Addition, Subtraction and Place Value Workshop. Purpose of this session is to.. have a clearer...

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

Number Boggle Bk4 p.33

13 6 7 1

11 2 5 12

9 4 3 15

12 8 16 11

9 - 2 = 7 5 + 3 + 8 = 16

Number Boggle Bk4 p.33

13 6 7 1

11 2 5 12

9 4 3 15

12 8 16 11

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

Place Value MisconceptionsDonald 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)

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 unitsmust 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?

Misconceptions with Decimal Place Value:

How do these children view decimals?

1. Bernie says that 0.657 is bigger than 0.7

2. Sam thinks that 0.27 is bigger than 0.395

3. James thinks that 0 is bigger than 0.5

4. Adey thinks that 0.2 is bigger than 0.4

5. Claire thinks that 10 x 4.5 is 4.50

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

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 2Level 3Level 4Level 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

Using Materials and Imagining

Hands Tens frames

Abacus Place Value Material

Number Lines

37 87 90

+ 50+ 3

1010

1223

Some examples of strategy lessons

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?

Stage 4, AC, Advanced CountingBook 5: page…


Start of Lesson• Required Knowledge Check• Diagnostic Snapshot

Why is this important?

8 + 3

1 2 3 4 5 6 7 8 9 10 11

8 + 3 = 11 9, 10, 11

The Number Strip, p.19

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……


Subtraction in Parts, p.27Start of Lesson • Required Knowledge Check• Diagnostic Snapshot

14 - 6 = 14 - 4 = 1010 - 2 = 8

Discuss: How would you move to imaging ?

Using Number Properties

Using Imaging



Strategies

Using Materials

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

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 Imaging



Strategies

Using Materials

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

533324 30

-20-3

-6

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

Compensation with tidy numbers

53 - 30 + 4

Place Value Partitioning

53 - 20 - 6

Equal Additions(subtraction only)

57 - 30

Reversibility26 + ? = 53

Standard Written Form

(decomposition)

53 - 26


Using Imaging



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 5327

-30

+4


27 5333

-20-3-3

30

Reversibility

Equal Additions

26 5753

+4+4

30

27

26 5330

+23

+4

53 - 26 Which strategy is being recorded?

Compensation with tidy numbers


Equal Additions(subtraction only)

Reversibility

Standard Written Form

(decomposition)

83 - 59

So, which strategy is best?

It depends on what the question is!

Which Strategy?

385 - 99

478 - 56

1002 - 987

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 formIt’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

I mentally estimate the

answer as a check

Will I use pencil and paper or a

calculator?

I work out the answer


calculatorpencil

No

Can I work out the answer mentally?


Yes

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!Level 1 (Yr 1-2) Level 2 (Yr 3-4) Level 3/4 (Yr5-8)

Ellie JudeJulia JustinEmma

Amanda Nicole Cameron Jacinda

Nikki Alison Marg Jessica

Stage 2-3 CACrossing the Five Barrier

Stage 5 EAUp Over the Tens

Adding in Parts

Stage 6 AAUsing Tidy Numbers Problems Like 73-19When One number is near 100Equal Additions

Stage 4 ACAdding Tens

Stage 7 AMIntroducing Decimal Fraction Place Value p.46

1. Long Term Planning Unit2. Book 5 Lesson. 3. Related Practice

Long Term Planning Units

1. 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

Independent Practice Ideas

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 Imaging

New Knowledge &

Strategies


Strategies

Using Materials

Thought for the day

“And, if it all just seems too much…..

STRESSEDbackwards spells

DESSERTS!

Addition, Subtraction and Place Value Workshop. Purpose of this session is to.. have a clearer...

Documents

Transcript of Addition, Subtraction and Place Value Workshop. Purpose of this session is to.. have a clearer...