1. Assignments
• Reading Response for two readings
Read the handout Data Analysis and Probability
Math Every Secondary… (12.8 -12.9 pp635-650)
Written Response: Which explorations
appeal/could you adapt – explain.
also, compare/contrast the two approaches –
how would you adapt each to your practice?
• POW due Wed (Abe’s Pennies)
• No articles for today

2. Article Response due
POW due Wednesday
Math 483

4. Crossing the river
Eight adults and two children need to cross a river. A
small boat is available that can hold one adult or up
to two children. Everyone can row the boat. How
many one-way trips does it take for all of them to
cross the river?

5. Crossing the river
Eight adults and two children need to cross a river. A
small boat is available that can hold one adult or up
to two children. Everyone can row the boat. How
many one-way trips does it take for all of them to
cross the river?
Can you describe how to work it out for 2 children
with any number of adults?
How does your rule work out for 100 adults?

6. Crossing the river
Eight adults and two children need to cross a river. A
small boat is available that can hold one adult or up
to two children. Everyone can row the boat. How
many one-way trips does it take for all of them to
cross the river?
What happens to the rule if there are different
numbers of children?
Write a rule for finding the number of trips needed
for A adults and C children.

7. Driscoll’s Algebra Habits of Mind
Doing-Undoing: reversibility of processes
example: solve 9x2 – 16 = 0
what equation has solutions
4
3
and −
4
3
?
Building Rules to represent Functions:
recognize patterns, organize data with in-out
realtionships
Abstracting from Computation:
computation freed from the particular numbers
they are tied to in arithmetic

8. Locker problem
There are 30 lockers in one hallway of Whatcom
Middle School. The first student goes down the row
and opens every locker. The second student then
goes and closes every second locker. Next, the third
student goes down the row and changes the state of
every third locker (closes if open, opens if closed).
Student #4 changes the state of every fourth locker,
student #5 every fifth, and so on until 30 students
have taken a turn.
Which lockers are open after the 20th student?
Which locker or lockers changed the most?

9. Locker problem
200 lockers and 200 students?
x lockers and x students?
• Can I write down a mechanical rule that will do
this job once and for all?
• How does the rule work?
• Why does the rule work the way it does?
• What if I start at the end?

10. n(x) = number of factors of x
n(6) = 4
n(24) = n(288) = n(23 32 54) =
Classify all numbers n so that n(n) =3
Classify all numbers n so that n(n) =2
Find two numbers n and m so that n(nm) = n(nm) - generalize
Find some n so n(n) =6

11. IN OUT
+5
x2
?
x4
÷8
?x6
-4
+2
+8

12. Cutting Through the Layers

13. Lots of Squares
Can you divide a square into a certain number of smaller squares?

14. Reversals
Take a three-digit number, reverse its digits, and subtract
the smaller from the larger. Reverse the digits of the result
and add.
123 -> 321, 321 – 123 = 198
198 -> 891, 198 + 891 = 1089

15. Assignments
• Reading Response for two articles will be e-mailed
today
• POW due Wed (Abe’s Pennies)
• Let me know your teaching schedule @SMS (e-mail
ok)
• Your plan for Monday @ SMS if teaching (e-mail ok)