PROBLEM SOLVINGIt can be fun. Believe it or not

INTRODUCTION

Fibonacci

TIPS process

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…..

STRATEGY 1; WORK BACKWARDS

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

p. 22 Racetrack Problem

STRETEGY 1; WORK BACKWARDS

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….

p. 22 Racetrack Problem

TESTING AND EXPERIMENTING

Use what information you have to make an approximation 19th Century (1800-

1900) After 1st Guess;

Should we try a higher or lower #? 422= 1764; too low

Yet again, use inductive reasoning to narrow your possibilities Multiple of 4 AND a

perfect square Keep guessing

within guidelines

p.23 Trial and Error p.24 Guess and Check

SIMILAR PROBLEMS

If a problem is too complex to calculate, try using a similar problem and look for patterns

22000 is a multiple of 2

Look for a pattern 21 = 2 22 = 4 23 = 8 24 = 16

25 = 32 26 = 64 27 =128 28 = 256 29 = 512 210 = 1024 211 = 2048 212 = 4096

Use Inductive reasoning; What pattern do you see?

The tens digit is 2, 4, 8, 6…

Every 4th tens digit is a 6

2000 will end up being a 4th term in the sequence..

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

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?”

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?