3. FIBONACCI
Leonardo of Pisa is credited (although Indians had
discovered it centuries before) with discovering
“Fibonacci’s Sequence”
Fibonacci used a table to solve his problem (p. 21)
Demo
Why is it remarkable?
This pattern is found over and over again in Nature; The
ratio of 1:2:3:5:8…..
4. STRATEGY 1; WORK BACKWARDS
p. 22 Racetrack Problem
T- You need to find out how much he started
with
I- What all happened to his $
Tripled it
Lost $12
Doubled it
Lost $40
Quadrupled it
5. STRETEGY 1; WORK BACKWARDS
p. 22 Racetrack Problem
P- Work Backwards, Starting at $224
Ended with $224
Was the result of quadrupling… $56
Before that, he had $40 more… $96
That was a result of doubling… $48
He had lost $12 before… $60
And before he’d had only 1/3 as much; $20
S- I found out, by working backwards that….
6. TESTING AND EXPERIMENTING
p.23 Trial and Error p.24 Guess and Check
Use what information Yet again, use
you have to make an inductive reasoning to
approximation narrow your
19th Century (1800- possibilities
1900) Multiple of 4 AND a
After 1st Guess; Should perfect square
we try a higher or lower Keep guessing within
#? guidelines
422= 1764; too low
7. SIMILAR PROBLEMS
25 = 32
If a problem is too 26 = 64
complex to 27 =128
calculate, try using a 28 = 256
29 = 512
similar problem and
210 = 1024
look for patterns 211 = 2048
22000 is a multiple of 2 212 = 4096
Look for a pattern Use Inductive reasoning;
21 = 2 What pattern do you see?
22 = 4 The tens digit is 2, 4, 8, 6…
23 = 8 Every 4th tens digit is a 6
24 = 16 2000 will end up being a 4th
term in the sequence..
8. DRAW A PICTURE
When you are given a problem that involves
representing a physical object, always, always,
ALWAYS draw a picture.
It can help you organize your thoughts and keep you
from making mistakes
9. TRICK QUESTIONS AND COMMON
SENSE
Don’t get stuck on the way something appears to be. Sometimes you have to look
at the problem in a different way; The answer may be more obvious than you think
“Today is your first day driving a city bus. When you
leave downtown, you have 23 passengers. At the first
stop, 5 people exit and twice as many people get on. At
the second stop, 11 people exit, and eight people get
on the bus. At the third stop twice as many people exit
as did the people at the first stop. What is the age of
the bus driver?”
10. DO THE FOLLOWING PROBLEM USING
THE TIPS FORMAT IN YOUR
NOTEBOOK
Some children are standing in a circle. They are evenly
spaced and marked in numerical order. The fourth
child is standing directly opposite the twelfth child.
How many children are there in the circle?
