1. Addition, Subtraction and Place Value Workshop

2. Purpose of this session is to..
have a clearer understanding of the strategy stages for addition and subtraction.
understand the teaching model used for teaching strategy.
understand misconceptions with place value.
explore equipment and activities used to teach addition & subtraction strategies including Book 5 and long term planning sheets.

3. Overview 9.15 – 2.45
Place Value
Framework Revision and links to Curriculum
Example Strategy Lessons Stage 2-5
MORNING TEA
Developing Stage 6 strategies
Split into focus groups for a modelled session.
LUNCH
Group Activity – Getting into Book 5
Exploring Independent Practice Ideas
What now?

4. Number Boggle Bk4 p.33
9 - 2 = 7 13 6 7 1 11 2 5 12 9 4 3 15 8 16
= 16

5. Number Boggle Bk4 p.33 13 6 7 1 11 2 5 12 9 4 3 15 8 16

6. Since our last workshop reflect on...
your class numeracy assessment data
something you have tried.
something you are still not sure of.

7. NZ Curriculum and Number Framework
What to teach
Effective Pedagogy
How you teach it
How you respond to students and their misconceptions

8. Place Value Understanding misconceptions

9. View DVD Clip (Gordonton School)
Place Value Misconceptions
Donald is in Year 1. He can count up to 29 but then gets stuck. What do you think he might say after 29?
Why has he done that? What might you do?
Stage 2 /3 pages 11-12, 17
Students need experiences initially making groups of ten by bundling and unbundling ten ones for one ten.
View DVD Clip (Gordonton School)

10. Place Value Misconceptions
Sarah can orally count up to 199 without any trouble but when writing down the numbers following 98, Sarah writes 99, 100, 1001,1002,
Why has she done that? What might you do?
The fundamental place value issue is that ten units
must be changed for one new unit.
The zero place holder idea is significant
but not the main problem.

11. Using Place Value Houses

12. Place Value Misconceptions
= 90
3 tens + sixty = ????
Why might a child not know this?

13. Bernie says that 0.657 is bigger than 0.7
Misconceptions with Decimal Place Value: How do these children view decimals?
Bernie says that is bigger than 0.7
Sam thinks that 0.27 is bigger than 0.395
James thinks that 0 is bigger than 0.5
Adey thinks that 0.2 is bigger than 0.4
Claire thinks that 10 x 4.5 is 4.50
May take out if not enough time as already covered this earlier.

14. Develop Place Value Understanding Using cards: make the biggest number you can
Write (numbers and words)
Make (place value equipment)
Say (two ways, 1, 10,100, …before and after)
Round (to nearest 10, 100, 1…)
Order
Dictation (numbers and words)
Match (word, number, expanded numerals/words)
Add/subtract:
Mix (symbols and words, e.g thirty)
“how many more / less ”, e.g. 35+?=40, 30+?=70
Exchanging/bundling tens and ones, e.g , Rolling Dice game

15. Place Value Keyboards

16. Addition and Subtraction Strategy Framework

17. Strategy Framework Revision
1 1-1 One-to-One Counting
2 CA Counting From One on Materials
3 CA Counting From One by Imaging
4 AC Advanced Counting
5 EA Early Additive Part-whole
6 AA Advanced Additive Part-whole
7 AM Advanced Multiplicative Part-whole
8 AP Advanced Proportional Part-whole
Level 1
Level 2
Level 3
Level 4
Level 5

18. “Effective teachers understand the big ideas”.
So - what do the stages mean? Choose one stage to explore.

19. The big picture – what do the stages mean?

20. Developing Strategy using the teaching model
Using Number Properties
Using Imaging
New Knowledge & Strategies
Existing Knowledge & Strategies
Using Materials
Developing Strategy using the teaching model

21. Using Materials and Imagining
Hands Tens frames
Abacus Place Value Material
Number Lines 12 23 10 37 87 90
+ 50
+ 3

22. Some examples of strategy lessons

23. Stage 2-3, CA, Counting From One Book 5: page…
What is the big idea - what are we trying to develop at this stage?
Start of Lesson
Required Knowledge Check
Diagnostic Snapshot
Why is this important?

24. Stage 4, AC, Advanced Counting Book 5: page…
What is the big idea - what are we trying to develop at this stage?
Start of Lesson
Required Knowledge Check
Diagnostic Snapshot
Why is this important?

25. The Number Strip, p.19
8 + 3 1 2 3 4 5 6 7 8 9 10 11
8 + 3 = , 10, 11
How could you extend this to imaging and then using number properties?

26. Story Problems
= 8
Start Unknown
Change Unknown
Result Unknown

27. Stage 5 EA Early Additive Part-Whole Book 5, p……
What is the big idea - what are we trying to develop at this stage?
Subtraction in Parts, p.27
Start of Lesson
Required Knowledge Check
Diagnostic Snapshot

28. =
= 10
= 8

29. Discuss: How would you move to imaging ?
Using Number Properties
Using Imaging
New Knowledge & Strategies
Existing Knowledge & Strategies
Using Materials
Discuss: How would you move to imaging ?
Now view the DVD and see how the teacher progresses to imaging

30. Discuss what you have just seen.
How do modelling books and thinking groups benefit both the teacher and the students?
Teacher
Students
Modelling Book
Thinking Groups

31. you are teaching a programme, you are not teaching the kids.”
Using Thinking Groups
“If you teach without observing and reacting to the children,
you are teaching a programme, you are not teaching the kids.”
Peter Hughes, The University of Auckland

32. How would you move to number properties?
Using Number Properties
Using Imaging
New Knowledge & Strategies
Existing Knowledge & Strategies
Using Materials
How would you move to number properties?
53 - 9
How would you extend into double digits, e.g

33. 53 - 29 using Place Value Partitioning
= 33
= 30
= 24 53 33 24 30
-20 -3 -6

34. Stage 6 AA Advanced Additive Part-Whole Book 5, p……
Is this the most efficient way of solving ?
Stage 6 AA Advanced Additive Part-Whole Book 5, p……
What are the big ideas at this stage?

35. Pyramids

36. 53 - 26 Compensation with tidy numbers 53 - 30 + 4
Place Value Partitioning
Equal Additions
(subtraction only)
Reversibility
26 + ? = 53
Standard Written Form (decomposition)

37. Using Number Properties
Using Imaging
New Knowledge & Strategies
Existing Knowledge & Strategies
Using Materials
Compensation with tidy numbers
Place Value Partitioning
Equal Additions
Reversibility

38. 53 - 26 Which strategy is being recorded?
Tidy Numbers 23 53 27
-30 +4
Place Value Partitioning -3 -3
-20 27 30 33 53

39. 53 - 26 Which strategy is being recorded?
Reversibility 26 53 30
+23 +4 27
Equal Additions 26 53 57 30 +4 +4

40. 83 - 59 Compensation with tidy numbers Place Value Partitioning
Equal Additions
(subtraction only)
Reversibility
Standard Written Form (decomposition)

41. So, which strategy is best?
It depends on what the question is!

42. Which Strategy?

43. Advanced Multiplicative
Stage 7 AM
Advanced Multiplicative
An extension of the strategies and written form used in Stage 6 but working with decimal numbers, e.g. 4.3 – 1.97

44. Discuss: Why bother teaching mental strategies,
Why can’t I just learn the written form
It’s faster?
It’s often quicker to work something out mentally
Merely following a procedure - rule following
Lack of real understanding - mistakes are often made or wrongly applied to problem solving
Mental ability needed to estimate and check answers

45. The Written Form Can I work out the answer mentally?
Yes
I mentally estimate the answer as a check
Will I use pencil and paper or a calculator?
I work out the answer
calculator
pencil No

46. Mental or Working Form? (MM5-13)

47. Jigsaw

48. A Strategy Teaching Session
Start of Lesson (to build on students’ thinking)
Required knowledge check
Diagnostic Snapshot (Can they already do it?)
Teaching (eliciting, supporting and extending thinking)
- Teaching Model (materials, imaging, number properties)
Consider thinking groups & modelling book.
End of Lesson (assessment for learning)
Feedback:
Who’s got it? Who hasn’t? Set practice.
Consider next steps

50. Have a Go! Long Term Planning Unit Book 5 Lesson. Related Practice
Level 1 (Yr 1-2)
Level 2 (Yr 3-4)
Level 3/4 (Yr5-8)
Ellie Jude
Julia Justin
Emma
Amanda Nicole
Cameron Jacinda
Nikki Alison
Marg Jessica
Stage 2-3 CA
Crossing the Five Barrier
Stage 5 EA
Up Over the Tens
Adding in Parts
Stage 6 AA
Using Tidy Numbers
Problems Like 73-19
When One number is near 100
Equal Additions
Stage 4 AC
Adding Tens
Stage 7 AM
Introducing Decimal Fraction Place Value p.46
Long Term Planning Unit
Book 5 Lesson.
Related Practice

51. Long Term Planning Units

52. Independent Practice Ideas
Similar Questions:
on board, modelling book, worksheets, computer
(Perhaps show thinking for 1 or 2 questions)
2. Textbooks: e.g. Figure It Out, Pearson, NCM
3. Games: Create or play specific to the strategy.
4. Process: Diary writing / Thinkboard
5. Word Story Problems: Write to match a number sentence, check, swap and solve
6. Relevant knowledge practice to support the strategy being developed

53. Creating Number Sentences

55. What Now? Group your children for teaching addition & subtraction
Teach 1 or 2 groups a day using Book 5 / Long Term Planning Units
Ask your lead teacher to organise a strategy session for you to observe.
Next workshop is on multiplication and division

56. Purpose of this session is to..
have a clearer understanding of the strategy stages for addition and subtraction.
understand the teaching model
understand misconceptions
with place value.
explore equipment and activities used
to teach addition & subtraction strategies
including Book 5 and long term planning
sheets.
Using Number Properties
Using Imaging
New Knowledge & Strategies
Existing Knowledge & Strategies
Using Materials

57. “And, if it all just seems too much…..
Thought for the day
“And, if it all just seems too much…..
STRESSED
backwards spells
DESSERTS!