Addition, Subtraction and Place Value Workshop

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Addition, Subtraction and Place Value Workshop
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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.

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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?

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Number Boggle Bk4 p.33
13 6 7 1
11 2 5 12
9 4 3 15
12 8 16 11
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Number Boggle Bk4 p.33
13 6 7 1
11 2 5 12
9 4 3 15
12 8 16 11
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Since our last workshop reflect on...

• your class numeracy assessment data
• something you have tried.
• something you are still not sure of.

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

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Place ValueUnderstanding misconceptions
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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.
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Sarah can orally count up to 199 without any
trouble but when writing down the numbers
following 98, Sarah writes 99, 100, 1001,1002,

Place Value Misconceptions
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.
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Using Place Value Houses
98 5
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Place Value Misconceptions
30 60 90 3 tens sixty ???? Why might
a child not know this?
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Misconceptions with Decimal Place ValueHow do
these children view decimals?

• Bernie says that 0.657 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

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Develop Place Value UnderstandingUsing 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. 43 thirty)
• how many more / less , e.g. 35?40, 30?70
• Exchanging/bundling tens and ones,
  e.g. 87 5, Rolling Dice game

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Place Value Keyboards
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Addition and Subtraction Strategy Framework
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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
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Effective teachers understand the big ideas. So
- what do the stages mean? Choose one stage to
explore.
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The big picture what do the stages mean?
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Developing Strategy using the teaching model
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Using Materials and Imagining
Hands Tens frames Abacus Place Value
Material Number Lines
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• Some examples of strategy lessons

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Stage 2-3, CA, Counting From OneBook 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?
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Stage 4, AC, Advanced CountingBook 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?
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8 3
The Number Strip, p.19
1 2 3 4 5 6 7 8 9 10 11
How could you extend this to imaging and then
using number properties?
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Story Problems

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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

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14 - 6
14 - 4 10
10 - 2 8










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Discuss How would you move to imaging ?
Now view the DVD and see how the teacher
progresses to imaging
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• 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
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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

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How would you move to number properties?
53 - 9
How would you extend into double digits, e.g. 53
- 29
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53 - 29 using Place Value Partitioning
53 - 20 33
33 - 3 30
30 - 6 24
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Stage 6 AA Advanced Additive Part-Whole
Book 5, p
Is this the most efficient way of solving 53 - 29?
What are the big ideas at this stage?
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Pyramids
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Compensation with tidy numbers 53 - 30 4
Place Value Partitioning 53 - 20 - 6
Equal Additions (subtraction only) 57 - 30
Reversibility 26 ? 53
Standard Written Form (decomposition)
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• Compensation with tidy numbers
• Place Value Partitioning
• Equal Additions
• Reversibility

53 - 26
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53 - 26 Which strategy is being recorded?
Tidy Numbers
Place Value Partitioning
-3
-3
-20
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53
33
30
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53 - 26 Which strategy is being recorded?
Reversibility
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Equal Additions
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53
26
30
4
4
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Compensation with tidy numbers
Place Value Partitioning
Equal Additions (subtraction only)
Reversibility
Standard Written Form (decomposition)
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So, which strategy is best?
It depends on what the question is!
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Which Strategy?
385 - 99
478 - 56
1002 - 987
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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
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Discuss
Why bother teaching mental strategies, Why cant
I just learn the written form Its faster?

• Its 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

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The Written Form
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Mental or Working Form? (MM5-13)
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Jigsaw
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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
• Whos got it? Who hasnt? Set practice.
• Consider next steps

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(No Transcript)
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Have a Go!
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

1. Long Term Planning Unit
2. Book 5 Lesson.
3. Related Practice

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Long Term Planning Units
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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

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Creating Number Sentences
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(No Transcript)
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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

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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.

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