# Do you remember Richard - the first winner from survivor

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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   Teacher
Modelling
Book

Thinking
Groups

Diagnostic
Snapshot at start
of lesson
Sums and Products

Product

42
product             15

6          7       3             5
13
sum                   8
sum
Let’s look at Stage 7 Division…
Tidy Numbers                Place Value

72 ÷ 4
Division Strategies
Tidy numbers                   Place Value Partitioning
(rounding)                           (splitting)

72 ÷
4
(alter both or just one number)

Standard Written Form
(algorithm)
Division Strategies
Tidy numbers                 Place Value Partitioning
(rounding)                         (splitting)
80 ÷ 4 = 20
40 ÷ 4 = 10
20 – 2 = 18
32 ÷ 4 = 8
10 + 8 = 18
72 ÷
4
(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
3,680 sheep.
How many sheep are
there in each
Division Strategies
Tidy numbers            Place Value Partitioning
(rounding)                    (splitting)

3680 ÷
8
Proportional                 Splitting Factors

Standard Written Forms
Reversibility
3, 680 ÷ 8        8 x ? = 3680     Place Value:

Proportional                   3200 ÷ 8 = 400
Adjustment:                     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
Place Value Partitioning
(splitting/written form)
Tidy numbers
(rounding)                     Paper Power 63-67
Not in book

Splitting Factors
Little Bites (76-79)

Divisibility Rules
Adjust the divisor only :            Nines and Threes (70-71)
Proportional Packets 54-57           Divisibility Rules Bk 8,33
The Royal Cooking Lessons 57-60
13 x 16 (Cross Products)
13 x 16
= 100+60+30+18 = 208
10              6

100        60
10

3        30         18
13 x 16
16     16
10        6
x 13   x 13
10    100       60                   18     48
30    160
3       30      18
60    208
100
The algorithm is essentially the    208
same as this place value method

36 x 28 =

20     8

30

6

36 x 28 = 1008

20     8

30    600   240

6     120    48
0.7 x 1.3   = 0.91
1            0.3

0.7          0.21
0.7
The Division Algorithm

Paper Power,            p 63

20 + 4           24
96 ÷ 4           (using partitioning first) 4 80 + 16   4 91 6

Moving to “chunking” calculations like 847 ÷ 3

Use partitioning to solve 162 ÷ 6

Use a “chunking” method to solve 837 ÷ 4
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                      Basic facts being
multiplication/division problem               learnt for recall
2/3 CA   Counting all the objects, making groups

4   AC   Skip counting for 2, 5, 10                    Skip counting sequences
(equal sharing for division)                  Groups of 2’s up to 20

5   EA   Repeated addition / Commutative property      X2, x5, x10 mult’n and
(using sharing and addition for division)     division facts

6   AA   Deriving (by splitting/doubling/ rounding)    X3, x4, x6, x7, x8, x9
(reversing/inverse operations for division)   multiplication facts

7   AM   Choosing efficiently from a range of          X3, x4, x6, x7, x8, x9
strategies and written form with larger       division facts
whole numbers

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?
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

Can you identify the strategies for multiplication and division

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:
• Group Boxes
• Independent Activities
• Learning Centre

Group Box           Learning        Teacher:
Explore ideas-      Centre          The Royal
Kyle,
Cory        what stage is                       Cooking
each intended                       Lesson, p57
for- how could it

Worksheet
Crocodillian   A Little Bit
Multiplication More, A Little
Bit Less, p32

game:
Cut and                             Learning
Metamorphasis   Centre
Paste,p49           (MM6-7)
Or, “Nice and
Easy”
Now share your experiences during you “Numeracy hour”

Group Box            Learning        Teacher:
Explore ideas-       Centre          The Royal
Kyle,
Cory                    what stage is                        Cooking
each intended                        Lesson, p57
for- how could it

Worksheet
Crocodillian   A Little Bit
Multiplication More, A Little
Bit Less, p32

game:
Cut and                              Learning
Metamorphasis   Centre
Paste,p49            (MM6-7)
Or, “Nice and
Easy”
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

school.
Thought for the day
Human beings share 99.4% of their DNA
with the chimpanzee and 50% of their
DNA with the cabbage.

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