Transcript Saudi_Arabia_DAY_4PP - MSD-ORD

Groups of TWO or THREE
Measure your friend's:
Height (approximate)
1st measurement
2nd measurement
Distance from the belly button to the toes (approximate)
Divide the 1st measurement by the 2nd
Approximate your answer to THREE places after the
decimal
The Ratio Should Be:
1.6180
…
The Fibonacci Series
Leonardo of Pisa (1170-1250), nickname Fibonacci.
He made many contributions to mathematics, but is best
known of numbers that carries his name:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377, 610, 987, 1597, ...
This sequence is constructed by
choosing the first two numbers
(the "seeds" of the sequence) then
assigning the rest by the rule that
each number be the sum of the
two preceding numbers.
RATIO
Take the
of two successive
numbers in Fibonacci's series, (1, 1, 2, 3, 5,
8, 13, ..) and divide each by the number
before it.
1/1 = 1, 2/1 = 2, 3/2 = 1·5, 5/3 = ?, 8/5 = ?, 13/8 = ?,
21/13 = ?
Use your calculator and plot a graph of these ratios
and see if anything is happening.
You'll have DISCOVERED a fundamental property of
RATIO when you find the limiting value of the new
this
series!
The Golden Ratio
Throughout history, the ratio for
length to width of rectangles of
1.61803 39887 49894 84820
has been considered the most
pleasing to the eye.
This ratio was named the golden
ratio by the Greeks. In the world of
mathematics, the numeric value is
called "phi", named for the Greek
sculptor Phidias. The space
between the columns form golden
rectangles. There are golden
rectangles throughout this
structure which is found in Athens,
Greece.
Examples of art and architecture which have
employed the golden rectangle. This first example
of the Great Pyramid of Giza is believed to be
4,600 years old, which was long before the Greeks.
Its dimensions are also based on the Golden Ratio.
Pythagoras of Samos
about 569 BC - about 475 BC
Unpacking
Course 2
12 – 2
640 - 645
Course 3
3–5
162 - 166
Course 3
3–6
167 - 171
Course 3
3–7
173 - 178
Algebra 1
Algebra 1
Geometry
Pythagoras of Samos
about 569 BC - about 475 BC
Very Interesting
Very Interesting
12 Equal sized Sticks
Area
Perimeter
9
Area
12
Perimeter
5
12
The Challenge
1
A  34   6
2
62  4
Objective:
Area
4
Perimeter
12
I
agree
I
should
agree
Very
Interesting
THIRD GRADE
Handout
Booklet:
Pages 1-2
THIRD GRADE
Handout
Booklet:
Pages 3
Pages 4- in today’s handout provide a
sampling of how Number Sense develops
across the grade levels.
Your task is to TEACH someone else about
the MacMillan math program. List six key
points you would include in your
presentation.
THIRD GRADE
Handout
Booklet:
Pages 4-
In Problem Solving Lessons
Handout
Booklet:
Pages 3-4
Handout
Booklet:
Pages 1-2
Handout
Booklet:
Pages 9-
Warm Up Fun
Activities
20
minutes
Find the sum of the
digits of the number
3 3 3 33 333 3 3 4
raised to the second
power !
Interesting Discovery!!!
1.1111 10
21
Interesting !!!
34
2
334
2
3334
2
33334
2
 1156
 111556
 11115556
 1111155556
Interesting Discovery!!!
33333333334
=
2
1111111111155555555556
11 + 50 + 6
67
Vik
How Would You Solve The Problem ?
3
115  
10
Help Me Get The Answer Using Sound
Mathematical Reasoning
“No Fuzzy Stuff”
3
115  
10
Help Me Get The Answer Using Sound
Mathematical Reasoning
“No Fuzzy Stuff”
6th Grade
3
115  
10
by long
division
7
114
10
115 3

10115  3 1147
 


1 10
10
10
Mathematical Reasoning
“No Fuzzy Stuff”
3
115  
10
3
114  1  
10
10 3
114   
10 10
7
114  
10
7
114
10
Vik
2 8 x 9
8 2 x 9
3
4
2
1
56
78 9
10
4
48
x 9 =
3
2
2 8 x 9
8 2 x 9
space
7
83
4
7
x 9 =
5
63
6
7
x 9 =
space
7
85
6
5
x 9 =
3
4
2
1
56
78 9
10
10
10
9
9
8 8
7
7
10
9
8
7
7
8
3
fingers
10
9
8
6
2
finger
s
7
5 fingers
times
10
50
3
4
3 fingers
X 10
12
30
2 1
10
9
8
7
70