Someone presents you with two packs of cards that you have to bet $1000 dollars of your own money on. Pack A contains 5 red cards and 5 black cards, pack B has 10 cards, but you are not told how many are red and how many are black. You double your money if the first card turned over (after shuffling the deck) is a black card and you lose all your money if the first card turned over is red. Which deck will you choose to put your $1000 on and why? 
The problemSet up as a 3act style task the video opposite was Act 1. I filmed 20 rolls of a 30sided dice but made sure they could not see what the last 5 of those rolls were. They needed to figure out what the last five numbers rolled were. In Act 2 they were first given the image below on the left (ACT 2A  click for a larger view) which was the numbers in roll order, numerical order and with the calculated values of mean, median and mode for the entire data set.  
No, we are right, the data is wrong.
We had begun our preliminary work in looking at probability and it became clear that students did not have a solid idea of the concept of uncertainty. So to demonstrate the concept I placed 10 coloured blocks into a box and told students that they were going to predict what was in the box. I then proceeded to have five of them draw out a block each and I recorded the colours. The blocks the drew out are shown opposite. 
.Following this two further blocks were revealed by the students and the green one came in. When it now came to guessing the final three blocks, there was much more variation in the, there was much more uncertainty, that new colour had led them to believe that there could be more colours they had not yet seen, So in this case i showed them the final colour they had not seen which was the yellow one, however they were told, that the two remaining blocks are colours they have already seen in the set of blocks already revealed. As I listened to their conversations about what the two remaining blocks may be I could tell the opinions now were much more divided, but also much more reasoned, they became to come to the unerstanding that there was no way to tell. they didn't know if having half blue meant that there were more blues in it or whether it meant that we had now picked them all out, there was nothing on which to base their opinion but guessed it would two of the same colour. Following this I did the final reveal of the two blocks remaining  
I have filled the box now with blocks according to the criteria below, can you tell me how many blocks of each colour are in the box?
Criteria: Pr (red) = 2/3 Pr ( blue) = 1/12 Pr (green) = 1/4 # blocks < 20

They were able to notice the trend of whenever you pull out a block of a certain colour the probability of drawing that colour goes down and the probability of drawing the other two goes up, but there were a few who were puzzled by how the fractions were changing. For example with the green block it started at 1/4, then went to 2/11 and then to 1/5. With further time to discuss it they were able to talk about how we started with 12 blocks so 1/4 could also be shown as 3/12. It goes to 2/11 next because the total number of blocks is now 11 as we drew out 1, and that block was green so the number of greens went from 3 to 2. The next one would be 10 blocks so 1/5 is really 2/10, so the block chosen was not green. They were able to clearly articulate reasons for what they were seeing. 
Maths anxiety can be defined as a state of apprehension or fear, and reduced performance, brought upon by the presentation of a mathematics problem. In the video it suggests that around 20% of the population suffer from it, however I have seen estimates in other sources that suggest if we include milder maths anxiety this number could be much higher. This is a large proportion of the students I teach and who I ask to engage in maths each day. It is not linked to current ability, it effects higher and lower achieving students alike.  
5 yo daughter asked me "how do you count to half?". Wasn't sure how to ans. More I thought, the more complex it became, any thoughts? #mtbos
— Shane Loader (@LoaderShane) June 1, 2017
Another colleague sent me this photo on a Saturday morning as we had talked about the problem earlier in the week. When I looked at the photo I had the feeling that a month ago I would have been confident in my answer, but now I was no longer confident, I can't even think of how I would have counted it a month ago, I didn't know if the count of the orange on the plate was 5 or 9, 5 whole oranges, which would allow me to count by halves, or just 9 pieces of orange. But the photo did help to put a theoretical base to my struggle. By counting the 9 pieces, you are counting "how many", but by counting 5 oranges you are counting "how much". I think I have always associated counting with how many, you can count how many objects are in your bag, even if they are not all the same, but I am just not sure if you can count "how much". By counting "how much" you are counting the relationship to the whole, it somewhat becomes a measurement. 