Title: Multiplication and Division Workshop
1Multiplication and Division Workshop
- Developing Multiplicative Thinking
- (through the Multiplication and Division Domain)
Fiona Fox Lisa Heap Mathematics Facilitator
2Multiplication Grid Game
e.g. Roll a three and a four 3 x 4 or 4 x 3
3Multiplication Grid Game
e.g. Roll a three and a four 3 x 4 or 4 x 3
4Objectives
- Reflect on addition subtraction strategy
teaching. - Understand the progressive strategy stages of
multiplication division - Explore the properties of multiplication.
- Know how to use planning sheets, numeracy book
six and other supportive resources to help teach
multiplication and division
5Reflection on Numeracy Teaching
- Discuss these expectations in your groups
- Teams sharing planning and teaching ideas.
- Teaching model used for strategy group
teaching. - Number knowledge being taught whole class as
well - as through independent activities.
- Modelling book used.
- Tried some Figure It Out or website
activities. - Using the long term planning units.
- Maths routines well established
- Listening to students thinking.
- Where are you at now? Whats your next
- step?
6The 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.
7Strategy 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
8Make 8 x 6 using animal strips or happy faces
98 x 6
Skip Counting AC
10Repeated Addition EA
8 x 6
11Derived Multiplication AA
8 x 6
12Derived Multiplication AA
8 x 6
10 x 6 60
60- (2x6) 48
13Multiplicative 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
14Discuss 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?
15Lets 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
16Another 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
17The 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
18Using 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!!
19Proportional 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!!
20A 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?
21Stage 2 - 3
- Aim Working towards children seeing sets of
numbers as a whole unit rather than by counting
one by one. - Building number knowledge i.e. skip counting in
2s, 5s and 10s. - Using bead strings, flip boards, body percussion,
hundreds squares, calculator constant, number
line pegs, animal strips. - Introduce multiplication language e.g.groups
of, lots of etc..
22A Strategy Teaching Lesson
- Start of Lesson Consider strategy stage of group
- Required knowledge check
- Diagnostic Snapshot (Can they already do it?)
- Teaching
- - Teaching Model (materials, imaging, number
properties) - Consider thinking groups modelling book
- End of Lesson
- Feedback Whos got it? Who hasnt? Set
practice. - Consider next teaching and learning steps.
23Exploring a lesson from Book 6
- Break into 3 groups to explore a mult/div lesson
- Stage 3-4
- Number Strips Pg.8
- Stage 4-5
- Animal Arrays Pg.15
- Stage 6-7
- Cut Paste Pg.49
24Stage 7 Advanced Multiplicative
- I give 3 lollies to every child in my class. I
have 18 children in my class, how many lollies
did I need to buy altogether?
Solve 3 x 18
253 x 18
Tidy Numbers using Compensation
263 x 18
Place Value Partitioning
30 24 54
27Proportional Adjustment
283 x 18
3 x 9
3 x 9
29Proportional Adjustment
6 x 9 54
30Using Number Lines
Proportional Adjustment Place value Tidy Numbers
54
A
30
54
B
54
60
C
31Lets look at Division
- In your thinking groups make up a division
problem for the following
6 x 3 18
32The Different Types of Division
- Division by Sharing (partitive) 18 lollies to
- share equally into 3 bags. How many lollies
in each bag? - Division by Measuring/Grouping (quotitive)
- John has 18 lollies, he puts them 6 lollies to
a bag. How many bags of lollies will he have?
33Why is this important?
- Try solving this problem..
- Is it division by sharing or by measuring and
grouping?
2 1/2 divided by 1/2
34Division 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?
3554 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
36Solving a Division Problem
- A sheep station has eight paddocks and 296 sheep.
How many sheep are there in each paddock?
37296 8
Reversibility 8 x 30 240 8 x 7 56
- Place Value
- 240 8 30
- 56 8 7
- 30 7 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
38The Strategy Teaching Model
Existing Knowledge Strategies
Using Number Properties
Using Imaging
Using Materials
Using Materials
New Knowledge Strategies
39Review Objectives
- Revise addition subtraction strategy teaching
- Understand the progressive strategy stages of
multiplication division - Explore the properties of multiplication and
division - Know how to use planning sheets, numeracy book
six and other supportive resources to help teach
multiplication and division
40Thought for the day
- Success is.
- getting up one more time than you fell down!
-
41A Strategy Teaching Lesson
- Start of Lesson Consider strategy stage of group
- Required knowledge check
- Diagnostic Snapshot (Can they already do it?)
- Teaching
- - Teaching Model (materials, imaging, number
properties) - Consider thinking groups modelling book
- End of Lesson
- Feedback Whos got it? Who hasnt? Set
practice. - Consider next teaching and learning steps.