Transcript 2011 add sub - mathsleadteachers

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
• What now?
– Getting into Book 5
» Exploring Independent Practice
Ideas
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 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?
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 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
2
3
4
1-1
CA
CA
AC
One-to-One Counting
Counting From One on Materials
Counting From One by Imaging
Advanced Counting
•
•
•
•
5
6
7
8
EA
AA
AM
AP
Early Additive Part-whole
Advanced Additive Part-whole
Advanced Multiplicative Part-whole
Advanced Proportional Part-whole
Level 1
Level
Level
Level
Level
2
3
4
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?
Existing
Knowledge &
Strategies
Developing
Strategy
using the
teaching
model
Using
Materials
Using Imaging
Using Number
Properties
New Knowledge
& Strategies
Using Materials and Imagining
Hands
Tens frames
Abacus
Place Value Material
10
10
23
+ 50
Number Lines
37
12
+3
87
90
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
8 + 3 = 11
5
6
7
8
9 10 11
9, 10, 11
How could you extend this to imaging and then using
number properties?
Story Problems
5
+
Start Unknown
Change Unknown
= 8
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
Existing
Knowledge &
Strategies
Discuss: How
would you move
to imaging ?
Using
Materials
Using Imaging
Now view the
DVD and see
how the teacher
progresses to
imaging
Using Number
Properties
New Knowledge
& Strategies
•
Discuss what you have just seen.
•
How do modelling books and thinking groups
benefit both the teacher and the students?
Teacher
Modelling
Book
Thinking
Groups
Students
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?
53 - 9
How would you
extend into
double digits,
e.g. 53 - 29
Existing
Knowledge &
Strategies
Using
Materials
Using Imaging
Using Number
Properties
New Knowledge
& Strategies
53 - 29 using Place Value Partitioning
53 - 20 = 33
33 - 3 = 30
30 - 6 = 24
-20
-3
-6
24
30
33
53
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
Place Value Partitioning
53 - 20 - 6
53 - 30 + 4
53 - 26
Equal Additions
(subtraction only)
57 - 30
Reversibility
26 + ? = 53
Standard
Written Form
(decomposition)
• Compensation with
tidy numbers
• Place Value
Partitioning
• Equal Additions
• Reversibility
Existing
Knowledge &
Strategies
Using
Materials
Using Imaging
Using Number
Properties
53 - 26
New Knowledge
& Strategies
53 - 26
Which strategy is being recorded?
Tidy Numbers
-30
+4
23
27
53
Place Value Partitioning
-3
27
-3
30
-20
33
53
53 - 26
Which strategy is being recorded?
Reversibility
+23
+4
26
30
27
Equal Additions
26
30
+4
53
53
57
+4
Compensation with tidy
numbers
Place Value Partitioning
83 - 59
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
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
I work out
the answer
Yes
Can I work out the
answer mentally?
No
pencil
I work out
the answer
calculator
Will I use pencil
and paper or a
calculator?
I mentally
estimate the
answer as a check
I work out
the answer
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)
Ellie
Julia
Emma
Jude
Justin
Stage 2-3 CA
Crossing the Five
Barrier
Level 2 (Yr 3-4)
Amanda
Cameron
Nicole
Jacinda
Stage 5 EA
Up Over the Tens
Adding in Parts
Stage 4 AC
Adding Tens
1. Long Term Planning Unit
2. Book 5 Lesson.
3. Related Practice
Level 3/4 (Yr5-8)
Nikki
Marg
Alison
Jessica
Stage 6 AA
Using Tidy Numbers
Problems Like 73-19
When One number is near 100
Equal Additions
Stage 7 AM
Introducing Decimal Fraction
Place Value p.46
Long Term Planning Units
Independent Practice Ideas
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
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. Existing
Knowledge &
Strategies
• understand the teaching model
• understand misconceptions
with place value.
Using
Materials
Using Imaging
Using Number
Properties
New
Knowledge &
Strategies
• explore equipment and activities used
to teach addition & subtraction strategies
including Book 5 and long term planning
sheets.
Thought for the day
“And, if it all just seems
too much…..
STRESSED
backwards spells
DESSERTS!