NCMSA10: Algebrafy Your Math Instruction

Algebrafy
11:00am – 12:00pm
3/15/10

NOTES FROM THE MATH TEACHER ON MY TEAM ALSO AT THE CONFERENCE TODAY!!
MY THOUGHTS IN CAPS

Presented by The Teacher Academy

Problem 1)A snail is crawling up a pole 5 feet in length went up 4 feet each day and 3 feet each night.
How long would it take the snail to reach the top? What if the pole were 7 feet in length?
28 feet in lenght? m feet in length?
        
        OUR GROUP FIRST THOUGHT 1 FT PER DAY(THEORY 1), WE THEN DISCUSSED WHAT WOULD BE THE DEFINITION OF A DAY, WHETHER THE SNAIL WOULD REACH THE DESTINATION BEFORE NIGHT(THEORY 2).

        THEORY 1 ANSWERS = 5 DAYS , 7 DAYS , 28 DAYS , M DAYS

        THEORY 2 ANSWERS = DAY 2, DAY 4, DAY 25, Y = M – 3 MOST AGREED WITH THEORY 2

Algebrafying a problem is going over every part of a problem and asking questions and explaining a problem,
its parts, solutions, and thought processes instead of racing through problems to get answers.
In the previous problem you would ask what does the y mean? the m? the 3? etc…

“Good questions and good problems are hard to come by”

Algebraic Habits of Mind – from a book by Mark Driscoll, ‘Fostering Algebraic Thinking’

        Doing/Undoing – input/output , working backwards
        Building Rules to Represent Functions – organizing info, predicting patterns, chunking info, describing
                rule, diff representations, describing change, justifying a rule
        Abstracting from Computation – computational shortcuts,calculating without computing, generalizing,
                equivalent expressions, symbolic expressions, justifying shortcuts

        *presenter also gave us a list of questions from his book for each section*

Problem 2) You have a balance scale, and you are trying to weigh 40 packages of meat ranging in weight from 1kg
         to 40 kg. You only have four weights with which to work: 1kg, 3kg, 9kg, 27kg. How can you weight each
         package of meat with just these four weights?

        ALL OF OUR ANSWERS RESULT IN A COMBINATION OF THESE WEIGHTS OBVIOUSLY. THEN WE EXPLORED THE POSSIBILITY
        OF A PATTERN. FOR THE ONES WE FOUND A 1, NO 1, SWITCH 1 PATTER. FOR THE 3’S WE FOUND A 3 IN A ROW, SWITCH
        3 IN A ROW, NO 3 IN A ROW. FOR THE 9’S YOU GET 9 IN A ROW, SWITCH 9 IN A ROW, NO 9 IN A ROW.

presenter recommended a full class period for students to solve this problem

Algebrafying Instruction
        select an activity and address the following categories
                What is the original task?
                What algebraic habits of mind are illustrated?
                how can i algebrafy the activity?

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