Thursday, 26 September 2013

Bad Question

We were doing a bit of an assessment review and I threw in this question. Please note that I did not refer to the name of card game that the 4 friends were playing - it could have been just about anything:

As I was going around looking at what the kids were doing, it suddenly dawned on me that this was a really bad question, quite apart from the fact that this deck seemed to have three 9 of diamonds.

Each of the "hands" had exactly the same chance of happening. And I had asked about the chances of getting each particular hand.

Bad question.

According to a reliable source, there are 2 598 960 possible hands that you can be dealt in 5 card poker. So each of the hands illustrated above has the exact same chance of happening, that is 1:2598960.

I had given too much information. I should have referred instead to "one pair", "all 5 cards diamonds", "four 9's" etc.

Incidentally, there is a greater chance of getting dealt a pair (2860 possible combinations) than getting dealt nothing (1277 possible combinations). Who would have thought?

Hmm, good thing I don't play cards for money...

Wednesday, 25 September 2013

The Unfair Game

One of the activities from our Week of Chance and Probability - which seems to have spilled over into a second week - is the make "The Unfair Game".

Here is an example of an Unfair Game from one keen student.

Here is how he set out his page - instruction, calculations, data - the thinking is very easy to see.

A clear set of rules - this is how he chose to make a game that is unfair.

Oh yes! The stuff he forgot!

And a bit of reflection and explanation to clarify the process.

He got very excited when he was tabulating the possible results from throwing 2 dice. He found that...

....there is only one way to roll 2 = 1 + 1

....there are 2 ways to make 3 = 1 + 2 or 2 + 1

....there are 3 ways to make 4 = 1 + 3 or 2 + 2 or 3 + 1

....there are 4 ways to make 5 = 1 + 4, 2 + 3, 3 + 2, 4 + 1

"When is this going to peak?!" he asked excitedly.

Well, here are his data and results. You and I probably both knew that it would happen when he got to 7. Now he knows it too and will probably always remember that "Ah-ha!" moment.

Why? Why did we go to all this trouble to make an unfair game?

Well, I think it shows really clearly what you understand about chance and probability if you can manipulate different variables to the advantage of one player. And the student's understanding is demonstrated explicitly here in this example. 

And - yes - it was fun.

Tuesday, 24 September 2013

My Name is 256

As a bit of fun this week, the boss has decided that teachers are going to wear a number around their necks - no, we are not all convicts doing time - it's a cunning plan to get the kids to look at numbers in new ways. We did a similar activity last year when we gave the kids a tables fact to wear for the day.

The whole idea is that the students are not allowed to use the names of the teachers. They need to call them by a number combination or calculation that equals their number.

For example, my number is 256, or as my daughter now calls me, 162  

Then, during the week, children are encouraged to record their calculations on white boards around the school. Here's an example of one:

AND we get to have some fun with Maths!

Monday, 23 September 2013

Probability With Our Kindergarten Buddies

We finished our week of Chance and Probability with a visit to our Kindergarten buddies. To make this visit interesting, we all designed probability games that we could share with them.

Here are a few of the results:

This was very simple and very effective. You get six cups (probably label them the right way up next time) and a stack of dice. Each time you roll one you put it in the corresponding cup to see which score occurs most frequently. Obviously, you are more likely to roll a 4 than a 2 when you play this game, disproving the idea that there is an equal chance of getting any number from 1-6.


A nice use of a colour wheel. You drop the marble on the centre point and see where it rolls. An unusual choice to have 13 sectors but a great way to have 3 chances that are equal and one that is slightly more probable than the others.
We had talked about the "Monty Hall" problem in class (click here to see a Youtube clip about it) so one student decided to make his own version, where you could win two brussels sprouts, two goats or a car and a lollypop. 


Here is a very elaborate game that one boy made for his buddy. There are two sets of marbles - one black and one silver. Each player chooses a colour and then rolls the marbles onto the board, recording what colour they land on. At the end of 5 rounds, the players compare the frequencies of each colour.



Some boys brought in their car collections and got their buddies to sort them based on colour. They prepared a data table and a set of questions for their buddies:

The data table as completed by the buddies.


And the set of questions. Love the last question!


This was a great activity because the student had thought through what they wanted to do and wrote an excellent set of instructions. 
As a writing task, it was excellent. 
As a maths task, it was excellenter.


Another very elaborate activity that involved heads and tails, a colour wheel, colour stars, glitter, sparkly things and coloured glass jewels. The buddy was in heaven! 


I always come away from these activities totally blown away by the creativity of my students. They always think of things that I would never have considered and never fail to demonstrate their own learning through what they choose to teach to their kindergarten buddies.

Ah, Year 6 - you've done it again!


Friday, 20 September 2013

What Are The Chances of That?

This week we have dedicated to Chance and Probability. It has been a lot of fun. We had a series of 10 activities for the kids to engage in and collect data. They were also required to design their own chance activities or games and share them with their Kindergarten buddies - I will share the results in a later post.

One of the biggest learnings for the week was all about recording data. When we were conducting probability activities like tossing a coin or dealing cards, it became important to keep an accurate record of what had happened. As a consequence, the students quickly discovered that poor recording led to inaccurate and unreliable conclusions. Conversely, careful recording resulted in accurate conclusions. 

Here are the 10 tasks that we embarked upon and some examples of how the students recorded their results:

Some very detailed recording of heads and tails.

Interesting use of colour to highlight features in the data such as most and least frequently occurring scores

Interesting to see who is familiar with a deck of cards - how many cards are there, what are the suits called, how do you shuffle cards - all useful insights. Setting out the data carefully makes it so much more useable when you need to discuss your results.

This is really interesting - and isn't anywhere near 365.

An interesting activity - if only to see who actually knew what their phone number was.
Most kids have it programmed into their phones so they don't have to remember it these days.

An interesting spread of data here. Not many big words on the front page - mostly 2, 3 or 4 letter words.

Not psychic I guess - even though the first 6 guesses were correct! 
What are the chances of that?

This was just for a bit of fun but also to see how everyday games involve chance. Surprising how many of the kids not know how to play this game. It was a great opportunity to learn a new game.

Haven't got this far yet and it's the end of the week!
Where did the time go?

A few groups got to this but the data display wasn't very interesting 
so I haven't posted a picture.

Wednesday, 18 September 2013

Maths in the Year 6 Exhibition 2013 - Part 2

It's been a few days now and the Exhibition has been and gone. I have reflected on what we experienced and have identified a few more ideas relating to Maths that came out of the kids' inquiries.

Here we go....


Quite a few groups used timelines to present information - after all our transdisciplinary theme was "Where we are in place and time." Lots of them were fairly traditional timelines but there were a few that showed some excellent creativity.

Here are a few:

One of the "Fashion" groups did a really good timeline using miniature dresses that they had made to demonstrate the changes to fashion over time.

Another (different) "Fashion" group used shoeboxes for a timeline. Inside each box was a pair of shoes that represented the fashion of that decade.

The "Women's Rights" group (ironically) used a clothesline to display their timeline of significant events in the history of the women's movement.

Voting and Polls

Several groups decided to ask their visitors questions about their inquiry and were able to represent their data in interesting ways.

The Women's Rights group asked a question about the Suffragette movement.

Then people were asked to place a gold (wedding ring-like) ring into a jam jar. (Irony again?)

Gold rings laid out on a beautiful silver tray.

Visitors got to put their "vote" into one of three jars.

Another group, inquiring into developments in medicine, conducted an activity that asked visitors to place a small coloured bead into empty medicine boxes if they thought that the product contained penicillin.

Results were tallied to see which products were most easily recognised as containing penicillin.

Another group looked at "Body Image" and the influence of Barbie dolls on young children. They asked people to decide which doll they preferred, Barbie or "Emme" - a doll with "real" proportions.

Vote by placing a picture into the correct box.

Representing Data

There were several other interesting ways that data was managed and presented.

A group that was looking at Post Traumatic Stress used plastic soldiers in a sand tray to demonstrate the percentages of soldiers who would experience PTSD.

Presented with this data, visitors were asked if they could model the percentages using the plastic soldiers in the sand tray

Showing that 1 in 5 veterans get PTSD - 4 soldiers on the left out of 20 on the right.

Another group was looking at sweatshops and sporting clothes manufacturing. They wanted to show different perspectives so they constructed a Venn diagram using hoops suspended by fishing line.

There ideas were organised to show their understandings of the issues involved.

I was impressed! I thought they had demonstrated their understandings in very creative ways. 

It's always good to give the kids some room to do things their own way - they will always come up with things that you don't expect!