The 8 Times Tables Can Be Cool

As many of my students know I do not enjoy times tables. I missed quite a bit of primary school maths so speedy tables are not my thing. In particular it's the 8s that make me pause the most. Speed doesn't matter, it's the process. For me it's just doubling my four times tables.

Bec Campbell shared the following with me and yes it is pretty cool. Even cooler is to ask why it happens....

It's been a while, babies and blue whales

Year 7 has been very busy in term two doing things like school camps and NAPLAN. 
Now we are back with our full weeks of math and looking at patterns in the real world. 

Today we looked at the growth rate of babies in their first 13 weeks. 

The WHO provides the data - we used every two weeks to develop models for predicting - interpolating and extrapolating. This way we could check our maths with the real data! 

We used tables, graphs and developing algebraic rules to make predictions and compared their results.  Alex pointed out how ridiculous it would be to keep using our models into teenage years to illustrate how extrapolation can be unreliable.  Here are some notes from today and Alex's example:

How reliable are our models?

Reasonably reliable for interpolating. 

Not as reliable for extrapolating. Remember Alex calculated the weight of a 13 year old at the same growth rate as babies in their first 13 weeks. 

13 years = 13 x 52 weeks

13 years = 676 weeks

Our formula/equation/rule

Let  t = time weeks   and   k = weight in kg

k = 0.25 x t + 3.3

for 13 years old

k = 0.25 x 676 + 3.3

k = 172.3 kg 

That's not average in any country for a 13 year old boy!

The CDC, in the USA,  says the average weight for a male at 13 years old is 51.68229 kg  That's more than 100 kg lighter than our formula says. 

Can you find the average weight of a 13 year old in another country?

Source: Growth Charts of Children - CDC

BABY BLUE WHALES

We talked about including units on our work to show kilograms otherwise our baby data could be in tonnes or even milligrams. A 3 tonne baby! Crazy!

... or not....? I did some searching....

For interest: Close to 3 tonnes are baby blue whales and their average difference is about 91 kg a day!!

Their formula would be k = 91 x d + 3000 and reliable for 365 days! 

where k = weight in kilograms and d = time in days. 3000 is the initial value (or 2700 - see below). 

After about a year inside its mother's womb, a baby blue whale emerges weighing up to 3 tons (2.7 metric tons) and stretching to 25 feet (8 meters). It gorges on nothing but mother's milk and gains about 200 pounds(91 kilograms) every day for its first year.

Blue Whales, Blue Whale Pictures, Blue Whale Facts - National ...

animals.nationalgeographic.com.au/animals/mammals/blue-whale/

Noodles, hair, atoms, exponential growth and decay and fractions.

This cool Youtube video has mathematics relevant for grade six and grade 11 courses right now.

For grade six - they can compare it with the doubling we did when we discussed ebola. They can also look at half of a half - multiplying a fraction by a fraction or as we say in mathsland the product of two fractions.

Grade 11 - this is exponential growth and decay simultaneously depending on how you view your noodles.

Maths and you guessed it... Christmas

Here is a gift for you from Mathsland - a game. It's the latest thing and Jo Boaler of Stanford likes it so much she is now on the team..

Download Mathbreakers and puzzle it out. It looks like Mathbreakers will just keep growing too.

And this ancient game - I haven't beaten the computer yet. Can you? Cool Math - Mancala

For the next game you will need a 10 by 10 grid - this is called How Close to 100? To make it more challenging try How Close to 1 and use decimals. This is from Jo Boaler.

You will need

• two players

• two dice

• recording sheet

This game is played in partners. Two children share a blank 100 grid. The first partner rolls two number dice.

The numbers that come up are the numbers the child uses to make an array on the 100 grid. They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible. After the player draws the array on the grid, she writes in the number sentence that describes the grid. The second player then rolls the dice, draws the number grid and records their number sentence. The game ends when both players have rolled the dice and cannot put any more arrays on the grid. How close to 100 can you get?

Variation Each child can have their own number grid. Play moves forward to see who can get closest to 100. 

pi 10 Trillion of its Digits - actually only 4 Million of them...

It took 371 days of computing TEN TRILLION decimal places of pi.
Doesn't sound impressive - that requires 44 TB of disk to find them and 7.6 TB to store them, when compressed.

In 1949 the ENIAC computer took 70 hours to calculate pi to 2037 digits.

Check out the Beautiful visualisation and effort in this very cool site and more on how long it would take humans to say all of these digits.

http://two-n.com/pi/

Why do we care? Because this number is everywhere, because it has no pattern, because they say inside these digits are all of our phone numbers, birth dates and every possible combination you could think of. BECAUSE humans and other animals need patterns to understand the world around them. pi is a beautiful mystery and mathematicians like you love puzzles.



"An average person can read out approximately 120 digits ..." 2012. 13 Oct. 2014 <http://www.two-n.com/pi/>

Nobel Prize goes to THE HEXAGON (and some persistent scientists)

"Neuroscience: Brains of Norway : Nature News & Comment." 7 Oct. 2014 <http://www.nature.com/news/neuroscience-brains-of-norway-1.16079>

Edvard and May-Britt Moser have been working together for 30 years. For 28 of those years they have also been married. 

These two scientists embody the learner profiles and show us how persistence, resilience and problem solving can lead to success. Not only that but mistakes along the way helped them to unravel the mystery of how our brains map out our environments. People are now calling it the GPS of our brains.

They have won the Nobel Prize in Physiology or Medicine, with neuroscientist John O’Keefe at University College London (their former supervisor).

There is no Nobel Prize for Maths as we have discussed in class, but the mathematics is everywhere. Here in our brains wonderful hexagons form the way we sense location.

Please read more about it in the Scientific American and in Nature Magazine. Very exciting brain research! 

Number Sense - Thanks Ajarn Dale

Hey there maths fans!

Ajarn Dale sent on some cool "Math Tricks". Some people think that these tricks are cheating, but in actual fact it's about understanding numbers and being able to make them work for YOU.

Check them out here in wisebread.com - thanks Ajarn Dale.
11 useful math tricks

Numbers in a City: New Haven / 1997 / SML by See-ming Lee licensed under CC by A SA

Welcome Back and BIG NEWS

The Fields Prize has been awarded to a woman for the first time.

"Iranian-born mathematician Maryam Mirzakhani on Wednesday became the first woman to be awarded the Fields Medal, mathematics' equivalent to the Nobel Prize." Please read more in the CBC online here. 

You can also read more in The Guardian - a nice interview piece and The Stanford University press release, where Maryam Mirzakhani is a Professor of Mathematics. 

Thanks to Ajarn Lana for sharing this with the Mathematics department.

We are all working with Stanford University this year to develop our Mathematics and a growth mindset and you can puzzle over the famous puzzle that ignited her mathematical curiosity.

Add all of the numbers from 1 to 100 with a system that isn't 1+2+3+4 <-- there is a shortcut (:

MYP3 Mathematicians Helping Others Understand Curves

Before I introduce three fabulous websites, I'd like to say that ALL of the MYP3 mathematicians have produced wonderful work demonstrating their understanding of curves and their transformations. Mathsland is proud to call them all citizens.

In our unit we were focusing on linear functions y=mx+p, and dipping into some quadratics but some decided they would like to go further and investigate other curves.

We had linear, quadratic, square root, Archimedes Spiral, sinusoidal and exponential curves. It was busy in Mathsland because everyone had different questions and a different adventure.

Three students, Annalis, Chanya and Eugene (alphabetical order chosen there), created websites using skills taught to them by the much beloved and missed Ajarn Marcus. By creating websites they are providing a service to other learners in the world of mathematics that want to know about sinusoidal waves and exponential functions.

Students used the desmos.com/calculator and its groovy sliders to play around with parameters to spot patterns.
check out some sliders here

Now for the websites:

Annalis' Exponentials are Cool

Eugene's Vas Are Sinusoidal Waves

Chanya's Parabolas

Pi - in it is everything π

Ask a Mathematician / Ask a Physicist

Q: Since pi is infinite, do its digits contain all finite sequences of numbers?

Posted on November 8, 2009 by The Mathematician

Mathematician: As it turns out, mathematicians do not yet know whether the digits of pi contains every single finite sequence of numbers. That being said, many mathematicians suspect that this is the case, which would imply not only that the digits of pi contain any number that you can think of, but also that they contains a binary representation of britney spears’ DNA.... read more in the site. Click the Question, the link 

Fascinating stuff!

Mathematical Dance Moves - What's yours?

On the windows of Mathsland are some formulas (formulae) to dance moves - check them out. What's your signature move? How would you graph it?

In MYP3 and MYP5 we have looked at graphing and patterns (different ones). Learning their signature moves on the axes can help us to understand how to graph them but also what they are trying to tell us about the pattern they represent.

Here's my  "squared triple circle cubed undefined gradient dance"



Play around with the formulas in the Desmos Calculator and check out some of the graphs other people have made like the minion...

This is HUGE!

Sorry about the lack of posts, I'm planning to make up for it.

And if you find something cool - a video or graphic or story that's mathematical, share it with me and I'll post it (referencing you of course).

It's about our universe, seconds after it began.

It's about theories and persistence

It's about patience and taking the time, a long time...

CHECK IT OUT HERE WOWOWOW

I love science and numbers

Here Come the MYP2 Coders!

Anda is first off the blocks with his two codes

A cool Spiral and something quite Disco (if you have epilepsy, Disco is not recommended because there is a lot of flashing).

Click on the links to see the fun.

Disco programming was developed initially by Tera, then Nom and then Anda took it on too. Excellent collaboration.

Anda's Spiral at code.org http://learn.code.org/sh/11921722

Do you want to learn to code - check out the  Hour of Code for lots of tutorials.

Stay tuned - next week all of MYP2s first programs will be live on the blog.

CODING - You should learn to do it.

MYP2 has begun their new unit on coding - computer programming.

The giants of programming and computing must have known that we were going to be doing this unit because they have put together an AWESOME site

code.org/

Below is the video we watched for you to enjoy. In this video you will see some of our high profile teachers.

As well as coding we will be enjoying some 'analogue' activities so that our MYP2s get to see how computers do all that magic inside.

We are starting small, just like Bill Gates did, and building from there.

The site has a wide range of tutorials from phone apps to computer science to first year college courses in programming. Once the MYP2s do the Beyond One Hour Computer Science course, they can take their independent learning in any direction they like.

Coding is a very cool area of mathematics.

MYP2 - please check your Managebac messages to sign up to our course.

If anyone else wants to join, please check out the amazing site and it's one hour introductions into many aspects of coding at code.org/learn

Synchronisation or Synchronization depending on your point of view, it's all pretty cool

Lots of people are posting a video about a murmuration of starlings on social networks. I came across this video and others many years ago and I wish to see it at a large scale one day.

For more collective noun names for animals that are as cool as a murmuration of starlings and a murder of crows check this out. It's about naming a group of animals, so technically they are mathematical terms. You can't be a called a group without counting to check if there are more than one of something present.

What's your favourite?
Do you do the same thing in your mother tongue?



On the TEDtalk page of our mathematics blog is a video about synchronisation in every day occurrences. I think you will enjoy it.  Steven Stogatz and his talk on "How things in nature tend to sync up" should be at the top of the blog page.

MYP3 Rock the First Ever PIADS CASINO

WOW - impressive work from the mathematicians in MYP3.

Two fun and profitable games were created for the amusement of students and teachers alike.  See below for a summary of the day. We hope to see you next year.

The Mathematics of Chance

The Mathematicians in MYP3 have recently held the first ever Casino at PIADS. 

MYP1, MYP2 and teachers joined us to "have a flutter" and try their luck with our PIADS Bucks. It was a fantastic mathematical experiment. 

The games made large profits - hundreds of Bucks for Bullseye and thousands of Bucks for Pop Mania. They made that money in only 30 minutes! 

How did they do it? The wonderful world of Mathematics, some clever psychology (to make customers feel like winners), visual art and design technology skills to make their games look great. Even if people felt like winners on the day, and many did, the games made the most money by far.  

Calculating probabilities, converting them to odds and then adjusting those odds to favour the house is how profit is made in casinos everywhere. They are rigged and the odds are never fair, but that's no secret. 

When you join MYP3 you can learn about the mathematics of chance and build your own casino.  If you can’t wait, ask an MYP3 to explain it to you.

Why does the house always win?  Mathematics.

Our Area of Interaction Focus was Health and Social Education.

• Looking after ourselves: Being aware of the differences between games of skill and games of chance. 
• Understanding ourselves: How games of chance make us feel. 
• Ourselves in the wider society: How gambling can affect society.

Our MYP3 students will never be fooled by games of chance. They understand how customers are manipulated into playing again and again and why some governments regulate gambling.

See you at the next casino - more games, longer opening times.

CASINO TIME

MYP3 have been busy analysing the mathematics of chance through games.
Their summative task is to design their own casino games.

Can you beat the house? What are your chances? If their mathematics is sound, they should make a profit on the day.

MYP1 and MYP2 (along with some teachers popping along) will try their luck to beat the house on Tuesday.

They know the secrets the casinos use to keep you playing and feel like a winner.

See you on Tuesday in Casino Land.

fake PIADS Bucks provided. No real money will be used.

MYP2 and the Giant Rubber Duck

Dutch artist Florentijn Hofman makes giant ducks.

Each one is unique and they have a message for the world.

What is that message?

The Arrival by Halanslicensed under CC by A NC SA 

MYP2 have been working on the mathematics of generalisation or algebra. They find patterns. They create formulas. They estimate. They justify. They compare methods. They discuss accuracy. They form hypothesis. They tackle long problems, not short one liners. MYP2 are mathematicians at work.

Now they have been asked to bring all of their skills together to work out if Phuket can produce enough rubber for one of these ducks. It is not a yes or no answer, we want details. 

How much rubber is produced right next to PIADS? 

How much rubber is needed?

What are those ducks all about?

Why spread the message with a rubber duck? 

We have more questions - check out the windows of the maths room.