## Wednesday, 31 July 2019

### DMIC observation

Today I had my latest observation/mentoring session from Don.
We are learning the DMIC way of teaching maths.

Today for the session, I had my lower half of the class working on this problem.
The following 4 photos are the 4 groups attempts to solve the problem.

This groups first attempt is the crossed out bit in the bottom left hand corner. They shared equally between Josh and Mele, but got stuck when they realised that Josh had \$4 and Mele had \$5. Knowing that they should have the same amount, they crossed this out and tried again next to it. The resilience here is awesome. They used the same strategy on the right hand side to solve the second part of the question.

I liked this groups approach to the second part of the question. You can see in the bottom left hand corner, one group member started drawing 17 stick people. The group then discussed and decided that's not what the 17 means, so decided to cross it out. Above this they drew 4 people and equally shared the 17 people as best they could. (Note the first stick person has \$5, whereas the others have \$4).

This group first split the \$9, into 3 lots of \$9. They gave \$2 to each smiley face, and then split the last \$3 into 3x \$1. They gave \$1 to each smiley face, leaving \$1 left over which they split into 2x 50c, and then shared these.
For the second part of the question, they drew the 4 faces, but didn't get far enough to solve this part.

This group started breaking up the \$9 and \$17 into smaller numbers which were more manageable, but weren't really sure what to do with them.

This is how the group (with the pink smiley faces on their paper) shared their explanation. It was awesome to see typically quiet students being able to stand in front of the class and clearly explain part of the problem. This is a big social phobia for some kids, so for them to do this so confidently was a huge achievement.

At this point Don encouraged me to sort of take over a little, and facilitate the second groups sharing. I had asked the second group (the ones that wrote in green felt) to share the second part (1/4 of \$17). Because of time factors, and considering how long the kids take to present, it was better for me to do it.
I asked the same child (call him J) who drew the above diagram, to draw 4 circles to represent the 4 people. Then we stopped and talked (altogether) about how we could try the same thing the pink group did, and split the \$17 into a number that is more easily divisible into 4 groups. So they came up with 4x4=16, and I asked 'J' to write the number 4 in each box. Next we talked about how we could split the leftover \$1. We had established with the pink group that half of \$1 is 50c, so now we needed to work out quarter of \$1. The students offered different answers - 10c, 15c etc. We checked these using skip counting and repeated addition,  but they didn't add up to 100 cents. Finally we got 25 cents. So each person gets 4.25.

Our connect and generalise was driven by me - at first I thought maybe if we can just understand the fractions of \$1, that would be awesome for today. So we did that.
We had established through our problem solving that 1/2 was 50c, 1/4 was 25c and \$1 = 100 cents.
I challenge the kids to think what might 1/5 of \$1 be..
eventually we figured out 20c. Same for 1/10.
So I made it even harder, what might 1/20 be..
At this stage I circled the 1/2and 1/4, and circled the 1/5 and 1/10, and asked them to think about halves and doubles.  This helped them to see that if 1/10 of \$1 was 10, 1/20 would be 5c, because 5 is half of 10.

Then one student offered her ideas that we could use times tables. I never thought this group would have realised that. I was quite happy with them realising the fractions of \$1. So we looked for patterns and were able to record the times tables that went with each one.

Overall it was a really good lesson.
Things for me to work on
- facilitating as a group instead of a 2nd or 3rd group presenting. It kept the kids engaged way more and we spent less time waiting for kids to draw stick people.
- sitting with the group before they present and rehearsing what they are going to say. Don modelled this with the pink group, who were able to present really well because they had practised with an adult. Don revoiced some of what they said (E.g. "we split the other 3 and got 50c" became "we split the last \$3 into \$1, \$1 and \$1, then gave \$1 to each person and split the last \$1 into two, so they got 50c). I had always been hesitant to do this, as I felt it took away from the kids thinking by revoicing and making them rehearse. But it worked really well, so this is something I will try.