1. Buckinghamshire School Improvement Service Mathematics Course – Year 5 teachers Becky Ellers (Maths) bellers@buckscc.gov.uk Cathy Tracy (SCC) ctracy@buckscc.gov.uk

2. Progression in Mental Calculations- reasoning and mathematical language Mirrors the Year 1 teachers course Runs alongside the Headteacher course Day 2 (9 th Jan 08)– AFL – Using the renewed framework to embed day-to-day assessment

3. Aims of day 1 Build subject knowledge Build a clear understanding of progression within and beyond year 5 Broaden your repertoire of teaching approaches Develop children’s reasoning skills

4. Session 1 To consider the prerequisites for an aspect of calculation from Year 5 To further your understanding of important aspects of mathematics that children need in order to develop mental calculation

5. The importance of Progression in calculation Look at the ‘Yearly Overviews’. Sort the year groups into the correct order.

6. 222 ÷ 3 = What knowledge, skills and concepts would children need in order to be able to do this calculation? Show the person next to you how you currently teach your Year 5 children to carry out this calculation.

7. Methods Chunking Number line Short division

8. What is the difference between three hundred and ninety-five and five hundred and one? -Taken from mental maths paper (15secs) What knowledge, skills and concepts would children need in order to be able to do this calculation? Show the person next to you how you would teach Year 5 children to carry out this calculation.

9. Methods

10. The use of the number line How do we develop children’s mental calculation skills using a number line?

11. Prerequisites for using an empty number line Position a number on a number line Jump to a number from zero Add /subtract a multiple of 10 to/from any 2 digit number (without crossing 100) Recall addition and subtraction facts for all numbers to at least 10 Use this knowledge to add / subtract a single digit number to or from a two-digit number, without crossing the tens boundary Bridge through 10 Use this strategy to add / subtract a single digit number to or from a two-digit number, crossing the tens boundary) Know the complement to the next multiple of 10 for any two-digit number Use knowledge of place value to add a single digit number to a multiple of 10

12. When might you use number lines?

13. Resources Bead strings Counting sticks Printed number lines and tracks ICT – Excel counting stickExcel counting stick

14. Session 2 To consider key characteristics of good mathematics teaching To identify teaching approaches, including the use of ICT, that support the development of reasoning To identify teaching approaches that support the development of mathematical language

15. What makes a good maths teacher? A good subject knowledge An understanding of progression in the curriculum being taught Recognition that some teaching approaches are better suited to promote particular learning and outcomes Enthusiasm!

16. In summary, mathematics teaching should: provide children with a balance of exploration, acquisition, consolidation and application ensure that children experience the excitement of learning mathematics direct and steer children to explore, identify and use rules, patterns and properties and model this process build in frequent short and sharp periods of practice and consolidation engage with children’s thinking, giving sufficient time for dialogue and discussion and space to think demonstrate the correct use of mathematical vocabulary, language and symbols, images, diagrams and models as tools to support and extend thinking give well-directed opportunities for children to use and apply their learning teach children how to evaluate solutions and analyse methods and understand why some methods are more efficient than others pause and take stock to review children’s learning with them model with children how they identify their learning skills, and manage and review their own learning.

17. Teaching Styles Direct – teaching tables (number dials, IWB Number dials, counting stick, hundred square)number dialsIWB Number dials hundred square Instructive – Using compensation Inductive – Multiplication excel grid Multiplication excel grid Applicable – Flexible line graph Flexible line graph Exploratory – Ball of Wool Reflective - Fractions (Planning Cycle )

18. Models and Images Models and Images charts

19. Year 5 Mental Calculation Session 3 Review and Planning

20. Buckinghamshire School Improvement Service How to plan a block. (In 3 easy steps!)

21. A Suggested Planning Process Summary 1.Read/Check Prior Learning 2.Read and organise the Objectives 3.Plan first 3 days of work using available resources

22. The teaching Sequence When planning a UNIT of 2 or 3 weeks of work, the structure of the teaching sequence requires thought to ensure that children get the opportunity to consolidate, secure and extend their learning through practice and application of their learning.

23. The Teaching and Learning Cycle Review – Teach – Practise – Apply – Review The cycle constitutes four teaching and learning foci: Focus A: Review prior learning and introduce new learning Focus B: Practise and Consolidate learning Focus C: Apply, secure and extend learning Focus D: Review and evaluate progress in learning

24. Examples of teaching sequences over a Unit (10 lessons) Focus A Review prior learning/ introduce new learning (2 lessons ) Focus B Practise and Consolidate (2 Lessons) Focus C Apply, secure and extend learning (3 Lessons) Focus D Review and evaluate progress in learning (1 Lesson) Foci B, C (1 Lesson) Focus D Review and evaluate progress in learning (1 Lesson) Focus A Review prior learning/ introduce new learning (1 lesson ) Focus B Practise and Consolidate (2 Lessons) Focus C Apply, secure and extend learning (4 Lessons) Focus B Practise and Consolidate (1 Lesson) Focus C Apply, secure and extend learning (1 Lesson) Focus D Review and evaluate progress in learning (1 Lesson) or

25. Modelling the Planning Process Year 5, Block D, Unit 1

26. Step one - Prior Learning Mathematics Planning Year 5 Block D Prior Learning

27. Step one - Prior Learning Year 5 Block D - Calculating, measuring and understanding shape Building on previous learning Check that children can already: talk about their methods and solutions to one- and two-step problems partition, round and order four-digit whole numbers and decimals to two places, and use decimal notation to record measurements, e.g. 1.3m or 0.6kg multiply and divide numbers to 1000 by 10 and 100 (whole-number answers) use written methods to add and subtract two- and three-digit whole numbers and.p, and to multiply and divide two-digit numbers by a one-digit number, including division with remainders, e.g. 15 9, 98 6 know that addition is the inverse of subtraction and that multiplication is the inverse of division, and vice versa use a calculator to carry out one- and two-step calculations involving all four operations know that angles are measured in degrees and that one whole turn is 360 read scales to the nearest tenth of a unit measure and calculate perimeters of rectangles and find the area of shapes drawn on a square grid by counting squares read time to the nearest minute; use am, pm and 12-hour clock notation, and calculate time intervals from clocks and timetables

28. How might the use of the Prior learning prompts in a block be built into the teaching and learning cycle?

29. Step 2 Make sense of the objectives Learning Objectives for Unit 5D1: 1.Solve one-step and two-step problems 2.Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000 3.Use a calculator to solve problems, (including decimals or fractions), interpret display 4.Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides 5.Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g) 6.Interpret a reading that lies between two unnumbered divisions on a scale 7.Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle’s area 8.Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals

30. Step 2 - Making sense of the objectives- Beginning to group the objectives Mental Skills:  Use understanding of place value to multiply/divide whole numbers and decimals by 10,100,1000  Interpret a reading that lies between two unnumbered divisions on a scale  Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals Length:  Read, choose, use and record standard metric units to estimate and measure length, convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g)  Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle’s area  Solve one-step and two-step problems  Use a calculator to solve problems, (including decimals or fractions), interpret display Coordinates:  Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides Time:  Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals  Solve one-step and two-step problems Outcome: Solve one-step and two-step problems (Mixed)

31. Step 3 Plan the 10 lessons in outline You don’t have to teach the objectives in any set order Have you previously taught lessons on these topics which have gone well in terms of children’s learning? (including Unit plans). You could incorporate and adapt these Keep in mind the appropriate teaching focus – Review / Teach / Practise / Apply Whole class work on reviewing prior learning must be limited to the items you know the majority of children still have difficulty with. Small amounts of prior learning should be dealt with at the beginning of the relevant lesson and specific individual or group needs through differentiation Make sure you include opportunities for:- – the children to use ICT – assessment – AT1 – links to other subjects

32. A Suggested Planning Process Summary 1.Read/Check Prior Learning 2.Read and organise the Objectives 3.Plan first 3 days of work using available resources

33. Questioning for assessment Questions can be used to assess: Children’s knowledge Children’s use of mathematical language Children’s use of models Children’s methods and strategies Children’s reasoning Children’s understanding

34. AFL questions in the learning objective section

35. Key Messages The learning objectives in the Primary Framework set out the essential learning steps for children to make effective progress in mathematics Looking at the objectives across two year groups highlights the ‘bigger picture’ for the year group and helps to identify the prior learning at the start of the year The learning overviews for the year and for a Unit provide more detail to inform long-term and short-term planning Building on prior learning requires some flexibility in planning; planning assessment questions helps to monitor children’s learning over a Unit

36. Year 1, 3 and 5 School-based activity Session 4 Review and Progression

37. Aims of the session To explain how teachers’ CPD and Head teachers’ CPD fit together To provide guidance on the CPD models To identify the contribution the school-based activity makes to school improvement To provide guidance on the school-based activity To discuss how outcomes of school-based activity will be fed into Day 2

38. Structure of the session Context of the Teachers’ and Head teachers’ CPD Supporting the activity back in school 1.Discussion with the head and school subject leader about how Day 1 will be fed back to all staff 2.Preparing for the collaborative tasks 3.Preparing for the diagnostic tasks Feedback into Day 2

39. 1.Discussion with the head and school subject leader about how Day 1 will be fed back to all staff Methods of calculation Exploring prerequisite skills Teaching styles Using the renewed framework to support planning (teachers knowledge of progression through the prior learning) How will you move forward with these areas?

40. 2. Preparing for the collaborative tasks In groups decide: which of the three models would be most beneficial to your own professional development the focus that the collaborative work will take how the collaborative work will be organised and who will be involved the actions that need to take to ensure that it can take place successfully for them.

41. 3. Preparing for the diagnostic tasks In your own class, Identify 3 children (1L/A, 1 M/A & 1 H/A) Ask the children to complete the questions on handout 4.1 Talk with the children (1:1) about barriers, challenges, next steps. Develop a teaching activity to help move the children on and consider the teaching style which would be most appropriate.

42. Feedback expectations Prepare a short presentation on the outcomes of the follow up work you have carried out in school. Structure 1.How did you feedback from day 1 to the SMT/whole school? Impact? 2.What models of CPD did the school use to support staff? Impact? 3.Briefly explain the outcomes of the diagnostic maths task carried out on 3 children in you class. Impact?

43. Dates Day 2 – Jan 9 th 2008