## 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

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