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Modelling Session
Choose one of the lessons you will see modelled to
think through:
(Stage 5-6) Fun with Fives, p38
(Stage 6-7)Cut and Paste, p49
NZ Curriculum and Number Framework
- Knowing what to teach based on assessment data
Effective Pedagogy
- Knowing how to teach it
- How you respond to students and their
misconceptions
- Notice, Understand, Respond
How does each person benefit?
Students
Modelling
Book
Thinking
Groups
Diagnostic
Snapshot at start
of lesson
Teacher
Sums and Products
Product
42
product
6
7
13
sum
15
3
5
8
sum
Let’s look at Stage 7 Division…
Tidy Numbers
Place Value
72 ÷ 4
Proportional Adjustment
Reversing
Division Strategies
Tidy numbers
(rounding)
Place Value Partitioning
(splitting)
72 ÷
4
Proportional Adjustment
(alter both or just one number)
Splitting Factors
Standard Written Form
(algorithm)
Division Strategies
Tidy numbers
(rounding)
Place Value Partitioning
(splitting)
80 ÷ 4 = 20
40 ÷ 4 = 10
20 – 2 = 18
32 ÷ 4 = 8
72 ÷
4
10 + 8 = 18
Proportional Adjustment
Splitting Factors
(Alter both or just one
72 ÷ 2 ÷2 = 18
number)
36 ÷ 2 = 18 or
(36 ÷ 4) x 2 or (72 ÷ 8) x
2
Standard Written Form
(algorithm)
Which strategy will you choose?
3680 ÷ 8 =
A sheep station has
eight paddocks and
3,680 sheep.
How many sheep are
there in each
paddock?
Division Strategies
Tidy numbers
(rounding)
Place Value Partitioning
(splitting)
3680 ÷
8
Proportional
Adjustment
Splitting Factors
Standard Written Forms
3, 680 ÷ 8
Proportional
Adjustment:
Reversibility
8 x ? = 3680
Place Value:
3200 ÷ 8 = 400
480 ÷ 8 = 60
3680 ÷ 8 =
1840 ÷ 4 =
920 ÷ 2 = 460
Tidy Numbers
Algorithm
4000 ÷ 8 = 500
500 - (320 ÷ 8)=
3680
500 - 40 = 460
Exploring Division Strategies
Tidy numbers
(rounding)
Place Value Partitioning
(splitting/written form)
Paper Power 63-67
Not in book
Splitting Factors
Little Bites (76-79)
Proportional Adjustment
Adjust the divisor only :
Proportional Packets 54-57
Adjust both numbers:
The Royal Cooking Lessons 57-60
Divisibility Rules
Nines and Threes (70-71)
Divisibility Rules Bk 8,33
13 x 16 (Cross Products)
= 100+60+30+18
= 208
13 x 16
10
6
100
60
30
18
10
3
13 x 16
10
6
10
100
60
3
30
18
The algorithm is essentially the
same as this place value method
16
x 13
18
30
60
100
208
16
x 13
48
160
208
Your Turn!
36 x 28 =
20
30
6
8
Your Turn!
36 x 28 = 1008
20
8
30
600
240
6
120
48
0.7 x 1.3
1
0.7
0.7
= 0.91
0.3
0.21
The Division Algorithm
Paper Power,
96 ÷ 4
p 63
20 + 4
24
(using partitioning first) 4 80 + 16
Moving to “chunking” calculations like 847 ÷ 3
Your Turn!
Use partitioning to solve 162 ÷ 6
Use a “chunking” method to solve 837 ÷ 4
4 91 6
Diagnostic Question
Stage 8 (AP) NZC Level 5
Choose efficiently from a range of
strategies including written form to solve
mult/div problems with fractions and
decimals
Stage
Strategy used to solve a
multiplication/division problem
2/3 CA
Counting all the objects, making groups
4
AC
Skip counting for 2, 5, 10
(equal sharing for division)
Skip counting sequences
Groups of 2’s up to 20
5
EA
Repeated addition / Commutative property
(using sharing and addition for division)
X2, x5, x10 mult’n and
division facts
6
AA
Deriving (by splitting/doubling/ rounding)
(reversing/inverse operations for division)
X3, x4, x6, x7, x8, x9
multiplication facts
7
AM
Choosing efficiently from a range of
strategies and written form with larger
whole numbers
X3, x4, x6, x7, x8, x9
division facts
8
AP
Choosing efficiently from a range of
strategies and written form with decimals
and fractions
Where were most of your class?
How will you group them?
Basic facts being
learnt for recall
Stages 2/3 (Counting From One)
• Short units
• Building Number Knowledge
i.e Skip Counting sequences for 2’s, 5’s and 10’s
e.g. using bead string, flip board, body clapping, hundreds
squares, calculator constant, Number line pegs, animal
strips.
• Simple strategy work to introduce multiplication language
e.g. groups of etc.
• * See “Further ideas..” handout.
Perception Check
In your thinking groups:
Can you identify the strategies for multiplication and division
on your “Scenarios” sheet?
Use you Framework (Book 1) to refer to if you need to.
A Numeracy Classroom in Action
Consider what purpose each of the following serves in a Maths
classroom:
• Taskboard
• Group Boxes
• Independent Activities
• Learning Centre
Maths Taskboard
Kyle,
Cory
Group Box
Explore ideas-
Learning
Centre
Teacher:
Game
Teacher:
Follow up work:
Worksheet
what stage is
each intended
for- how could it
be adapted?
A Little Bit
Crocodillian
Multiplication More, A Little
The Royal
Cooking
Lesson, p57
Bit Less, p32
Teacher:
Cut and
Paste,p49
Follow up
game:
Metamorphasis
(MM6-7)
Or, “Nice and
Easy”
Group Box/
Learning
Centre
Maths Taskboard
Now share your experiences during you “Numeracy hour”
Kyle,
Cory
Group Box
Explore ideas-
Learning
Centre
Teacher:
Game
Teacher:
Follow up work:
Worksheet
what stage is
each intended
for- how could it
be adapted?
A Little Bit
Crocodillian
Multiplication More, A Little
The Royal
Cooking
Lesson, p57
Bit Less, p32
Teacher:
Cut and
Paste,p49
Follow up
game:
Metamorphasis
(MM6-7)
Or, “Nice and
Easy”
Group Box/
Learning
Centre
What now?
Use Mult/Div data and re-group if necessary.
Source appropriate long term planning units for mult/div. Ask for
support for planning and locating resources if needed
Ask Lead Teachers for you to observe strategy teaching in your
school.
Thought for the day
Human beings share 99.4% of their DNA
with the chimpanzee and 50% of their
DNA with the cabbage.