## Tuesday, 2 August 2016

### Collaborative Planning in Maths

A real focus for TPS this year has been collaborative planning in maths. It is a focus because we are receiving Professional Development [PD] around the problem-solving approach in maths.

This term, our syndicate has really taken the collaborative planning aspect on board. This means, that the whole syndicate, roughly 100 students, aged between 7-13, will be working on the same problem. The only difference between classes, is that the numbers in the problem may change to reflect the level of students, or even new and harder concepts may be added.

This is the plan for week 2.

The yellow sections are for EVERY class.
The green section is aimed at Level 2, year 3-4 in school (my class). These answers focus on using halves and quarters.
The blue section, introduces fractions such as thirds and fifths, and are aimed at Level 3 of the curriculum (years 5 and 6).
The red section is for the year 7 and 8 students. This question is even harder again, as thirteen students cannot easily share six chocolates - each person gets six thirteenths of a chocolate bar, which is way more demanding and difficult to figure out.

As noted in the top of that image, we have a shared focus for the whole syndicate - "finding fractions of a region". This is what we are ALL focusing on for this week, just at varying levels. How this works, for example with my own class, is that they will start at the beginning. If they understand concepts around halves and quarters, and identify patterns about how many friends and how many chocolate bars, we will challenge them by asking them the blue questions (aimed at year 5 and 6). It pushes them to think beyond their year 4 knowledge, which reinforces a growth mindset. If they show understanding at this level, we will push them even more with the year 7 & 8 section. Each section is not exclusive to its own year group - each teacher can take the parts of the question their students need and use it.

Today we used this question with our class.
They originally only received the top yellow, and green sections.

Lets see what they did..

 Cutting the chocolate bars in 'half'

 Some misconceptions evident very quickly.. (It is actually 3/4, and the opposite to groups)

 Giving one 'half' and one 'quarter' to each of the four people.

 One student drew the three chocolate bars, then straight away cut them up into quarters, giving three pieces (coloured) to one person. Note - this is what I would have done as an adult!

 Then we came together as a class and talked about how to solve it. Students gave Archana their ideas and she recorded them. Here you can see some confusion about how to add one half and one quarter - she had to reiterate that one half IS the same as two quarters, therefore you are just adding three quarters.

 Students who don't typically engage with maths tasks getting involved - YAY!

 For the second green question, students think about how six chocolate bars can be split equally between eight people. Again, they cut up the chocolate bars and give each person one half and one quarter each.

 Each of the eight people receiving one half and one quarter.

 This group drew the chocolate bars, cut them up till each person had half, then two bars were left over. As the question clearly says that no chocolate can be leftover, they cut the leftover bars into smaller pieces and shared these out as well.

 A bonus question - how much chocolate does each person get, if there are 12 chocolate bars shared between 16 people..

 12 Chocolate bars shared between 16 people - one half and one quarter each.

 A different group, again showing one half and one quarter for each person.
Tomorrow we will give harder questions (the blue ones, aimed at years 5-6) to most of our class, who clearly showed they understood how to find fractions of a region. With the others, who did not show the same understanding, we will have in small groups with both myself and Archana, and use DATs (Direct Actions of Teaching), to help them fill in those gaps and get them to the level of understanding they need.