1. Dr Jenni Back Host Schools Project Lead
Arithmetic proficiency: achieving fluency with understanding in arithmetic
Dr Jenni Back
Host Schools Project Lead

2. Welcome and introductions
The Host Schools Network
27 Host Schools and 152 Visiting Schools
The HS Team
Rachel Ball and Jenni
Support from the NCETM
Celia Hoyles, Jane Imrie, Debbie Morgan, Laurie Jacques, the Portal team
Welcome to everyone
Thrilled to have managed to start such a vibrant network of enthusiastic teachers from all over the country
Key focus on arithmetic proficiency in years 3 and 4 and working together to support fluency and understanding for all learners
Exciting day ahead and hope that you all get lots out of it both through the presented sessions and the opportunity to network with others in the network.

3. Building relationships in networks
Alison Peacock Headteacher at The Wroxham School in Potters Bar
Thrilled to welcome Alison Peacock.
Effective head teacher and inspiring leader with experience of supporting and empowering people to change their professional practice through working in partnership with them. She is going to share with us some suggestions to help you to build effective and supportive working relationships in your networks.

4. The Host Schools Network
An Introduction by Professor Celia Hoyles OBE, Director, NCETM
Professor Celia Hoyles has been the Director of the NCETM over most of its existence and it gives me great pleasure to call upon her to fill in some more details about the Host Schools Network and how NCETM see it developing.

5. A Mathematical Task
Exploring the key mathematical issues in years 3 and 4 Where do we start?

6. Strike it out

7. Rich tasks: low threshold, high ceiling
Accessible to all at the start of the lesson
Allows the most confident/ competent to go as far as they can and offers the opportunity to ask their own questions
Plenty of supporting activity of those who will benefit from it
Allows different types of thinking and different approaches
Article on NRICH website at
Rich tasks offer a meaningful context that provokes the students to learn in order to solve it

8. Progression from EYFS to KS2 and beyond
Recognising number symbols to 10 – restrict the number line and use concrete apparatus
KS1
Developing skills in addition and subtraction of numbers to 20
Lower KS2
Recording results systematically
Conjecturing about possible choices
Relating addition and subtraction facts
Upper KS2
Building fluency with number bonds to 20
Predicting results, developing strategies
Beyond KS2
Developing mathematical thinking: exemplify, visualise, generalise, do/undo, conjecture, prove

9. Calculation policy
Need for a clear and consistent approach across the school
Importance of communicating the policy at transition points
Importance of fluency - only possible once the concepts make sense
Moving away from procedures to conceptual understanding and reasoning

10. Key thresholds in mathematical development in arithmetic
KS1 entry: conservation and counting
KS2 entry: addition/subtraction, number bonds to 20, place value
KS3 entry: multiplication/division, multiplication tables
KS4 entry: proportional reasoning

11. The issues in years 3 and 4 Securing conservation and counting
Additive reasoning, fluent recall and application of number bonds to 20, understanding place value
Developing ideas of multiplication and division
Intuitive understanding of proportional reasoning

12. The Big Ideas in arithmetic in Y3 & 4
Doing and undoing
The number system and place value
Securing and deepening understanding of addition and subtraction
Building repertoire of known facts
Developing understanding of multiplication

13. Models and images for multiplication
Barmby et al’s Nuffield funded project ‘Developing the use of visual representations in the primary classroom’ CPD course on developing children’s understandings of multiplication and fractions through using a variety of models and images All resources have been made available to us for the Host Schools Project

14. Plates of strawberries

15. Beads on a rail

16. +6 +6 +6 +6 +6 +6 +6 6 12 18 24 30 36 42
Jumps on the number line

17. Array without spaces

19. Array with spaces

20. Area model of multiplication

21. TU x TU Grid method 10 8 10 6

22. 10 5 3 10
TU x TU Grid method but splitting the units further 5 1

23. How can we teach them?
Exploring the key educational ideas in teaching arithmetic in years 3 and 4 A number of statements about teaching arithmetic Discuss them in your groups and sort them according to their importance What would you include/ignore? Why? Make a poster showing your thoughts Share our findings as a group

24. Sharing experiences from across the Network
Doncaster: Thorne Brooke Network Northampton: Great Bowden Network London: Eleanor Palmer Network Cumbria: Heversham St Peter’s Network

25. Using the Portal
Getting your usernames to Rachel Each Network will have its own community There will be a national community to which all the Host Schools will have access Use it to communicate, to share resources and to ask us for input and advice Advantage that anything put up can be seen by all in your group.

26. Next Steps: questions and answers
Debbie Morgan, NCETM Primary Director
Admin: Rachel – purchase orders & complete lists of Usernames
Completion of Questionnaires
Date for Jenni’s visit should be fixed as soon as possible
Resources

27. References
Andrews, P., Sayers, J. & Back, J. (draft) The development of foundational number sense in England and Hungary: a case study comparison. Submitted for CERME 2013 Anghileri, J. (2000) Teaching Number Sense. London: Continuum Back, J. (2011) Maths without translation. Primary Mathematics 15(2) Back, J. (2011) The Story of Six. Primary Mathematics 15(3) Barmby, P., Bolden, D., Raine, S. & Thompson, L. (2012) Developing the use of visual representations in the primary classroom: A Nuffield Foundation Project

28. Thank you for your hard work and attention.
Dr Jenni Back
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