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