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MDM4U week 4. Back to f2f.
“My name is Jamie. I make passwords by rearranging the letters in my name. eimaj is one way. ajmei is another way.”
“How many different four letter passwords can my friends Alex, Addy, Anna and Aada each make?”
To the boards!
#ThinkingClassroom
“My name is Jamie. I make passwords by rearranging the letters in my name. eimaj is one way. ajmei is another way.”
“How many different four letter passwords can my friends Alex, Addy, Anna and Aada each make?”
To the boards!
#ThinkingClassroom
Students are good with this routine. We’ve been collaborating virtually. They know they have to work on individual boards but can chat.
They look to the red marker for hints.
We lean on our knowledge of Permutations from two weeks ago.
They look to the red marker for hints.
We lean on our knowledge of Permutations from two weeks ago.
Easy to brute force this problem.
“How about my friends Archie, Archer and Apollo?”
And they get there...the formula for Permutations with repeated elements.
“How about my friends Archie, Archer and Apollo?”
And they get there...the formula for Permutations with repeated elements.
So let’s dial this up.
“Margot makes passwords by picking 0 to 6 letters from her name. Her computer will accept any arrangement of these letters as long as she inputs the right letters. How many passwords can she make?”
“This is a dumb way to do passwords”
“Maybe. Show me why”
“Margot makes passwords by picking 0 to 6 letters from her name. Her computer will accept any arrangement of these letters as long as she inputs the right letters. How many passwords can she make?”
“This is a dumb way to do passwords”
“Maybe. Show me why”
At first this was harder for the kids to get their heads around.
“It makes no sense to make a password using zero letters from her name!”
“Well how many ways could she do that?
“Zero. Wait. No! One!”
“Carry on”
“It makes no sense to make a password using zero letters from her name!”
“Well how many ways could she do that?
“Zero. Wait. No! One!”
“Carry on”
And we got there too!
Combinations (a brand new concept) and some decent understanding of the formula.
“What if my other friend has an eight letter name?”
Combinations (a brand new concept) and some decent understanding of the formula.
“What if my other friend has an eight letter name?”
Turned up the difficulty by adding letters.
Prompted with “What if you make this problem smaller first?”
“Like...a three letter name?”
“Smaller.”
“A one letter name?”
“Smaller.”
“You are saying go as small as possible and look for patterns”
“Please!”
Prompted with “What if you make this problem smaller first?”
“Like...a three letter name?”
“Smaller.”
“A one letter name?”
“Smaller.”
“You are saying go as small as possible and look for patterns”
“Please!”
Now students are trying to find all the ways people with zero, one, two, three, four or five letter names can make passwords using the Margot method”
Guess what they discovered.
Pascals Triangle! Also new to them.
Guess what they discovered.
Pascals Triangle! Also new to them.
Finished the class by consolidating their knowledge and showing off my favourite piece of Pascals Triangle (powers of 11).
All told in three hours of face to face time I probably did less than 15 minutes of teacher directed instruction.
I’ll take f2f over online any day!
All told in three hours of face to face time I probably did less than 15 minutes of teacher directed instruction.
I’ll take f2f over online any day!
