Multiplication and Division Workshop

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Multiplication and Division Workshop

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

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






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






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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

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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?

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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.

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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

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Make 8 x 6 using animal strips or happy faces
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8 x 6
Stage 4 - Skip Counting AC
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Stage 5 - Repeated Addition EA
8 x 6
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Stage 6 - Derived Multiplication AA
8 x 6
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Stage 7 - Derived Multiplication AM
8 x 6
10 x 6 60
60- (2x6) 48
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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

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

Proportional Adjustment
6 x 9 54
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Using Number Lines
Proportional Adjustment Place value Tidy Numbers
54
A
30
54
B
54
60
C
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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?

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Morning Tea

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

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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?

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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

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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

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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

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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!!

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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!!

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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?

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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)

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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
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Lets look at Division

• In your thinking groups make up a division
  problem for the following

6 x 3 18
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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?

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Why is this important?

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

2 ½ ½
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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?

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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

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Solving a Division Problem

• A sheep station has eight paddocks and 296 sheep.
  How many sheep are there in each paddock?

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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
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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

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Thought for the day

• Success is.
• getting up one more time than you fell down!