1. Year 3 Number Concepts and Guided Writing April 2008

2. 2 Objectives To build subject knowledge To help understand progression within and beyond Year 3 To broaden the repertoire of teaching approaches To develop understanding of the interrelationship between the elements in the cycle of reviewing, planning, teaching and assessing.

3. 3 Outline of the day 09:00 Refreshments on arrival 09:15 Number Concepts 10:30 Refreshments 10:45 Number Concepts continued 12:30 Lunch 13:15 Guided Writing 14:30 Refreshments 15:15 School based activities 15:45 Close

4. 4 Number Concepts Outline Session 1 - Establishing end-of-year expectations Session 2 - Review and progression Session 3 - Broadening the teaching and learning experience Session 4 - School-based activity

5. 5 School-based activity Plan and teach Block E summer term and Block A autumn term. Include elements covered in this CPD. Prepare a short presentation for day 2 to feedback on your planning process, teaching and learning. How did the blocks differ? Feedback to HT and Maths Subject Leader key points of the CPD.

6. Year 3 Number Concepts Session 1 Establishing end-of-year expectations

7. 7 ‘Numeracy is a proficiency which involves confidence and competence with numbers and measures. It requires an understanding of the number system, a repertoire of computational skills and an inclination to solve problems in a variety of contexts.’ Framework for teaching mathematics, 1999

8. 8 Planning cycle Review (AfL) Prior learning to establish pitch of the work and any children who may need additional support or challenge Plan What and how to teach the children the mathematics so they build on their prior learning Teach / Apply Use fit-for- purpose approach which gives children time to think, practise, apply their learning Assess & review Assess progress with focus on particular children, engage children in review of learning and next steps

9. 9 Number concepts within other strands Knowing and using number facts – they use doubles that they know to find other doubles or near doubles Calculating – children develop strategies for dealing with special cases e.g. finding 57 – 30, how numbers remain constant, using a number line to indicate steps, work out approximations by rounding numbers Measuring – children read scales and measure to the nearest division, they know the relationship between units, they read time to the nearest 5 minutes Understanding shape – children draw an angle and estimate its size in relation to a right angle e.g. about 1/3 of a right angle Handling data – they organise data using frequency tables, they understand how to interpret their tables and charts

10. 10 Year 3 Counting and understanding number Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to zero in single-digit steps or multiples of 10 Partition three-digit numbers into multiples of 100, 10 and 1 in different ways Round two-digit or three-digit numbers to the nearest 10 or 100 and give estimates for their sums and differences Read and write proper fractions interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents

11. Block A Counting, partitioning and calculating Block B Securing number Facts, understanding shape Block C Handling data and measures Block D Calculating, measuring and understanding shape Block E Securing number facts, calculation and relationships Using and applying mathematics Counting and understanding number Calculating Using and applying mathematics Knowing and using number facts Understanding shape Using and applying mathematics Measuring Handling data Using and applying mathematics Calculating Measuring Counting and understanding number Knowing and using number facts Calculating Understanding shape

12. Block C Unit 3 Block D Unit 3 Block E Unit 3 Block A Unit 3 Block A Unit 2 Block A Unit 1 Block A Counting, partitioning and calculating Block B Unit 3 Block C Unit 2 Block B Unit 2 Block B Unit 1 Block B Securing number Facts, understanding shape Block E Unit 2 Block E Unit 1 Block E Securing number Facts, calculation And relationships Block D Unit 2 Block D Unit 1 Block D Calculating, Measuring and Understanding shape Block C Unit 1 Block C Handling data and measures

13. 13 Draw an empty number line and mark the numbers 456, 465 and 546 on it. Explain to someone how you did it.

14. 14 Discussion How did you approach and carry out the task? What decisions did you have to make when drawing and labelling the number line? Did the number line you drew start at zero? Did it need to? What knowledge, skills and understanding did you need?

15. 15 500 456 465 546

16. Year 3 Number Concepts Session 2 Review and progression

17. 17 Progression from Year 2 to Year 3 Use the tracking poster to compare the objectives under the Counting and Understanding number strand in Year 2 and Year 3. What are the main differences? What knowledge, skills and understanding would we expect children to have at the start of Year 3?

18. 18 Counting and understanding number strand Year 2 – Year 3: Partitioning - two-digit numbers in Year 2 and three-digit in Year 3; Ordering - order two digit numbers in Year 2 and numbers up to 1000 in Year 3; Rounding - round two-digit numbers to the nearest 10 in Year 2 and 2/3 digit numbers to nearest 10/100 in Year 3; Fractions - Year 2 has a focus on one half, one quarter and three quarters. This is extended in Year 3 to include a greater understanding of the denominator and numerator and by a focus on comparing fractions and establishes equivalents; Inequality – use of the greater than and less than signs is part of a Year 2 objective. It will therefore be important that understanding of these signs continues to develop into Year 3.

19. 19 0-9 digit cards Make five odd numbers using each card once - 1 three-digit number - 3 two-digit numbers - 1 one-digit number One person from each pair needs to explain how to put the numbers in order from smallest to largest. These instructions should be followed exactly. As a pair now work together to refine the original instructions ensuring the language used is a precise as possible. Finally join another pair and take it in turns to try out your instructions on each other..

20. 20 Discussion How did it help to talk informally in pairs first? How did your original instructions need refining? Did your use of language change as you refined your instructions? If you didn’t have access to mathematical language how would creating the instructions have been harder? Would the task have been harder if you couldn’t see each other e.g. if you were giving instructions over the phone? How would you need to refine your instructions if you were asked to order even numbers?

21. 21 Equality, inequality and equivalence Use language such as ‘more’ or ‘less’ to compare two numbers (Foundation Stage) Compare and order numbers, using the related vocabulary; use the equals (=) sign (Year 1) Order two-digit numbers and position them on a number line; use the greater than (>) and less than (<) signs (Year 2) Use diagrams to compare fractions and establish equivalents. (Year 3)

22. 22 Key experiences for children A clear understanding of the concepts of equality and inequality The ability to read and write proper fractions Recognising and representing fractions of a variety of shapes Knowing how to use diagrams to compare fractions and appreciate their relative size Gaining appreciation that fractions can be numbers that label a position on a number line

23. 23 Equality What is equality? What is equality in mathematics? When might children encounter the mathematical concept of equality in everyday life?

24. 24 Fractions of shapes

25. 25 Comparing fractions Convince me that 1/2 is smaller than 3/5 but larger than 3/10. Record two ways of convincing me that 1/2 is smaller than 3/5 but larger than 3/10

26. 26 Fractions and number lines

27. 27 Year 6 Karen makes a fraction using two number cards. She says, 'My fraction is equivalent to ½. One of the number cards is 6' What could Karen's fraction be? Give both possible answers. What do the fractions 6/9,14/21 and 18/27 have in common?

28. Year 3 Number Concepts Session 3 Broadening the teaching and learning experience

29. 29 Good mathematics teaching Carefully planned blend of approaches Children are challenged to think They like to be challenged and enjoy the opportunities to practice and apply their learning They are happy to share their ideas and to explain their reasoning and methods Broad repertoire of teaching and organisational approaches

30. 30 Good mathematics teaching ‘The teaching sequence incorporates practical, visual and ICT resources that children can use to test and confirm their learning. Children have access to these resources and understand how to use them. There are models and images demonstrated and displayed to support methods, promote thinking and develop strategies and these are used to build links between areas of mathematics.’

31. 31 Models and images Place value cards Place value ITP Partly numbered lines Bundles of straws Money Beadsticks ITP

32. 32 ICT models and images

33. 33 Teaching approaches ‘Children use partitioning to add or subtract mentally one- and two-digit numbers. For example, they calculate 37+26 by using 37+20+6 and 37-26 by working out 37-20-6, recording the steps on a number line.’