FAST Thursday

Finding Answers and Solutions Together (FAST)

What is it:  Focus on problem solving steps and strategies

When is it:  Every other Thursday (I refer to it as FAST Thursday)

Why:  Utilize problem solving steps and strategies, practice using different strategies and following the steps, expand on problem solving thought process, practice explaining problem solving process by writing and sharing with peers.

Plus, it's a break away from the book and worksheets!  Students like variety and I hate to use the word 'fun,' but math is serious enough and having fun in math makes it more bearable.

First FAST Thursday:  Preparing Students
I hand out a packet that shows steps and strategies for problem solving.  We go over the steps and one example for each strategy.  It usually takes about 1.5 class periods, so I finish everything up the following day.

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Side Note:  Formatting on google drive is different than the actual word document - I don't like google drive, but don't know how else to share.

The following document was found online while I conducted research for my Master's program, which was focused on problem solving in math.  I use a 5 step process, but this is a good starting point, with 4 steps.
https://docs.google.com/document/d/13AuFpcooFNDIFqDY1jHcHzTRbTQdXYpsDezWgvp7jU8/edit
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Second FAST Thursday:  Introduce Step-by-Step Problem Solving Process

My fist activity is very basic.  I stress that I am interested in the PROCESS not the 'right' answer.  It takes a while for students to get used to explaining their problem solving process, but they make leaps and bounds from the beginning to the end!  I don't tell students whether their solutions are 'right' or 'wrong' since I'm not grading on the correct answer.  I tell them if their process is explained and connects back to their visual then they will be okay.

I tried using Scribd. after looking at another post from this week, it works great!  I'll try to convert everything over later this evening.

The following document was presented at a conference on problem solving in math.
PS - Step by Step

Second FAST Thursday Activity:  How many rectangles?

First I pass out the step-by-step worksheet and discuss that I expect them to fill out the paper as they work.  Again, I tell them to focus on the process, not the 'right' answer.  Instead of jumping right in and finding a solution quickly, they need to take their time and analyze what they are supposed to do and how they are going to do it.

After discussing the steps page, I pass out the rectangle activity.  I set my timer for 8 minutes and let them work alone.  I expect that they have 3-5 sentences for their explanation (later in the year, my expectations are 5 or more sentences, but since this is the first activity, I let them have 3 or more).  After the timer goes off, I have students work with a partner and discuss their individual steps and strategies.  Then we discuss as a class and compare the different ways to solve.  So far, I have about 7 different ways to solve (some are very similar to others).  I have a compiled list at school and will try to take a picture of it and post it later this week.

At the end of the class or the beginning of the next class, I ask students what was the point of doing the rectangle activity.
We come up with a list:
To get us to use problem solving steps and strategies
So we can share how we solved
To give use a break from daily practice from book lessons
So we know we aren't suppose to focus on the answer, but the process
To show that there is more than one way to solve problems

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Third FAST Thursday:  Introduce HOM (habit of mind) concept

HOM's are extended problem solving activities.  They take 2 days, so I only do them about every other month.

First HOM:  Handshake Problem

Students get the problem on one page and the step-by-step page stapled on top.  Most of the time I use this after a test or quiz.  So students spend about 15 min on a quiz and then work on this after for the remaining time.  They are supposed to complete it by themselves before sharing with a partner the next day.  This is where I start stressing 5 or more sentences to explain the problem solving process and tying back to the visual and strategy used.

On day 2, students get with a partner (sometimes students pick, other times it's random or I pick - see grouping students post http://msmilleson32.blogspot.com/2012/09/grouping-students.html)
Once paired up, students compare individual work with one another.  Then, they make a poster using pieces from each student or from one individual idea.
The poster must include:
Title
Strategy used
Visual
Bullet points explaining key concepts (i.e. strategy used, what was know, not known, etc.)

Rubric for grading:

Here are some examples of posters:

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Other FAST Thursday ideas:  Used throughout the year, 2011-2012 (The activities don't all require the use of the step-by-step worksheet)

The Weird Number:  http://msmilleson32.blogspot.com/2012/11/the-weird-number-natural-numbers-or.html

Shape of Name:  http://msmilleson32.blogspot.com/2012/09/shape-of-name.html
Integer Poster:  http://msmilleson32.blogspot.com/2012/09/integer-posters.html
Congruent Figures:  http://msmilleson32.blogspot.com/2012/05/congruent-figures.html
Unit Rates and Tootsie Rolls Activity:  http://msmilleson32.blogspot.com/2012/03/unit-rates-tootsie-roll-paper-chain.html
Probability and Odds with Skittles:  http://msmilleson32.blogspot.com/2012/03/probability-and-odds-skittles-activity.html
Proportions (capture/recapture):  http://msmilleson32.blogspot.com/2012/03/capturerecapture-proportions-math.html
Golden Apples HOM:  http://msmilleson32.blogspot.com/2012/11/golden-apples-hom.html

I'm slowly trying to explain projects instead of just posting the students' work without explanations.  That is one of my goals for the school year - post and explain more frequently, so hopefully some of the items above are helpful.