Addition, Subtraction and Place Value Workshop

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.

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?

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

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

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

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

Place Value Understanding misconceptions

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)

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.

Using Place Value Houses 98 + 5

Place Value Misconceptions 30 + 60 = 90 3 tens + sixty = ???? Why might a child not know this?

Bernie says that 0.657 is bigger than 0.7 Misconceptions with Decimal Place Value: How 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 May take out if not enough time as already covered this earlier.

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. 43 + thirty) “how many more / less ”, e.g. 35+?=40, 30+?=70 Exchanging/bundling tens and ones, e.g. 87 + 5, Rolling Dice game

Place Value Keyboards

Addition and Subtraction Strategy Framework

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

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

The big picture – what do the stages mean?

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

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

Some examples of strategy lessons

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?

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?

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

Story Problems 5 + = 8 Start Unknown Change Unknown Result Unknown

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

14 - 6 = 14 - 4 = 10 10 - 2 = 8

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

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

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

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. 53 - 29

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

Stage 6 AA Advanced Additive Part-Whole Book 5, p…… Is this the most efficient way of solving 53 - 29? Stage 6 AA Advanced Additive Part-Whole Book 5, p…… What are the big ideas at this stage?

Pyramids

53 - 26 Compensation with tidy numbers 53 - 30 + 4 Place Value Partitioning 53 - 20 - 6 53 - 26 Equal Additions (subtraction only) 57 - 30 Reversibility 26 + ? = 53 Standard Written Form (decomposition)

Using Number Properties Using Imaging New Knowledge & Strategies Existing Knowledge & Strategies Using Materials Compensation with tidy numbers Place Value Partitioning Equal Additions Reversibility 53 - 26

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

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

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

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

Which Strategy? 385 - 99 478 - 56 1002 - 987

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

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

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

Mental or Working Form? (MM5-13)

Jigsaw

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

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

Long Term Planning Units

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

Creating Number Sentences

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

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

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