1. CPA at Freegrounds Junior School 2017-2018
Y3 and Y4 Parent workshop 21/11/17

2. Mastery in Mathematics Mathematics mastery is about deepening children’s understanding so that they are able to make rich connections across mathematical ideas and solve increasingly sophisticated problems. In order for children to become masters in maths they should be able to apply their understanding in unfamiliar situations and across other subjects in the curriculum.
The 2014 curriculum put huge emphasis on mathematical mastery.
What do we mean to become a master? Journey to Shamblehurst analogy

3. Mastery in Mathematics
Another analogy.
All three of these children are in the same water. Liken to working on the same area of maths.
The deeper a childs understanding of maths the more they are able to understand and access. The more they understand about the ocean.
If pupils stay paddling in the water- they are able to enjoy the water, say that they ‘GET’ what the water is about.
Mathematics mastery is about not moving from one ocean to another, it’s about appreciating it and fully understanding it and building a toolkit to apply to other situations

4. What is CPA?
During their time in the infants pupils will have explored mathematical problems using real life objects. If a question was about the number of apples they would have used real apples. If it was about pencils or flowers they would have been handling real pencils or flowers. This allowed the children an opportunity to visualize and really understand the maths that was taking place. They may have drawn flowers or pencils to represent the maths that they were doing.
As we move through key stage 2 and when they are ready and conceptually understand pupils move away from real life objects to using other resources as representations- like the multilink above! They may also draw dots, circles or bars to represent the numbers objects they are working with alongside the physical resource.
Concrete resources and mathematical images are used right the way through key stage two and often at secondary school too and are vital for pupils understanding and for when pupils are explaining and proving their ideas.

5. Mastery in Mathematics
Multi-representations and the CPA approach
Concrete resources
Pictorial resources and images
Abstract ideas
Share egg box and cake tins

6. Place Value
Place value underpins children’s mathematical understanding and is fundamental to children’s mathematical success.
Being able to partition numbers into Th H T and O’s and discuss the relationship between each place value column is a sophisticated skill.
In year 3 pupils work up to 3 digit numbers and in year 4 they work using four digit numbers
Knowing that there are 10 ones in a ten and ten tens in a hundred etc.

7. 3 4 1 2 3412 Place Value Partitioning 3000 400 10 2
3000
400 10 2
In year 3 pupils work up to 3 digit numbers and in year 4 they work using four digit numbers

8. Task…
In groups choose a 3 or 4-digit number
Can you make as many multi-representations as possible for that number?
What resources will you use?
FEEDBACK

9. Structured Resources
Place value counters
Dienes
Bead strings
Numicon

10. How are structured resources used in class? Subtraction

11. Pictorial- mathematical images
Model on whiteboard
Share an array- demonstrate on whiteboard
Go back to egg box or cake tin
Prime numbers- timestables- understanding that multiplication facts are commutative

12. Bar Modelling- A pictorial representation of a problem
Share an array- demonstrate on whiteboard
Go back to egg box or cake tin
Prime numbers- timestables- understanding that multiplication facts are commutative

13. Bar Modelling- Problem Solving

14. Bar Modelling- Problem Solving
It is important to understand that the pictures do not solve the maths but allow pupils to sort their thinking and understand the calculation needed

15. Bar Modelling- Problem Solving

16. Bar Modelling- Problem Solving
Moving through the keystage the bar model is a highly effective way to solve complex problems including fractions percentages ratio
SHARE MORE EXAMPLES OF BAR MODELLING CARDS

17. Number Facts Symbols Formal Methods Digits Number Bonds
Abstract
Number Facts
Symbols
3 x 4 = 12
4 x 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
Formal Methods
Digits
Number Bonds

18. CPA is often used alongside each other and rarely in isolation.

19. What next? am – an opportunity to participate in some classroom activities with your children. If there are any questions or comments please come and speak to us.