1. Key Updates

2. What has changed? National Curriculum Early Years baseline assessment SATS Teacher Assessments Assessment without levels, expected standards Scaled score for key stage 1 and 2 SATS

3. What has stayed the same? Early Years Profile Phonics screening check

4. Summative Assessment Key Stage 1 Paper 1: Arithmetic Paper 2: Reasoning

5. Test Content Paper 1: arithmetic, worth 25 marks and taking around 20 minutes. Paper 2: mathematical fluency, problem-solving and reasoning, worth 35 marks and taking 35 minutes, with a break if necessary. There will be a variety of question types: multiple choice, matching, true/false, constrained (e.g. completing a chart or table; drawing a shape) and less constrained (e.g. where children have to show or explain their method). Children will not be able to use any tools such as calculators or number lines.

6. Key Stage 2 Paper 1: Arithmetic – 30 minutes Paper 2: Reasoning – 40 minutes Paper 3: Reasoning – 40 minutes No separate ‘level 6’ papers - tests will include a small number of questions that will stretch the most able pupils

7. Test Content Paper 1 will consist of fixed response questions, where children have to give the correct answer to calculations, including long multiplication and division. Papers 2 and 3 will involve a number of question types, including: Multiple choice True or false Constrained questions, e.g. giving the answer to a calculation, drawing a shape or completing a table or chart Less constrained questions, where children will have to explain their approach for solving a problem

8. Buckinghamshire Learning Tracks

9. New Curriculum Aims The National Curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

10. Fluency

11. Strategies Develop children’s fluency with basic number facts Develop children’s fluency in mental calculation Develop children’s fluency in the use of written methods Develop children’s understanding of the = symbol Teach inequality alongside teaching equality Don’t count, calculate Look for patterns and make connections Use intelligent practice Use empty box problems Expose mathematical structure and work systematically Move between the concrete and the abstract Contextualise the mathematics

12. Reasoning Research by Nunes (2009)Research by Nunes (2009) identified the ability to reason mathematically as the most important factor in a pupil’s success in mathematics.

13. Odd One Out Which might be the odd one out? Why? 0.55½ What might another person’s reasoning be? What might the two not chosen have in common?

14. Always, Sometimes, Never? Is it always, sometimes or never true that an even number that is divisible by 3 is also divisible by 6? Is it always, sometimes or never true that the sum of four even numbers is divisible by 4? What responses might we expect from children?

15. Reasoning Spot the mistake / Which is correct? True or false? What comes next? Do, then explain Make up an example / Write more statements / Create a question / Another and another Possible answers / Other possibilities What do you notice? Continue the pattern Missing numbers / Missing symbols / Missing information/Connected calculations Working backwards / Use the inverse / Undoing / Unpicking Hard and easy questions What else do you know? / Use a fact Fact families Convince me / Prove it / Generalising / Explain thinking Make an estimate / Size of an answer Always, sometimes, never Making links / Application Can you find? What’s the same, what’s different? Odd one out Complete the pattern / Continue the pattern Another and another Ordering Testing conditions The answer is… Visualising

16. I Have a Problem… We start each lesson/sequence of lessons with a problem Children break down the skills needed to solve it Practise those skills Return to the problem after practising skills

17. Problem Solving Skills

18. Comprehension This stage is about making sense of the problem by using strategies such as retelling, identifying relevant information and creating images. This can be helped by encouraging students to re-read the problem several times and record in some way what they understand the problem to be about (for example by drawing a picture or making notes).

19. Representation This stage is about "homing in" on what the problem is actually asking solvers to investigate. Can they represent the situation mathematically? What is it that they are trying to find? What do they think the answer might be (conjecturing and hypothesising)? What might they need to find out before they can get started? Central to this stage is identifying what is unknown and what needs finding.

20. Planning, Analysis and Synthesis This stage is about planning a pathway to the solution. You might encourage pupils to think about whether they have seen something similar before and what strategies they adopted then. Particular knowledge and skills gaps that need addressing may become evident at this stage.

21. Execution and communication During this phase, pupils will need to consider how they will keep track of what they have done and how they will communicate their findings. This will lead on to interpreting results and drawing conclusions.

22. Evaluation Pupils can learn as much from reflecting on and evaluating what they have done as they can from the process of solving the problem. Pupils should be expected to reflect on the effectiveness of their approach as well as other people's approaches, justify their conclusions and assess their own learning. Evaluation may also lead to thinking about other questions that could now be investigated.