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Multiplication and Division Workshop

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Developing Multiplicative Thinking (through the Multiplication and Division Domain) Multiplication and Division Workshop Lisa Heap, Jill Smythe and Alison Howard – PowerPoint PPT presentation

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Title: Multiplication and Division Workshop


1
Multiplication and Division Workshop
  • Developing Multiplicative Thinking
  • (through the Multiplication and Division Domain)

Lisa Heap, Jill Smythe and Alison
Howard Mathematics Facilitators
2
Multiplication Grid Game
e.g. Roll a three and a four 3 x 4 or 4 x 3






3
Multiplication Grid Game
e.g. Roll a three and a four 3 x 4 or 4 x 3






4
Objectives
  • Understand the progressive strategy stages of
    multiplication division
  • Explore the properties of multiplication.
  • Know how to use numeracy book six and other
    resources to help teach multiplication and
    division

5
Reflection on Numeracy Teaching
  • Discuss these expectations in your groups
  • Teaching model used for strategy group
    teaching.
  • Number knowledge being taught whole class, in
    groups
  • as well as through independent activities.
  • Modelling book used.
  • Group boxes established.
  • Planning from assessment to meet identified
    needs.
  • Maths routines well established.
  • Wait time for students to process their
    thinking.
  • Listening to and beginning to respond to
    students thinking.
  • Where are you at now? Whats your next
  • step?

6
The Development of Multiplicative Thinking
  • There are 6 minivans outside the school, they are
    going on a school trip. There are 5 children in
    each minivan. How many children are going on the
    trip?
  • How would a student at the different stages solve
    this problem?
  • Hint..use your Framework
  • as a reference.

7

8
Strategy Framework Revision
  • 2/3 CA Counts all the objects
  • 4 AC Uses skip counting
  • 5 EA Repeated addition or using known
  • facts
  • 6 AA Derived multiplication
  • 7 AM Choosing efficiently from a range of
    strategies and written form with whole
    numbers
  • 8 AP Choosing efficiently from a range of
    strategies with decimals and fractions

9
Make 8 x 6 using animal strips or happy faces
10
8 x 6
Stage 4 - Skip Counting AC
11
Stage 5 - Repeated Addition EA
8 x 6
12
Stage 6 - Derived Multiplication AA
8 x 6
13
Stage 7 - Derived Multiplication AM
8 x 6
10 x 6 60
60- (2x6) 48
14
Multiplicative Thinking
What is multiplicative thinking?
  • Multiplicative thinking is not about the type of
    problems you solve but how you solve it.
  • E.g. Although 3 x 23 is a multiplication
    problem, if it is solved by adding 23 23 23
    then you are not thinking multiplicatively but
    are using an additive strategy.
  • Similarly an addition problem e.g. 27 54 can be
    solved multiplicatively by doing (3 x 9) (6 x
    9) 9 x 9

15
The Strategy Teaching Model
Existing Knowledge Strategies
Using Number Properties
Using Imaging
Using Materials
Using Materials
New Knowledge Strategies
16
3 x 18
Place Value Partitioning
30 24 54
17
3 x 18
Tidy Numbers using Compensation
18
Proportional Adjustment
19
3 x 18
3 x 9
3 x 9
20

Proportional Adjustment
6 x 9 54
21
Using Number Lines
Proportional Adjustment Place value Tidy Numbers
54
A
30
54
B
54
60
C
22
Discuss the strategies you would use to solve the
following problem
  • Each carton holds 36 cans of spaghetti
  • There are five cartons.
  • How many cans of spaghetti is that?

23
Morning Tea
  • After morning tea
  • Y0 - 2 teachers with Alison
  • Y3 8 teachers with Lisa Jill

24
Discuss the strategies you would use to solve the
following problem
  • Each carton holds 36 cans of spaghetti
  • There are five cartons.
  • How many cans of spaghetti is that?

25
Lets Look at the Possibilities..
  • You may have used the distributive property.
    This meant that one of the factors was split
    additively.
  • 5 x 36 (5 x 30) (5 x 6)
  • 150 30
  • 180
  • The 36 was split (distributed) into 30 6

26
Another Strategy
  • You may have used the commutative property in
    conjunction with the associative property.
  • 5 x 36 36 x 5 (commutative)
  • 18 x 10 (associative)
  • 180

27
The Associative Property is about grouping the
factors
  • So in 36 x 5, the 36 was split multiplicatively
  • 36 x 5 (18 x 2) x 5
  • 18 x 10
  • 180

28
Using the Associative Property
  • There were 12 children. Each had 33 marbles. How
    many marbles are altogether?
  • Using the Associative Property, regroup the
    factors to make this an easier problem to solve!!

29
Proportional Adjustment
  • Transforming the factors to create a simpler
    problem.
  • 12 x 33 becomes
  • (4 x 3) x 33
  • 4 x ( 3 x 33)
  • 4 x 99 EASY!!

30
A Multiplication lesson
  • Watch the video and in your thinking groups
    discuss the following
  • What was the key purpose of the lesson? What
    stage was the lesson aimed at?
  • How was the key idea developed throughout the
    lesson?
  • What mathematical language was being developed?
    When were the mathematic symbols introduced?
  • How did written recording support the students
    understanding?

31
Exploring Lessons in Book 6
  • Stage 4-5
  • Animal Arrays (pg. 15)
  • Biscuit Boxes (pg. 19)
  • Stage 5-6
  • Fun with Fives (pg.28)
  • A little Bit More, A little Bit Less (pg. 32)
  • Stage 6-7
  • Cut and Paste (pg. 49)
  • Proportional Packets (pg.54)

32
Stage 7 Advanced Multiplicative
  • I have 3 children. I give them 18 lollies each,
    how many lollies do I need to buy altogether?

Solve 3 x 18
33
Lets look at Division
  • In your thinking groups make up a division
    problem for the following

6 x 3 18
34
The Different Types of Division
  • Division by Sharing (partitive) 18 lollies to
  • share equally into 6 bags. How many lollies
    in each bag?
  • Division by Measuring/Grouping (quotitive)
  • John has 18 lollies, he puts them 3 lollies to
    a bag. How many bags of lollies will he have?

35
Why is this important?
  • Try solving this problem..
  • Is it division by sharing or by measuring and
    grouping?

2 ½ ½
36
Division DelightsFIO N3-4 18
  • The Goodwill gang get paid 54 for picking
    blueberries. There are 3 people in the gang. What
    is each persons share of the money?

37
54 3
  • Using Place Value
  • 30 3 10 24 3 8 10 8 18
  • Using Tidy Numbers
  • 60 3 20 6 3 2 20 - 2 18
  • Using Proportional Adjustment
  • 54 6 9 54 3 2 x 9 18

38
Solving a Division Problem
  • A sheep station has eight paddocks and 296 sheep.
    How many sheep are there in each paddock?

39
296 8
Reversibility 8 x 30 240 8 x 7 56
  • Place Value
  • 240 8 30
  • 56 8 7
  • 30 7 37
  • 296 8
  • 148 4
  • 74 2 37

Proportional Adjustment

Tidy Numbers 4000 8 500 500 - (320 8) 500
- 40 460
Rounding and Compensating
320 8 40 40 - (24 8) 40 - 3 37
Algorithm
40
Review Objectives
  • Understand the progressive strategy stages of
    multiplication division
  • Explore the properties of multiplication and
    division
  • Know how to use numeracy book six and other
    resources to help teach multiplication and
    division

41
Thought for the day
  • Success is.
  • getting up one more time than you fell down!
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