f un e xperiment o n r atios
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Fun Experiment On Ratios
Groups of TWO or THREE
Measure your friend's:
Height (approximate)
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
1st measurement
2nd measurement
Fun Experiment On Ratios
The Ratio Should Be:
1.6180 …
Experiment !
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.
Take the RATIO 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
this RATIO when you find the limiting value of the new series!
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.
The Golden Ratio
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.
Pythagorean
Connection
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
Pythagorean
Connections
Pythagoras of Samos
about 569 BC - about 475 BC
Pythagorean
Connections
Very Interesting
Very Interesting
12 Equal sized Sticks
Area 9
Perimeter 12
Area 5
Perimeter 12
The Challenge
Area 4
Perimeter 12
6432
1A
426
Objective:
I should agree
I agree
Very Interesting
Handout Booklet:
Pages 1-2
THIRD GRADE
THIRD GRADEHandout 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 GRADEHandout Booklet: Pages 4-
Handout Booklet:
Pages 3-4
In Problem Solving Lessons
Handout Booklet:
Pages 1-2
Handout Booklet: Pages 9-
Warm Up Fun Activities
You may use
calculators
20minutes
Find the sum of the digits of the number
3 3 3 3 3 33 3 3 3 4
raised to the second power !
Interesting Discovery!!!
21101111.1
Interesting !!!
115634 2
111556334 2
111155563334 2
111115555633334 2
Interesting Discovery!!!
243333333333
5615555555551111111111=
11 + 50 + 667
Answer
67
VikHelp Me Explain
How Would You Solve The Problem ?
10
3115
Any
volunteers ?
Help Me Get The Answer Using Sound Mathematical Reasoning
“No Fuzzy Stuff”
10
3115
Help Me Get The Answer Using Sound Mathematical Reasoning
“No Fuzzy Stuff”
10
3115
6th Grade
10
3
1
115
10
311510
10
1147
10
7114
by long division
Mathematical Reasoning“No Fuzzy Stuff”
10
3115
1410
13
1
10
1114
00
3
1
1147
10
1147
10
Vik
2 8 x 9 28 x 9
1
2 3 45 6
7 8 9
10
48 x 9 =
space
fold
4 3 2
2 8 x 9 28 x 9
83 x 9 =
spacefold
7 4
7
63 x 9 =
spacefold
5 6
7
85 x 9 =
space
fold
7 6
5
1
2 3 45 6
7 8 9
10
6
7
8
9
10
67
8
9
10
6
7
9
10
6
7
8
910
8
6
7
89
10
67
8
9
10
7 8
5 fingers
times10
3 fingers
2 finger
s
6
50
Greater than 5
3 fingersX 10
4 12
30
3
6
789
10
67
8
9
10
70
2 1
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