Advent Maths

So, this year (2018), 1st December was on a Saturday. Doors opened on Advent calendars all around the land. Go to church on 2nd December and they're lighting their candle and saying that it was the first day of Advent.

So,

There are four Sundays in Advent. The four Sundays leading up to Christmas Day.

What's the earliest date the First Sunday of Advent can be in a given year.

And,

What the latest date the First Sunday of Advent can be in a given year?

Part Part Whole, Bar Model & Perimeter

Earlier this year, we were calculating perimeter of compound shapes with some missing measurements. Some children were struggling to work out which measurements were missing. 

So, we took to using the bar model to offer some support.

1. Count the sides of the shape
2. Colour horizontal sides one colour and vertical sides another colour
3. Identify which sides have an unknown length
4. Use 'Part Part Whole' bar model (one for horizontal and one for vertical) to help find missing lengths
4a. The bar models can also be colour coded the same as the sides
5. Check the number of lengths found matches number of sides and looks sensible 
6. Add them up...

It worked well for us. Of course, as always with the bar model, it will help work towards an answer, but not give an answer. 

The Story of the Rugby Match

In rugby (union and league), points are earned in various different ways during a game. 

Here's the scoring system in rugby union:

- try, 5 points (and then the opportunity to kick a conversion for 2 points);

- penalty, 3 points;

- drop goal, 3 points (not frequent).

So, looking at a scoreline from a game, can pupils work out how the teams achieved the scores they have? These could be mid-game (like the ones below), full time or even fictional.

@PrimaryIdeas @alanpeat @gareth_metcalfe @PrimaryRocks1 @gazneedle @dughall in RL 4pts try 2 for conversion or penalty and 1 for drop goal

— Mark Boylan (@ictlinks) 23 March 2017

Are all scorelines possible? Can any scores only be gained in one way?

@PrimaryIdeas could also compare scores between codes, what would the score line be in the other code?

— Mark Boylan (@ictlinks) 23 March 2017

Christmas Countdown Problem

The above shows a Christmas countdown that we have on a window in our kitchen at home from the 1st of December. It's designed to be used like an Advent calendar and only in December (hence having 2 lots of 2 for '22 days to go' and 2 lots of 1 for '11 days to go', but not 2 lots of the other numbers). Today, I noticed that someone has begun a countdown towards Christmas 2017 (don't worry, it's coming down shortly). However, if we were to continue, how many days could not be shown with the numbers available and what 'days to go' are they? For example '222 days to go' can't be shown as there are only 2 lots of 2, but 357 and 356 can both be shown.

Resource Here

Maths and Mariokart

One of the best video games in recent times (and much further back) is the consistently excellent Mariokart available on the various Nintendo devices.

We recently looked at how we can make use of this video game to do some 'real-life' context problem solving.

To start we asked the question: how fast is Mario driving?

Mathematically, this led to an excellent discussion on what information we needed to know in order to answer the question. We talked about units of measurement, distance and (inevitably from a  scientific point of view) the different variables we needed to control. After this discussion, we were able to move forward with carrying out some experimental races.

In order to keep things accurate we used the time trial race (which took out the danger of flying mushrooms or turning into a rocket); avoided the use of speed up pads and completed the race several times.

 Practical maths part one was finding an average from the times we got after the first round of races. Then we needed to find out the distance of the track we were racing on. Initially, we could not find the distance so we fired off a message to Nintendo and they, brilliantly for the class, replied and directed us to a different wiki site to the one we had visited in our early research. Now, armed with our times and distances, the class was able to try and find the speed average speed that Mario was travelling at around the track.

The kids were very excited to take part in this activity and eagerly engaged with the problem. All children were able to take part in the initial maths discussion and, working in mixed ability groups, were able to come up with a solution.

Next we are going to work on coming with comparative speeds for the different vehicles in Mariokart.

Rolls and Flips: Probability All Done

Covering probability or data handling in maths and using lesson time to generate data? Well, it's already been done for you:

@RollADay are rolling a dice each day. The data can be found here: rolladay.com

Image credit: @RollADay

@FlipADay are flipping a coin each day. The data can be found here: tadfry.com/flipaday

Image credit: @FlipADay

Follow the accounts. Use the data. Maybe even share with the accounts what's been produced using the flips and rolls.

Both of these are operated by Tad Fry. Other useful online tools can be found on his site.

Looking for Sport's nth Term

I noticed that in the 2014 FIFA World Cup there are 32 participating nations and 64 matches. That's half participants to matches. 1:2 if you like. I noticed that as a possible pattern and wondered if it'd continue for a competition of 16 teams and therefore 32 matches. However, I didn't investigate. I'm going to get my class to...

Click here for our resource.

Feel free to edit and adapt for your own class.

Puzzle Games in Maths

As part of a recent problem solving week, we decided to use a puzzle video game as an introductory element to our maths lessons.

The Professor Layton games are available on Nintendo DS and 3DS and each game consists of an extensive range of puzzles within a mystery story to be solved by the character of Professor Layton. This, coupled with the fact that there are six games within the franchise, means that there are a vast amount of puzzles to choose from. The fact that these are available on the Nintendo DS means that you can make use of a visualiser to project the game onto the big screen. Alternatively, there are many websites on the web which have images of the puzzles which can be used to create paper copies of the puzzles.

The puzzles themselves are incredibly diverse, both in terms of the skills needed to solve them and in the level of difficulty. Over a series of lessons, you can cover a wide range of problem solving skills and target all levels within your classroom. In case you do not want to go to the trouble of solving the puzzles, there are many websites with solutions.

The children were motivated by the puzzles within the class in part because of the high quality delivery of the game, the fact that solving them moves you along in the game with a reward and because the puzzles are designed to be accessible to a range of people. There were several times when children announced that the puzzle was 'impossible'. It was an excellent opportunity to take children through problem solving strategies as you work together towards a solution. Many children asked if there was a way of taking the puzzle home to show parents and others.

There are, of course, many different puzzle games available across all sorts of formats, but these are favourites of ours. We will certainly be continuing to use these puzzles to inspire problem solving in the classroom.

Codes of the Cryptographic Kind

Recently, our classes took part in a writing week. Our focus was on writing in the style of a Sherlock Holmes story. With the emphasis on writing, we were eager to find different ways of keeping children's engagement throughout the week. One way was to give children a different code each day to solve.

The idea was that there would be a new code each day and by solving that code, children would gain one word in a sentence which would lead them to a chocolate-based prize on the final day.

The inspiration for these started with the dancing man code from the Sherlock Holmes story 'The Adventure of the Dancing Man'. In this story, a code of dancing figures is used to communicate with one of the main characters. I used this code for the first day of the week. In order to do this, I downloaded a dancing man font from the internet and used this to help create the code.

Image credit: celebwallpp.com/745795-cool-letter-fonts-to-draw-displaying-19-images-for-easy-cool-letter

The second day was a simple numerical code with numbers replacing letters. This proved rather simple for the children in the class, which was fine as they still were working on the clue from Monday.

The next clue was written in Morse code. Most children were unclear what the dots and dashes might represent, but there were a couple of children who knew what it was. This led to a great learning opportunity around what Morse code was and how it developed.

Image credit: lh3.ggpht.com

At this point there was a small group of children engaged in the code-breaking so I revealed the final prize on offer which inspired more children to take part.

On the Thursday, in order to draw the children in, I used reversed words as the simple code. The children were feeling confident with groups coming together to solve the problems.

When I released the code for the final day, it was a humdinger. There was a combination of the previous codes with some wrinkles. There was a repetition of the dancing man code which only a few children had solved. Instead of the backwards words I used the phonetic alphabet to represent letters and instead of numbers I provided calculations with the numerical answers representing letters.

The children were particularly motivated by now and a group worked over the start of lunchtime to solve the problem and achieve their treats at home time.

As a whole class problem it was great as it allowed me to personalise problems for different groups of children. By the end there was a significant number of children taking part using a range of different skills.

More information on codes can be found on the Bletchley Park website.