1. Structuring numeracy lessons to engage all students: R – 4 Peter Sullivan

2. Overview We will work through three lessons I have taught this year as part of classroom modelling in years R – 4. The lessons are structured to maximise engagement of all students, especially those who experience difficulty and those who complete the work quickly. I will ask you to examine the commonalities and differences between the lessons and identify key teacher actions in supporting this lesson structure. I will ask you to reflect upon the implications for leading whole school Numeracy improvement.

3. Assumptions We do not want to tell the students what to do before they have had a chance to explore their own strategy We want to step back to allow ALL students to engage with the task for themselves We want them to see new ways of thinking about the mathematics There is no need to hurry We want them to know they can learn (as distinct from knowing they can be taught)

4. GROWING PATTERNS (Intended for Reception)

5. Copy the pattern and draw the group that would come next

6. From the Australian Curriculum The AC for Foundation year includes the following: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005) (ACMNA005)

7. For the students You can copy a pattern by looking at what is there. Sometimes the pattern is growing bigger.

8. As an introduction

9. Enabling prompt(s) for students experiencing difficulty Students who are having difficulty can look at the pattern again. For others, you might have the pattern on a sheet of paper and they can copy it onto their mini whiteboards.

10. Extending prompt(s) for those that finish quickly Students who finish can be asked to continue the pattern to the next group (and so on). Maybe some students can write the number of objects in each group.

11. Consolidating task Only looking for a short time, the students can copy and continue these patterns

12. Lesson 2 Finding a difference Years 1 - 2 finding difference

13. Basketball scores Parrots106 Galahs97 finding difference How much did the Parrots win by? (Work out the answer in two different ways)

14. Basketball scores Wombats26 Possums18 finding difference How much did the Wombats win by? (Work out the answer in two different ways)

15. Enabling prompt finding difference

16. Basketball scores Eels18 Carp13 finding difference How much did the Eels win by? (Work out the answer in two different ways)

17. Basketball scores Cats8 Dogs3 finding difference How much did the Cats win by? (Work out the answer in two different ways)

18. Extending prompt finding difference

19. Darts scores Parrots1005 Galahs988 finding difference How much did the Parrots win by? (Work out the answer in two different ways)

20. Football scores finding difference

21. Football scores Seagulls63 Kingfishers55 finding difference How much more did the Seagulls score? (Work out the answer in two different ways)

22. Football scores Seagulls72 Kingfishers55 finding difference How much more did the Seagulls score? (Work out the answer in two different ways)

23. Football scores Seagulls83 Kingfishers47 finding difference How much more did the Seagulls score? (Work out the answer in two different ways)

24. Lesson 3 Finding ways to add numbers in your head Years 3 - 4

25. FINDING WAYS TO ADD IN YOUR HEAD

26. Work out how to add 298+35 in your head. What advice would you give to someone on how to work out answers to questions like this in their head?

27. How might you run that class? How much would you tell the students? What approach do you recommend to doing this task? How much confusion can you cope with? When is challenge and uncertainty productive? What is meant by “cognitive activation”?

28. From the Australian Curriculum This lesson addresses the following descriptor from the AC for year 1: Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)counting onpartitioning(ACMNA015) The lesson addresses the following descriptor from AC for year 3 (year 4 is similar): Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)place value (ACMNA053) There is also potential for students to build Understanding of number relationships, to be more Fluent with the mental calculations, to find their own solution by Problem Solving, and to develop Reasoning by explaining their thinking.

29. For the students You can work out efficient strategies for adding numbers in your head for yourself. You can also explain your thinking to others.

30. Enabling prompt(s) for students experiencing difficulty Work out the answer to 28 + 7 in your head. Work out the answer to 98 + 7 in your head.

31. Extending prompt(s) for those that finish quickly Work out how to add 98 + 97 + 67 in your head.

32. Consolidating task The consolidating task is a set of similar questions on the attached worksheet.

33. Your answerShow how you did it 1. 195+68 1. 496+36 1. 195+47 1. 997+27

34. Shepp Neighbourhood Cluster new staff visit 2

42. What is your reaction to those lesson?

43. What might make it difficult to teach like that in your school?

44. In what ways were those lessons similar?

45. What actions might you take to encourage teachers to adopt such approaches, at least sometimes?