The ideas of Zero and Infinity. Watch this video
Discuss the following:
1. What are the natural numbers?
2. Do we count with zero? Is zero really a number?
3. What was 0 originally used for? About what time in history did this happen?
4. Where did the idea that the symbol 0 represented the quantity "nothing" come from?
Al'Khwarizmi (a 7th century middle eastern Mathematician) wrote a very famous book about numbers and how they worked.
5. Where did he get his ideas from?
6. What else happened about that time that allowed his work to be seen by lots of people.
Bhramagupta (a 7th century Indian Mathematician) did some calculations with zero.
7. Which of his calculations did he have difficulty with?
8. Is infinity a number? 9. Hilbert's hotel is a special place. Describe Hilbert's hotel.
10. How does Hilbert fit new guests into his hotel when it is full?
11. Copy and complete the following statements.
" Infinity plus infinity is .........." , "infinity multiplied by infinity is ........."
12. Are all infinities the same size? Give an example to support your answer.
13. Can you "divide infinity by infinity? Why?

We now use a common set of scientific measurements around the world (the SI units).

Work your way through this internet site to learn all about it. Do the tutorials along the way.

Answer the following questions in your workbook:

What is a measurement system?

List the quantities that we have measurement systems for.

What are the units of:

the metric system?

the imperial system?

4. Not all countries in the world have adopted the metric system. Here is a map showing counties who use the metric system in green.
The United States has not officially adopted the metric system although it is taught in schools there.
a. Read through this website ( Why hasn't America adopted the metric system?) (all 6 pages) and watch the videos to learn the reasons.
b. Write a brief explanation for why the US has not gone metric officially and why it is now slowly doing so.
Just imagine having to work in the imperial system: Doing calculations in the imperial system

What is a meter?
How has the measurement of the length of a meter changed over time?
How big are our measurement units? Scroll through The scale of the universe to find out.

3

How long is a piece of string?
1. What is a measurement standard?
2. Professor Marcus DuSautoy say " How you go about measuring something can change the result." What does he mean?
3. The Koch triangle has a perimeter that is infinitely long. How does this apply to the piece of string so that "in theory" the string has an infinite length?
4. To find the end of the piece of string, Alan decides to measure it in atoms. What makes up most of an atom?
5. To find the actual position of the atom at the end of the piece of string is a difficult task. Use the double slit experiment to explain why?

4

What time is it? How long until home time?
1. Use the web page Measuring time to help you write a summary of how human beings have measured time.
2. Why are there 24 hours in a day and 60 seconds in an hour? In your workbooks write a brief answer to the question asked.
3. We use the metric system for most other measurements. In your table group, discuss the following questions:
a. What if we replaced all the current clocks in the world with clocks that told the time in metric units? Would there be problems?
b. How would that metric time work? What would you use as your base unit and why? You might like to read Metric time to inform your discussion.
c. If we could design our own metric day and year, what would it look like?
4. a. The young man in this video ( What is metric time? What is "swatch internet time"? ) discussed metric time. What does he say are the issues with metric time?
b. The young man also introduced the idea of "internet time". The calculator he mentions is here: Swatch internet time calculator
What are the advantages and disadvantages on internet time? Do you think it will become more or less useful in the future? Why? Further reading: The experience and perception of timeHow does the brain measure time?Do animals experience time at a different rate to humans?

5

Representing 3D shapes in 2D - Maths of drawings.

There is a big difference between a 2D and 3D cartoon animation watch this video to see what is different in how they are made.
1. How do you represent a sphere in 2D?
2. How are the cube and the drawing of the cube similar and different?
3. What properties of the cube are compromised in the 2D representation of a cube?
4. TASK: Can you create a sphere from a flat piece of paper? 3D Drawing Activity

Measuring the Earth and other astrological objects

1. What are the lines of latitude and longitude that appear on maps of the earth? Where do the measurements for these lines come from? 2. How are the positions of the equator, tropics of cancer and capricorn and the arctic and antarctic circle related to the sun? Use Wikipedia to find out. Hint: What is a subsolar point? 3. The radius of the Earth was calculated before we had satellites. How did the ancient astronomers measure the radius of the earth using nothing but a stick in the ground, the rays of the sun and some mathematics? 4. Determining your position on the earth means determining your latitude and longitude. Determining longitude is a difficult task. Watch this video 5. Measuring the distance to the moon and the diameter of the moon 6. How light is used to measure distance in space in current times. 7. Light years, Astrological measurement units and parsecs. What are they and what are they used for? A video to help

Chance

1

Are you truly random?
1. Create a random list of results for an experiment where a coin is flipped 20 times.
2 Compare your list with some of the people around you. How are you lists the same? How are your lists different?
3. Make a summary table on the board showing the toatol number of heads and tails from the experiments of all the people in the room. What do you notice?
4. Use an online coin flipping program (choose one of the links below or Google your own) and repeat steps 1 - 3. Random.orgvirtual coin toss
5. a. A coin that is not biased in any way, has just been flipped 10 times and has landed as Tails each time. What it the probability that the next flip will land tails as well?
b. What is "The Gambler's fallacy" and why is it a fallacy (it appears that it should be true but is actually not true)?
6. Your teacher will give you a list of outcomes from real and imaginary coin tosses, can you tell the difference?
7. a. How often, according to Professor Littlewood of Cambridge University, should you expect to witness a miracle?
b. Do you agree with Professor Littlewood? If not, what do you think the probability should be and how often would you then expect to witness a miracle?
More info: Littlewood's Law of Miracles

2

Paper, scissor rock
Answer the following questions
1. Is paper, scissors, rock a fair game? How do you know?
2. a. Do you have a strategy for playing paper, scissors rock?
b. What is your strategy?
c. Does your strategy work? Try it out on some other people in games of paper, scissors, rock.
Try to identify the strategy your opponent is using and determine which strategy is the most effective.
3. Are you truly random in your choices? Play the game (Paper,scissors, rock vs the computer ) against a computer who has gathered data on thousands
of games of paper, scissors, rock.
Can you beat the computer and its predictions?
4. In Big Bang Theory, Sheldon mentions an expanded version of paper, scissors, rock: Paper, scissors, Rock, Lizard, Spock.
a. Why does Sheldon think Paper, scissors, rock is a poor game? Do you agree?
b. Is Paper, Scissors, Rock, Lizard Spock a 'better' game? Why?
c. Is this version of the game fair?
d. Here is the "who wins" diagram. If you had to design a strategy for Paper,Scissors, Rock, Lizard, Spock, what would you do? Try it out on someone.
5. Both games have an odd number of options to chose from. What happens with and even number of options?
6. The game can be extended even further adding more options. Here are some examples: example 1, example 2 What are the difficulties with some of these games?

## Number systems

What are numbers?Number systemsWatch the following video The development of number systems

In your workbooks

Design your own number system.- it can be any of the number system types covered in the previous video.
- you need symbols and names for each quantity
- you need to show how you would represent some larger quantities and give their names.

After creating your number systems, as a table discuss the following questions- What things are important to consider when creating symbols for a number system?
- What things are important to consider when developing names for a number system?

Now write the answers to the questions above in your workbook.Number systems with bases other than 10.Other number systems

Counting to 1000 on your hands using binary numbersHexadecimal numbersWriting numbers in other base number systems & converting between number systems.Check your conversions work with: Number base converter

Number base games:

Uses of other base number systemsBinary numbers: Binary numbers & computersAll about binary code

Hexadecimal numbers and colours:

Adding and subtracting in the Binary Number System

Octal Addition

Octal multiplication

The ideas of Zero and Infinity. Watch this videoDiscuss the following:

1. What are the natural numbers?

2. Do we count with zero? Is zero really a number?

3. What was 0 originally used for? About what time in history did this happen?

4. Where did the idea that the symbol 0 represented the quantity "nothing" come from?

Al'Khwarizmi (a 7th century middle eastern Mathematician) wrote a very famous book about numbers and how they worked.

5. Where did he get his ideas from?

6. What else happened about that time that allowed his work to be seen by lots of people.

Bhramagupta (a 7th century Indian Mathematician) did some calculations with zero.

7. Which of his calculations did he have difficulty with?

8. Is

infinitya number?9. Hilbert's hotel is a special place. Describe Hilbert's hotel.

10. How does Hilbert fit new guests into his hotel when it is full?

11. Copy and complete the following statements.

" Infinity plus infinity is .........." , "infinity multiplied by infinity is ........."

12. Are all infinities the same size? Give an example to support your answer.

13. Can you "divide infinity by infinity? Why?

A different number system:The Chinese NumeralsHand gestures for counting to 10

How to use an abacus

Using an ancient calculator Use this site to learn about how to use an abacus to add, subtract, multiply and divide.

An abacus to work with

How fast can you go? It's all in the mind.

## Measurement systems & Geometry

1Work your way through this internet site to learn all about it. Do the tutorials along the way.

4. Not all countries in the world have adopted the metric system. Here is a map showing counties who use the metric system in green.

The United States has not officially adopted the metric system although it is taught in schools there.

a. Read through this website ( Why hasn't America adopted the metric system?) (all 6 pages) and watch the videos to learn the reasons.

b. Write a brief explanation for why the US has not gone metric officially and why it is now slowly doing so.

Just imagine having to work in the imperial system: Doing calculations in the imperial system

5. Read through the history of the Metric System. In your workbook, create a brief summary of major dates and ideas.

2How has the measurement of the length of a meter changed over time?

How big are our measurement units? Scroll through The scale of the universe to find out.

31. What is a measurement standard?

2. Professor Marcus DuSautoy say " How you go about measuring something can change the result." What does he mean?

3. The Koch triangle has a perimeter that is infinitely long. How does this apply to the piece of string so that "in theory" the string has an infinite length?

4. To find the end of the piece of string, Alan decides to measure it in atoms. What makes up most of an atom?

5. To find the actual position of the atom at the end of the piece of string is a difficult task. Use the double slit experiment to explain why?

4What time is it? How long until home time?1. Use the web page Measuring time to help you write a summary of how human beings have measured time.

2. Why are there 24 hours in a day and 60 seconds in an hour? In your workbooks write a brief answer to the question asked.

3. We use the metric system for most other measurements. In your table group, discuss the following questions:

a. What if we replaced all the current clocks in the world with clocks that told the time in metric units? Would there be problems?

b. How would that metric time work? What would you use as your base unit and why? You might like to read Metric time to inform your discussion.

c. If we could design our own metric day and year, what would it look like?

4. a. The young man in this video ( What is metric time? What is "swatch internet time"? ) discussed metric time. What does he say are the issues with metric time?

b. The young man also introduced the idea of "internet time". The calculator he mentions is here: Swatch internet time calculator

What are the advantages and disadvantages on internet time? Do you think it will become more or less useful in the future? Why?

Further reading: The experience and perception of time How does the brain measure time? Do animals experience time at a different rate to humans?

## Representing 3D shapes in 2D - Maths of drawings.

There is a big difference between a 2D and 3D cartoon animation watch this video to see what is different in how they are made.1. How do you represent a sphere in 2D?

2. How are the cube and the drawing of the cube similar and different?

3. What properties of the cube are compromised in the 2D representation of a cube?

4. TASK: Can you create a sphere from a flat piece of paper?

3D Drawing Activity

6## Mapping the Earth:

1.The problem with creating a map of the Earth.2.Maps - What properties of the earth do they show?

3. Types of Map projections

## Measuring the Earth and other astrological objects

1. What are the lines of latitude and longitude that appear on maps of the earth? Where do the measurements for these lines come from?2. How are the positions of the equator, tropics of cancer and capricorn and the arctic and antarctic circle related to the sun? Use Wikipedia to find out. Hint: What is a subsolar point?

3. The radius of the Earth was calculated before we had satellites. How did the ancient astronomers measure the radius of the earth using nothing but a stick in the ground, the rays of the sun and some mathematics?

4. Determining your position on the earth means determining your latitude and longitude. Determining longitude is a difficult task. Watch this video

5. Measuring the distance to the moon and the diameter of the moon

6. How light is used to measure distance in space in current times.

7. Light years, Astrological measurement units and parsecs. What are they and what are they used for? A video to help

## Chance

Are you truly random?1. Create a random list of results for an experiment where a coin is flipped 20 times.

2 Compare your list with some of the people around you. How are you lists the same? How are your lists different?

3. Make a summary table on the board showing the toatol number of heads and tails from the experiments of all the people in the room. What do you notice?

4. Use an online coin flipping program (choose one of the links below or Google your own) and repeat steps 1 - 3.

Random.org virtual coin toss

5. a. A coin that is not biased in any way, has just been flipped 10 times and has landed as Tails each time. What it the probability that the next flip will land tails as well?

b. What is "The Gambler's fallacy" and why is it a fallacy (it appears that it should be true but is actually not true)?

6. Your teacher will give you a list of outcomes from real and imaginary coin tosses, can you tell the difference?

7. a. How often, according to Professor Littlewood of Cambridge University, should you expect to witness a miracle?

b. Do you agree with Professor Littlewood? If not, what do you think the probability should be and how often would you then expect to witness a miracle?

More info: Littlewood's Law of Miracles

Paper, scissor rockAnswer the following questions

1. Is paper, scissors, rock a fair game? How do you know?

2. a. Do you have a strategy for playing paper, scissors rock?

b. What is your strategy?

c. Does your strategy work? Try it out on some other people in games of paper, scissors, rock.

Try to identify the strategy your opponent is using and determine which strategy is the most effective.

3. Are you truly random in your choices? Play the game (Paper,scissors, rock vs the computer ) against a computer who has gathered data on thousands

of games of paper, scissors, rock.

Can you beat the computer and its predictions?

4. In Big Bang Theory, Sheldon mentions an expanded version of paper, scissors, rock: Paper, scissors, Rock, Lizard, Spock.

a. Why does Sheldon think Paper, scissors, rock is a poor game? Do you agree?

b. Is Paper, Scissors, Rock, Lizard Spock a 'better' game? Why?

c. Is this version of the game fair?

d. Here is the "who wins" diagram. If you had to design a strategy for Paper,Scissors, Rock, Lizard, Spock, what would you do? Try it out on someone.

5. Both games have an odd number of options to chose from. What happens with and even number of options?

6. The game can be extended even further adding more options. Here are some examples: example 1, example 2 What are the difficulties with some of these games?

## Amazing maths activities to try:

## Problem solving.

Monty Hall problemTower of Hanoi

The frogs problem

Khan academy brain teasers

Dara O'Braian's School of Hard sums

The knight's problem MAC users - Knight's moving problem

The counterfeit coin

Brainbashers

## Logic Puzzles

Online Logic puzzle pageHow the grid works in a logic puzzle

How to solve Logic puzzles

Advanced Logic puzzle techniques

Other types of puzzles: Puzzle Pages

## Different ways of thinking about Mathematical operations.

Why do they work? Do they ALWAYS work? Can you prove it?"Japanese" multiplication

Quick division

More Maths "tricks"

Mental Maths tricks

Students using an abacus

How to use an abacus