## Tuesday, 30 June 2015

### My unsolved problem - the magic triangle.

## Monday, 29 June 2015

### Bearings in the hall - well worth a go!

Well what fun I had with my Year 8s today! The introductory lesson on bearings, with a twist...no writing or drawing at all! Instead we were down in the hall having fun with direction, playing team games and challenges. So much enthusiasm and energy involved, it tired me out just watching them!

On a practical note, the equipment used was:

A ball of wool

Scissors

Tape

Board sized protractors

8 or 9 hula hoops.

Activity 1: North, South, East, West.

You haven't lived if you didn't play this game as a child - someone stands in the middle of a large space and shouts directions, which everyone has to run to. I started by standing in one of the hoops in the middle of the hall and only defining North, and leaving them to figure out where the others are, and then off we went. Following a few of the cardinal directions, I then started to throw in NE, SW etc and ultimately things like NNE. This of course is where it started to get interesting as to how precise I could be, and is what motivated the need for bearings. After a brief discussion about using angle measures, and the need for two lines to create an angle (one, the direction of travel, the other a line pointing due North) and the need to measure clockwise (otherwise two different directions for the same angle), we moved on to Activity 2...

Activity 2: Find your bearing.

Leaving the hoop in the middle we tied a piece of wool to it and then stretched it out and taped it down to create a North line. I then threw the hoops around the hall and got teams of three to try and measure the bearing from the centre hoop to their assigned hoop. They used the board-sized protractors and more wool (typically each group had one person stood in the hoop in the middle, one person standing on a line to their assigned hoop, and then one person measuring) and had to be accurate enough to satisfy me to score points. This was my checking and consolidation exercise, used to pick up on an early misconceptions (i.e. people not measuring clockwise etc). This finally led on to the fun Activity 3....

Activity 3: Jump in the hoop.

To finish with we went back in to the teams and each team lined up at different points around the room. I put 2 of the board practors down back to back (and overlapping a bit) to create a makeshift 360 degree protractor and we played a game where I would shout a bearing, and the first team to put their circle on the bearing and stand in it scored the point. Each team then had to run back and give the hoop to the next one in line, and join the back of the queue ready to go again. The scramble to get hoops down was a definite sight to behold!

I cant say I have ever enjoyed the start to a topic more; however taxing it was really to manage all of the practical elements (I think I was as exhausted as some of the kids by the end of it), it was definitely worth it!

## Thursday, 25 June 2015

### Q & A with Nicky Morgan report.

**Pupil premium funding to be held at current levels as per the manifesto pledge through the life of the parliament.**

## Tuesday, 23 June 2015

### Plans and Elevations - Some approaches

## Sunday, 21 June 2015

### Ivan the jumping flea and negatives

The way Ivan moves is governed by the following rules:

1) Ivan starts at 0 facing the 'positive direction' (i.e. the direction of increasing numbers).

2) Positive numbers cause forward jumps.

3) Negative numbers cause backwards jumps.

4) The operation of addition makes Ivan face the 'positive direction' (i.e. the direction of increasing numbers).

5) The operation of subtraction makes Ivan face the 'negative direction' (i.e. the direction of decreasing numbers).

So lets say Ivan is completing the calculation 3 + (-5). Ivan would start at 0 facing up the number line and the first thing he would do is jump forwards 3 places, as the first part of the calculation is the positive number 3. The next thing Ivan would do is face the 'positive direction' (which would mean he did nothing as he is already facing the positive direction), as the next part of the calculation is the operation addition. The next thing Ivan would do is jump backwards 5, as the last part of the calculation is -5. Once these steps are completed Ivan would be at the value -2, showing 3+(-5) = -2.

Compare this to the calculation 3 - (-5). The first step would be the same, as Ivan still starts at 0 and still jumps to 3 as before. This time the operation is subtraction, so Ivan turns to face the 'negative direction'. Ivan then jumps backwards 5 as before, but because he is facing the 'negative direction' he is actually jumping up the number line, and so ends up at the number 8; showing that 3 - (-5) = 8.

I have a PowerPoint here which shows Ivan solving both of these questions (which I made some changes to in order to have a completely animated sequence, once you click to get going on each slide) which people are free to adapt for other questions as you see fit (provided you can alter the motion paths etc).

## Wednesday, 17 June 2015

### 'Pointless' bar charts

Instead of just putting the picture on the board I organised the kids into 11 groups and gave each group a copy of the bar chart stuck into the middle of the paper and told them to write as many bits of factual information from the chart as they could around the outside. After about 10 minutes they had to choose one of the bits of information that they thought was their "best shot" at a pointless answer. They were then given points in the true pointless style - however many groups had the bit of information scored them that many points, or for an incorrect answer the maximum of 10 points (11 teams = maximum of 10 points when counting from 0 to 10).

The kids really enjoyed the competitive element and trying to come up with obscure information, and obviously we got some interesting maths that I wouldn't have thought to ask [how about the bar is 7.5 cm long and 1 cm wide!] We got some great discussion and discord about whether people were right or wrong, and whether two pieces of information were the same. One group said the frequencies add up to 390; and meant the values on the frequency axis rather than the frequencies indicated by the bars; we didn't give that as it was ambiguous.

I can see this working for lots of things; I think putting a straight line graph on the paper and asking for facts here as well, or a two-way table, or any other way of presenting factual information. So if you are looking to get kids answering questions you would never think of asking, try a Pointless Page.

## Sunday, 14 June 2015

### I can read your mind - now that is what I call an hypothesis test.

It starts by explaining to pupils that you are going to test if any of them are psychic. Obviously it is nice to ham this up a little bit, give it a bit of dramatic flair etc. Explain to them that the test is that you are going to flip a coin 20 times and keep each result hidden from them. You are then going to concentrate very hard on the result and they have to write down the impression they get from you.

Do the experiment and then see how the kids get on; normally about the maximum you will get is 13 or 14 (any more and you may well actually have a psychic on your hands!) and so the conversation turns to, "well is this enough evidence? What is the probability of someone getting 13/14 by random guessing? How many would be good enough?" This gives me all the tools I need to form a formal hypothesis and discuss things like the significance level (at what point does the probability become so remote we have to agree this is not happening by chance - when it is less than 5%? 1% etc), confidence interval (how many must someone get right before we believe they can read minds) etc.

I find that having this early practical hook to keep coming back to really helps pupils as they navigate what can be quite a tricky topic simply because of the sheer number of different contexts to which it can be applied. So the next time you are teaching kids about hypothesis testing, try giving them a fun hypothesis they can see practically happening in front of them.

P.S. to develop it, ask about what would happen if you switched the coin for a die, and how that would change their views on how many needed to be sure etc...

## Wednesday, 10 June 2015

### Inspired by JustMaths, looking beyond the basic skill.

## Tuesday, 9 June 2015

### Probability Scales - worth spending time on.

2) Use alternative language freely and force pupils to describe in different ways.

3) Ensure you hold them to reasonable accuracy when placing values on the number line (I had a lad who told me that a probability that numerically was 1/7 mark an arrow too close to 0 and we challenged this as a class by looking at 1/7 as 14.29% and whether we thought that his arrow was nearly 15% of the way up the line).

4) Use a number line broken into segments (I was nice and went for 10ths) to ensure they have to think about at which point or between which points does it go (and apply point 3 here as well, I was penalising for probabilities of 1/3 being closer to the 4th mark then the 3rd mark)

5) Teach this as a follow on from writing probabilities as fractions, rather than before it (as is often the case), so that you can tie fractional ideas to scales.

## Friday, 5 June 2015

### Hannah's sweets and the new GCSE.

## Wednesday, 3 June 2015

### Singing for memory...it really works!

She was a bit embarrassed to sing in front of me, so I sang in front of her instead! I am now seriously considering teaching all of my lessons in song! The reaction I got was brilliant - she couldn't look me in the eye and was laughing her a** off! Talk about engaging them emotionally, the cringe and humour factor is brilliant. I sang Journey's "Don't stop believing" with the quadratic formula as part of the lyrics, basically like this:

"Just a small town girl,

Living in a lonely world;

Minus b plus or minus,

the square root offfff,

B squared,

minus 4ac;

all over 2a

that gives you

the 2 values that solve

the equaaaaaation!"

I explained to her that everyone has a song that they just know the lyrics to, without even thinking about it, so if she can put this sort of information to that tune, she can use her knowledge of the lyrics and tune to support her. Of course the most difficult bit in remembering the lyrics of a song is getting started, so I left the start the same. I guarantee that when I have Year 11 (and I will probably do it with some stuff in Year 7 all the way through), I will be using this for a revision technique!

## Monday, 1 June 2015

### I have never probability

a) I have never flown in an aeroplane.

b) I have never been to a live concert.

c) I have never been to a live sporting event.

d) I have never broken a bone.

e) I have never been abroad.

f) I have never been camping.

g) I have never done the ironing.

h) I have never been on a train

i) I have never ridden a horse.

j) I have never been ice skating.

I am sure I could come up with more if I really thought about it. Think I have my starter for tomorrow!(Or if I can find some way to tie in mutually exclusive/exhaustive events I might use it during the lesson).