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. Since our last meeting share...
something you have tried.
something you are still not sure of

4. Place Value Effective Pedagogy-Understanding misconceptions

5. Place Value Misconceptions
Donald is in Year 1. He can count up to 20 but what do you think he might say after 29?
Why has he done that? What might you do?
Stage 2 /3 pages……..
Students need experiences initially making groups of ten by bundling and unbundling ten ones for one ten.

6. 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.

7. Place Value Houses & Play Money

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

9. Read, say, do - Peter Hughes
Say the numeral one
way, e.g. 63 is sixty three
Say the numeral in the
other way, e.g. 63 is 6 tens
and three ones
Read 63 as “sixty three” and
Sixty three as “sixty three”
Model the PV form of the
numeral e.g. 63
is 6 tens and 3 ones
Model the numeral
as ones
e.g. as 63 ones

10. 7 ones and 5 ones equals 12 ones. trade 10 ones for 1 ten, to make
Children need to understand…
7 ones and 5 ones equals 12 ones.
trade 10 ones for 1 ten, to make
1 ten and 2 ones.
They need to make connections between
Read/Write the number
Say the number in two ways
Make the number in two ways

11. 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

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

13. The Strategy Teaching Model
Using Number Properties
Using Imaging
Using Materials
New Knowledge & Strategies
Existing Knowledge & Strategies

14. Using Materials and Imaging
Hands Tens frames
Abacus Place Value Material 12 23 10

15. Stage 4 AC Advanced Counting
Aim: Solve problems by counting on or back in
ones and tens
Find this in Book 5
Start of Lesson
Required Knowledge Check
Diagnostic Snapshot
Why is this important?

16. 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?

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

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

19. =
= 10
= 8

20. 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

21. Practice Questions on board or in Modelling Book
Resource Book/worksheets e.g.Figure it Out
Games: Create or play specific to the strategy.
Process: Diary writing / Thinkboard
Story Problems: Write to match a number sentence, check, swap and solve story problems.
Relevant knowledge practice to support the strategy being developed
How could written recording reflect
this thinking?

22. Long Term Planning Units

23. What Now?
Find out what misconceptions the children have about place value
Focus on using materials, imaging and number properties
Begin planning for the introduction of strategy teaching for the stage the children are at
Groups of four and talking partners

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