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Friday 21 August 2015

2015 is the International Year of Light.

Let’s shine a light on the Proficiencies on Friday 21 August.

Have some fun (and integrate the Proficiencies) by exploring these rich tasks with your students.

Friday 22 August 2014

Twist your brain on Friday 22 August with these paradoxes!

Some are counter-intuitive, some are tricky and others are just baffling!

Consider this:

Tomorrow never comes.

In the paradoxes below, click on More… to find the ‘solution’ or explanation. And if you have a favourite paradox, send it to us.

Friday 16 August 2013

2013 is the International Year of Statistics, so on National Mathematics Day, students and teachers are invited to collect data, display data and interpret data. Being statistically literate is a vital skill for all students today—not just to be an informed consumer and citizen, but in order to understand the world in which we live and how it works.

Friday 18 May 2012

2012 marks the centenary of the birth of Alan Turing, noted for his significant contributions to mathematics and computer science. Turing is remembered particularly for leading the codebreaking teams of Bletchley Park during World War II and the subsequent cracking of the Enigma Code. This year, National Mathematics Day activities focus on codes and code breaking.

Friday 20 May 2011

National Mathematics Day is Friday 20 May. To help you celebrate, AAMT in collaboration with Questacon in Canberra, has developed some ‘out of this world’ activities linked to Australia’s bid for the Square Kilometre Array telescope.

Activities

Click on ‘more’ to discover the many possibilities of “low threshold, high ceiling” tasks. These are sourced from NRICH, University of Cambridge. There is also commentary on integrating the Proficiencies.

Activity: Magic Vs

Place each of the numbers from 1 to 5 in a V shape so that the two arms of the V have the same total sum.

Activity: Happy halving

Can you split various shapes in half so that the two parts are exactly the same?

Activity: Reach 100

Your challenge is to place four different digits from 1 to 9 in a 2 x 2 grid that give four two-digit numbers which add to a total of 100.

Activity: Triangle midpoints

Construct a triangle from its three midpoints.

Activity: Strike it out

A game that involves calculations from crossing out numbers on a number line from 0 to 20.

Linking it all together

Paper by Lynne McClure (former director of NRICH) on ‘low threshold, high ceiling tasks’, published 2015 in Mathematics: Learn, Lead, Link (Proceedings of the 25th Biennial Conference of the Australian Association of Mathematics Teachers Inc.).

The birthday paradox

How many people do you need to have in a room for there to be a 50% chance of two people with a birthday on the same day (but not necessarily the same year)? How many to have a 99% probability of a match?

There only needs to be 23 people in a room for there to be a 50% chance of a shared birthday and only 57 people for there to be a 99% chance! Surprised?

Test it out by doing birthday surveys in your school. How many people before you get a match?

Grandi’s series

Consider 1 – 1 + 1 – 1 + ….

Is the answer 0, 1 or ½? Or all three?

The liar’s paradox

This statement is false.

Think about it!

‘Proof’ that 2 = 1

let a = b, then a2 = ab

a2 – b2 = ab-b2

(a-b)(a+b) = b(a-b)

a+b = b, substituting gives b+b = b

2b = b therefore 2 = 1

Where is the error made?

Hilbert’s paradox of the Grand Hotel

The Grand Hotel has an infinite number of rooms, all of which are occupied. Can the hotel accommodate any more guests?

Does 0.999… = 1?

Sometimes this seems counter-intuitive. Try using fractions or algebra to show that this is true.

Zeno’s paradox

The finish line is 2 metres away. The runner must first reach half the distance to the finish line (1m) but when there must cover half of the remaining distance (1/2 m). Having done that the runner must cover half of the new remainder (1/4m), then 1/8m, then 1/16m etc.

Will the runner ever reach the finish line?

The potato paradox

You have 100kg of Martian potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water. How much do they weigh now?

A twist on Gardner’s two children problem

Mr Jones has two children. The older child is a girl. What is the probability that both children are girls?

Mr Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

The twist:

Mr Ng has two children. One is a boy born on a Tuesday. What is the probability that both children are boys?

The Monty Hall problem

You are a contestant on a game show. At the show’s conclusion you are presented with three doors, each of which conceals a prize. Behind one of the doors is a car. Behind each of the other two doors is a goat.

After you have selected one of the doors, the host will open one of the two remaining doors to reveal a goat. At this point you will have the option of opening the door you originally selected and taking the prize behind it, or switching to the remaining unopened door and going home with the prize it conceals.

Is it in your best interest to switch? Will it improve your odds?

The missing square

Cut this triangle into pieces and reassemble it.

Why is there a missing square?

missing_square1           missing_square3
The two-envelope paradox

There are two envelopes, both containing money. One envelope has exactly twice the amount of money as the other. You can keep the money inside the envelope that you choose.

You pick one of the envelopes and open it. Inside is $20. Should you switch envelopes?

There are lots of activities based around two main themes.

Your place in the world relates to families (heritage, language spoken, time in Australia) and food (what we eat, how much, sources of food). The activities are developed from a personal perspective for the early years leading to the global for the secondary years.

About our world has a scientific focus, relating to weather and probability, and sustainability of food resources. The time frames start with a single day for the early years, progressing to weeks, months and years for primary students and then to hundreds of years for secondary classes.

Information and downloadable worksheets are broadly based. You are welcome to take and use ideas and activities that suit you and your students.

 

Early years activities

Your place in the world relates to families and food. The activities are developed from a personal perspective.

About our world relates to weather and probability. The time frames start with a single day.

Lower primary activities

Your place in the world relates to languages spoken in the home, and food sources. The activities are developed from a class and school perspective, moving into the local neighbourhood.

About our world relates to weather prediction around Australia, and the differences in weather, food and culture in the African country of Malawi.

Upper primary activities

Your place in the world relates to languages spoken in the home and family origins, and food choices. The activities are developed from a world perspective.

About our world relates to weather extremes around Australia, and the effect of climate change on the maize production in the African country of Malawi.

Junior secondary activities

Your place in the world relates to refugees and to agriculture. The activities are developed through an Australian then world perspective.

About our world looks at climate change. The time frames vary from years to decades.

Activities

Each cipher and code activity has a suggested level. However, many of the activities can be enjoyed by students (and teachers!) of all ages. Click on the links to download the activity sheets.

 

National Mathematics Day poster

Want to promote National Mathematics Day in your school? Print out this (PDF) poster and stick it up. (Formatted for A4 but can printed at any size.)

 

More teaching ideas

More teaching ideas for the various activities

More to look at

Links and suggestions

About the SKA
SKA telescope NMD

Vastly more sensitive than the world’s best existing radio-telescopes, the Square Kilometre Array (SKA) will be one of the largest and most ambitious international science projects ever devised. It will help us answer fundamental questions about the evolution of the Universe.

Why the SKA on National Mathematics Day 2011?

National Mathematics Day is about celebrating mathematics, so in 2011, our theme is some of the mathematics in one of the great scientific adventures of our times.

Classroom activities

AAMT has collaborated with the staff at Questacon to bring you some classroom activities that will give your students some insights into the mathematics of the SKA and in astronomy more generally.

More on the SKA

More information about the SKA is available for teachers and students.