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Amidakuji: The Japanese way to make decisions

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Amidakuji: The Japanese way to make decisions

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- Permutations
- One-to-one correspondence
- Randomness

- Amidakuji Story Telling / Essay writing

* Links to Art
* Links to Random Decision Making / Random Assigning of Duties
* Links to Language

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Combinatorics:

You can use rods of integer sizes to build "trains" that all share a common length. A "train of length 5" is a row of rods whose combined length is 5. Here are some examples:

Notice that the 1-2-2 train and the 2-1-2 train contain the same rods but are listed separately. If you use identical rods in a different order, this is a separate train.

How many trains of length 5 are there?

Come up with a formula for the number of trains of length n. (Assume you have rods of every possible integer length available.) Prove that your formula is correct.

Come up with an algorithm that will generate all the trains of length n.

http://www2.edc.org/makingmath/mathprojects/trains/trains.asp

* Links to Pattern Recognition and Problem Solving

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Numbers:
Counting from 1 to 10 in different languages.

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Drawing Parallel Lines and Perpendicular Lines

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Drawing Parallel Lines and Perpendicular Lines

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Parallel Lines and Perpendicular Lines:

* Links to Art

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Pascal's Triangle:

1. How many odd numbers are in the 100th row of Pascal’s triangle?

2. How many entries in the 100th row of Pascal’s triangle are divisible by 3? By 5?

3. When you divide a number by 2, the remainder is 0 or 1. Color the entries in Pascal’s triangle according to this remainder. You get a beautiful visual pattern. Can you explain it? Can you generate the pattern on a computer?

4. What about the patterns you get when you divide by other numbers? When you divide a number by 3, the remainder is 0, 1, or 2. Divide the entries in Pascal’s triangle by 3 and color them according to their remainder. Can you explain your picture?

5. Etc.

http://www2.edc.org/makingmath/mathprojects/pascal/pascal.asp

* Links to Art

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* Links to Art
http://origamitutorials.com/category/origami-kusudama/

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Geometry
To test how strong is the paper structure to balance objects on top of it.
Test the creativity of kids.

Links to engineering

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Use of any statistical software to calculate and analyze data.

Links to technology

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Investigating chance and probability
-Rolling dice
Fair games
-Rock, Paper, Scissors
-  Rock, Paper, Scissors, Lizard, Spock  and
-What’s in the bag?

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Investigating Chance and Probability (1)

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Constructions of pyramid based on pyramid numbers which is the sum of the first n square of integers.

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Construction of bridge challenge using parabola shape

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-Reflection
-Rotation
-Translation

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Collecting data : low and high tide in a year and ploting the graph using geogebra.

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Shapes that relate to Fibonacci sequences which can be found in nature e.g sun flower, snails, pineapple and etc.

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- can be used to develop spatial and logic skills.
-require a bit of lateral thinking and in fact are a good way of exercising different parts of your brain and different thinking styles

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- to learn a formulae through songs

Links to Art

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-Simple explanation by creating a wheel with liquid to demonstrate the Pythagorean theorem.
- Before introducing the given formula
a² + b ² = c2

Links to Engineering and Science

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Platonic and Archimedean Solids:

- Study the regular solids (platonic and Archimidean), their properties, geometry, and occurance in nature (e.g. virus shapes, fullerene molecules, crystals).
- Build models.

* Links to Art

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Geometry:

* Links Art

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Tessellations:

- Suitable activity to be repeated at Upper Primary / Lower Secondary Level, where Geogebra is used to create the tessellations, instead of drawing them on paper

* Links to Art
* Links to Technology

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Arithmetic:

- Long division
- Introduction to the concept of PI
- Suitable PI Day Activity

* Links to Art

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Time:

* Links to Art
* Links to Technology

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Matrices:

- Keeping stock / inventory
- Calculating cost
- Adding, subtracting, multiplying matrices using Spreadsheet

Solving simultaneous equations with a large number of unknowns using inverse matrices using Spreadsheet.

* Links to Technology

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Optimization:

* Links to Physics, Engineering and Technology
* Links to Art

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Mensuration,  Graphing, Proportionality:

- Designing a parachute that can stay in the air the longest
- Understanding air resistance
- Variability can be introduced by setting different requirements / restriction conditions and aesthetics

* Links to Physics
* Links to Engineering and Technology
* Links to Art

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Planning a Dream Vacation with a given a Budget

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Planning a Dream Vacation with a given a Budget

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Money, Costing:

- Use of Internet to obtain information
- Use of Spreadsheet
- Presentation skills
- Application of Planning and Optimization Skills
- Extension: Setting up a Tour Agency

* Links to Personal Financial Management / Budgeting Skills
* Links to Technology
* Links to Planning Skills

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Solar Powered / CO2 Powered Toy Car Design / Competition

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Solar Powered / CO2 Powered Toy Car Design / Competition

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Mensuration and Graphing:

- Variability can be introduced by setting different requirements / restriction conditions and aesthetics

* Links to Physics
* Links to Engineering and Technology
* Links to Chemistry
* Links to Art

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Paper Airplane Construction / Competition

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Paper Airplane Construction / Competition

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Mensuration and Graphing:

- Suitable project to be repeated at Lower and Upper Secondary Levels
- Variability can be introduced by setting different requirements / restriction conditions and aesthetics
- Difficulty can be increased by requiring the plane to be powered by elastic band / carbon dioxide produced in-situ, or remote controlled.

* Links to Physics
* Links to Engineering and Technology
* Links to Chemistry
* Links to Art

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Construction and Usage of an Inclinometer

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Construction and Usage of an Inclinometer

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Trigonometry / Angle of Elevation and Depression:

Measuring the height of tall objects (e.g. flag poles) and buildings.

* Links to Engineering and Technology

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Trigonometry:
- Lissajous patterns

- x = A sin (at + k)
- y = B sin (bt)

* Links to Engineering, and Technology
* Links to Physics
* Links to Art

- Other similar projects: Making a Harmonograph, Making a Spirograph

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Money, Percentage, and Introduction to Geometric Series:

- Understanding and comparing the different methods simple interest and compound interest are calculated.

* Links to Personal Financial Management

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Angles:

- Law of Reflection

* Links to Physics
* Links to Engineering
* Links to Art

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Arc Lengths of Semicircles / Algebraic Proof

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Arc Lengths of Semicircles / Algebraic Proof

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Length of Circumference:

- Which is longer, the red line or the blue line?

- Proving that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.

- Exploring other methods of measuring length, e.g. using a thread and meter rule, using an opisometer, etc.

* Links to Physics & Technology.

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Probability:

The birthday paradox, also known as the birthday problem, states that in a random gathering of 23 people, there is a 50% chance that two people will have the same birthday. Is this really true?

* Links to Social Intelligence

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27 Card Magic Trick / 47 Card Magic Trick

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27 Card Magic Trick / 47 Card Magic Trick

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Indices / Number bases:

* Links to Art / Performing Magic

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Arithmetic:

- Competing against peers to add two / three cards fastest
- Emphasis of adding  using whole tens.

* The game can be modified to include subtraction and (introduction of ) negative numbers, as well as multiplication.

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*Links to Art

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Exploring Geodesic Domes using toothpicks and plasticine / candy

* Links to Physics
* Links to Engineering
* Links to Architecture

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Exploring axioms and theorems related to Origami:
- Huzita-Hatori axioms
- Kawasaki's Theorem
- Maekawa's Theorem

Applications:
-Air bags,
- Stent,
- Space telescope,
- Etc

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Parabola / Quadratic Functions:
- Kinematic Equations
- Time of Flight
- Maximum Height
- Horizontal Range

* Links to Physics

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1) Wind instruments
- Standing waves and Resonance

2) String instruments
- Octave=2:1
- Fifth=3:2
- Fourth=4:3

* Links to Music
* Links to Physics

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Ratio:
Investigating the concept of beauty and the Golden Ratio.

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Marion's theorem states that the are of the central hexagonal region determined by trisection of each side of a triangle and connecting the corresponding points with the opposite vertex is given by 1/10 the area of the original triangle.

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Trigonometry:
Using trigonometric functions to model climate

* Links to Meteorology

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Solutions of Triangle:
Triangulation

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Graphing skills:
- Investigation the relationships between mass of dough, quantity and type of yeast, temperature, time and volume of dough.

- Fermenting the dough (First Rise)
- Proofing (Second Rise)

* Links to Chemistry / Biology
* Links to Physics

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Ratio:
- Gear ratio
- Lever systems
- Pulley systems

* Links to Physics
* Links to Technology

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Logarithms:
- Decibel scale

* Links to Physics

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Circles:
- Understanding that the ratio of the circumference of any circle and its diameter is a constant
- E.g. : Estimating the length of the skirting needed for a round table when given the diameter of the table.
- Deriving the formula C = 2πr

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Logarithms:
- Understanding P-waves and S-waves
- Richter Scale

Solution of Triangles:
- Triangulation

* Links to Geoscience

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Logarithms:
- Calculating the concentration of Hydrogen cations from the pH value

* Links to Chemistry

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Trigonometry:
- Using the shadow at noon to calculate Earth's diameter.
- Collaborating with students from other schools / countries to collect data (Video conferencing)

* Links to Physics

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Time:
Telling the time

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Numbers:
1) Handling money
2) Conversions of fractions, decimals and percentages
3) Calculating discounts

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Fractions:
Learning fractions, i.e. numerators and denominators.