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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
Proportional Adjustment            Reversing
                 Division Strategies
     Tidy numbers                   Place Value Partitioning
      (rounding)                           (splitting)




                             72 ÷
                               4
Proportional Adjustment                  Splitting Factors
(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
 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            Place Value Partitioning
 (rounding)                    (splitting)




               3680 ÷
                  8
Proportional                 Splitting Factors
Adjustment


           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)


   Proportional Adjustment
                                     Divisibility Rules
Adjust the divisor only :            Nines and Threes (70-71)
Proportional Packets 54-57           Divisibility Rules Bk 8,33
Adjust both numbers:
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
     Your Turn!

     36 x 28 =

      20     8

30

6
     Your Turn!

     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


Your Turn!
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

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

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


            Game                Teacher:        Follow up work:
                                                Worksheet
            Crocodillian   A Little Bit
            Multiplication More, A Little
                                Bit Less, p32


            Teacher:            Follow up       Group Box/
                                game:
            Cut and                             Learning
                                Metamorphasis   Centre
            Paste,p49           (MM6-7)
                                Or, “Nice and
                                Easy”
                  Maths Taskboard
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
                        be adapted?


                        Game                 Teacher:        Follow up work:
                                                             Worksheet
                        Crocodillian   A Little Bit
                        Multiplication More, A Little
                                             Bit Less, p32


                        Teacher:             Follow up       Group Box/
                                             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

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.

				
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posted:5/7/2013
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