worked on a couple of weeks ago.  This was a Friday assessment, so it was on a half sheet of paper, rather than in their books.  Most students understood how to solve the problem and I was pleased to see a variety of different ways that students showed how they solved the problem.

This student decided to break down the numbers into tens and ones and then add them together.

This student broke down the digits in the tens place into tens, but then mentally multiplied the ones.

This student multiplied the 20's by 3 (even though he is showing them as 2's) and then added the ones

This student decided she was going to line them up vertically and add them up...the 'traditional' way.  She surprised me because Math and organization are not her strengths, but her work was very organized AND logical! LOL

This students decided to just add the numbers horizontally...the preferred method with many students

This student decided he wanted to be a 'lazy' mathematician and just multiply (his favourite way of adding up stuff)

This is a student created problem modeled after the problem given

Most of my students are very comfortable with this problem solving format, so I decided to switch it up a bit the other day and give them a different type of problem.  This is an example of the problem I gave them:

I am an even number.

I am greater than 20.

I am less than 50.

My digits add up to 11.

Who am I?

Some figured it out fairly quickly, but others balked at the problem.  So we reviewed what good problem solvers do and what strategies might be appropriate to try.  I was surprised that a number of students did not understand what the word digit meant...which prompted a quick mini lesson! And then I reviewed what an even and odd number were to my math challenged students.  I find this particular problem very useful for incorporating the math vocabulary we want our kids to know.

Now, they enjoy creating their own Who Am I? problems and beg me to use their example for the next problem. I think that's a good indicator of the level of engagement these kids are demonstrating.

Math as a Teachable Moment: Weekly Set Up

OK, I wasn't as quick posting this as I would have liked but. . . better late than never. :)

 The math program I use comes with a suggested yearly plan for each grade level that addresses all the prescribed learning outcomes (standards) for my province.  I keep the monthly plans in the math section of my teacher organizer/daybook and refer to them often, just to make sure I am staying on track.  The plans are by no means a prescribed program (it's actually very open-ended, allowing for what actually happens in the classroom and based on student needs/weaknesses) but I find it's nice to have some kind of frame to work with.

We have an hour long daily math block, which is split into 3 parts, allowing me to incorporate a number of activities into each math session. In planning the week, I choose 3 out of 5 possible activities to do each day.  I find this works really well in: 

1. keeping students focused and 
2. allowing for the diversity of learning strengths and interests in the classroom

The 5 activities I choose from are:

1. Problem Solving (PS)
2. All the Facts (AF)
3. How Many Ways (HMW)
4. Weekly Graph
5. Games/Project

This year the weekly schedule looks like this:

Monday        - Weekly Graph, AF, HMW
Tuesday        - PS, HMW,  Game/Project
Wednesday   - PS, AF, Game/Project
Thursday      - PS, AF, HMW
Friday           - PS, AF, HMW, Game

I'm pretty happy with the way it's set up but I think I would switch the weekly graph to a different day and start with problem solving on Monday, as the problem on Monday can be a springboard for the rest of the week's problems.  And I'm not happy with the way the game/project activities are going. . .or not, as the case may be. <sheepish grin>  Needs some tweaking in that dept., FOR SURE!

Friday activities are used for assessments.  I mark the PS, AF, and HMW activities and record them in my Math Assessment & Evaluation Binder.  Each student has a binder pocket where we keep the samples of their work.  I'll write about this in a separate post.

Next time, I'll go into more detail about each of the activities and how it looks in the class and what I'd like to change/keep the same. . .there's always room for tweaking. :)

Note: Please ignore the grid below...I tried to remove it from my post but can't seem to.  Not sure why, I can't??

Mathematics a Teachable Moment

Our district uses a text-based math program called "Math Makes Sense", which isn't too bad, but I really don't like curriculum that is driven by a text book.  First of all, there is a fair amount of reading involved which isn't so great if you are a student who is reading 2 grades below grade level!. . . and let's face it we have a few of them in our class every year.  And secondly, I always find that in a text-based math program you tend to teach the unit and then kind of forget about the concept. . . except for an occasional review.  Can you tell I'm a bit dissatisfied with the program?

Last summer, I decided to look at a program that I had hanging around for a few years. . . I had used parts of it in the past, but didn't really incorporate the whole system as I was a bit afraid thinking I would ease into it gradually.  Because I was switching from intermediate to primary, I thought this might be a good time to revisit the program. . . because you know . . . they do things more 'wholistically' in the primary grades <grin/smirk> and I wanted to embrace my "primariness" (invented vocabulary):))

The program is called Mathematics As A Teachable Moment and was a resource developed in my province by a very talented man named Trevor Calkins.  To make a very long explanation/introduction short . . . I LOVE his way of teaching math.  I think I will have to spend a number of blogs going through all the specific things I do during our math time, but I will let you know that my hour long daily math block goes by sooo fast and we cover so many concepts through the variety of routine activities we do daily that it is awesome . . it's one of those 'where have you been all of my life' kind of things.

If you're interested in brain-based learning, meeting the needs of all learners, want to know how you can meet all your state/province standards, or you're just plain curious,  check out the above website and stay tuned as i attempt to share how the program is working in my classroom. :)