Transcript for 8 x 6 - mathsleadteachers

Multiplication & Division Workshop
Teacher: Who can tell me what 7 x 6 is?
Pupil: 42!
Teacher: Very good. Now who can tell me
what 6 x 7 is?
Pupil: 24!
Learning Facts are Easy
“According to Jim”
Purpose of this session…
• Understand strategies for multiplication and
division
• Know how to plan and teach multiplication and
division
• Develop an independent number knowledge
programme in the classroom
Overview
• Introduce Strategy Stages for Mult/Div
• Stage 5 and Stage 6
• Morning tea
• Modelling Session (Stage 6-7)
• Content higher stages
Multiplication Grid Game
e.g. Roll a three and a four: 3 x 4 or 4 x 3
Multiplication Grid Game
e.g. Roll a three and a four: 3 x 4 or 4 x 3
Show 6 x 5 on your
Happy Hundreds Board
The convention in New
Zealand is to regard
6 x 5 as 6 groups of 5
How many cups in
each row?
How many rows of
cups?
How many cups are
there altogether?
Counting All From One (Stage2-3)
Skip Counting AC (Stage 4)
5
10
15
20
25
30
Repeated Addition EA (Stage 5)
10 5
++
105+=10
10 = 30
10
10
Stage
Strategy used to solve a
multiplication/division problem
Basic facts being
learnt for recall
2/3 CA
Counting all the objects, making groups
4
AC
Skip counting for 2, 5, 10
(equal sharing for division)
Skip counting sequences
Groups of 2’s up to 20
5
EA
Repeated addition / Commutative property
(using sharing and addition for division)
X2, x5, x10 mult’n and
division facts
Stage
Strategy used to solve a
multiplication/division problem
2/3 CA
Counting all the objects, making groups
4
AC
Skip counting for 2, 5, 10
(equal sharing for division)
Skip counting sequences
Groups of 2’s up to 20
5
EA
Repeated addition / Commutative property
(using sharing and addition for division)
X2, x5, x10 mult’n and
division facts
6
AA
Deriving (by splitting/doubling/ rounding)
(reversing/inverse operations for division)
X3, x4, x6, x7, x8, x9
multiplication facts
7
AM
Choosing efficiently from a range of
strategies and written form with larger
whole numbers
X3, x4, x6, x7, x8, x9
division facts
8
AP
Choosing efficiently from a range of
strategies and written form with decimals
and fractions
Where were most of your class?
Basic facts being
learnt for recall
Derived Multiplication AA (Stage 6)
for 8 x 6
8 x 5 = 40
8x1=8
So 40 + 8 =48
Derived Multiplication AA (Stage 6)
8x6
10 x 6 = 60
60- (2x6) =48
2 x 6 = 12
Focusing on Stage 5 and Stage 6
Knowledge
Basic Facts can be
effectively taught with
understanding through
using strategies.
Knowledge of Basic Facts to
10x10 are then useful for
using advanced strategies
for harder problems.
Strategies
How you solve a
mult/div problem.
Using Basic Fact Data
•What assessment information do/can you use
for basic facts?
IKAN?
Basic Fact Tests?
•How is it used summatively /
formatively?
• Which facts do they know already?,
• What needs to be taught and then practiced
next?
Teaching Multiplication Basic Facts Efficiently
Assessing
Analysing data
Planning
Teaching
Practicing / Applying
Multiplication Counter Game
Teaching
Practising
Assessing
Which of the basic facts activities in your
classroom are focusing on teaching?
Teaching to develop understanding and application
of basic facts rather than just fact recalling
Early Additive: Stage 5
• Establish link between multiplication and
repeated addition. E.g. 3 x 6 = 6 + 6 + 6
x0
x1
x2
x5
x10
Advanced Additive: Stage 6
• Deriving unknown facts from known facts and
apply deriving strategies to larger numbers
x9
x3
x4
x6
x7
x8
Stage 6
Deriving unknown
facts through using strategies
x9, x3 x4 x6, x7 x8
(and apply these strategies to larger numbers)
How can we solve the 18x table?
What else do I know?
3 x 5 =15
Stage 6: Multiplying by 10
How do you describe what happens?
Not just “add a zero”
The numbers move one place value along
Thousands
Hundreds
2
Tens
Ones
2
3
3
0
Division
Share a division story problem for
the following:
8÷2=4
Different Types of Division
8÷2=4
• Division by Sharing:
8 lollies shared between 2 people. How many
lollies does each person have?
• Division by Grouping:
John has 8 lollies, he puts 2 lollies into each bag.
How many bags of lollies will he have?
Play “Is it divisible?”
FINISH
FINISH
30
30
15
15
16
16
9
9
18
18
4
4
24
24
12
12
START
START
Dice:
2,3,4,5,6
choice
Stage 6 Advanced Additive
(NC Level 3)
Existing
Book 6
A Little Bit More a
Little Bit Less.
The Royal Cooking
Lesson
What diagnostic snapshot
would you ask?
Knowledge &
Strategies
Using
Material
s
Using
Imaging
Using Number
Properties
New
Knowledge &
Strategies
Modelling Session
How does each person benefit?
Students
Modelling
Book
Thinking
Groups
Diagnostic
Snapshot at start
of lesson
Teacher
Arithmefacts
6
7
+
x
÷
+
x
÷
3
4
6+3= 9
6-3= 3
6 x 3 = 18
6÷3= 2
“6 - 3 = 3, and
7 - 4 = 3”
What is Multiplicative Thinking?
Multiplicative thinking is not about the type of
problems you solve but how you solve it.
Although 3 x 18 is a multiplication problem, if it is
solved by adding 18 + 18 + 18 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
Stage 7 AM
(NC Level 4)
book 6 Page 41
Take a moment to read…..
• Required Knowledge?
• Knowledge being developed?
• Key Ideas?
3 x 18
There were 3 minivans each with 18
children on them going on a school trip.
How many children were there
altogether?
Compensation with tidy
numbers (rounding)
Place Value Partitioning
(splitting)
(3 x 20) - (3 x 2)
(3 x 10) + (3 x 8)
3 x 18
Proportional
Adjustment
6x9
Splitting Factors
3 x (3 x 3 x2)
Standard Written Forms
How would you use the teaching model to teach these
strategies? Book 6 p.52 onwards
Place Value Partitioning 3 x 18
3 x 10 = 30
30 + 24 = 54
3 x 8 = 24
10
10
10
Tidy Numbers
3 x 18
3 x 20 = 60
60 - (3 x 2) = 54
10 10
10 10
10 10
6x4=3x8
Using Imaging for 3 x 18
3 x 18
3x9
3x9
3 x 18 = 6 x 9
3 x 18
x2
÷
6x9 2
Generalise using number properties:
Proportional Adjustment
6482 x 5
is about re-arranging the
factors to create a simpler
problem
(Associative Property)
12 x 33
12 x 33
(2 x 6) x 33
2 x 2 x 3 x 33
4 x 99
Using Number Lines to show 3 x 18
18
0
9
A
9
18
9
9
18
9
54
9
54
3 x 10
Place value
3x8
30
0
54
B
Tidy
Numbers
3 x 20
- (3 x 2)
C
0
Proportional
Adjustment
54
60
Multiplication Roundabout
(MM6-6)
Start
42
28
13
59
51
34
48
17
Multiplication Roundabout
(MM6-6)
E.g. Roll a 3. Move 3 places then multiply the number by 3
42
13
28
59
51
34
48
17
Multiplication Roundabout
(MM6-6)
E.g. Roll a 3. Move 3 places then multiply the number by 3
42
13
28
59
51
34
48
17
Multiplication Roundabout
(MM6-6)
59 x 3 =
180 - 3 = 177
(place counter between 150 & 200)
42
13
28
59
51
34
48
17
Let’s look at Stage 7 Division…
Tidy Numbers
Place Value
72 ÷ 4
Proportional
Adjustment
Reversing
Compensation with tidy
numbers (rounding)
Place Value Partitioning
(splitting)
72 ÷
4
Proportional
Adjustment
Splitting Factors
Standard Written Forms
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?
Compensation with tidy
numbers (rounding)
Place Value Partitioning
(splitting)
3680 ÷
8
Proportional
Adjustment
Splitting Factors
Standard Written Forms
3, 680 ÷ 8
Proportional
Adjustment:
Reversibility
8 x ? = 3680
Place Value:
3200 ÷ 8 = 400
480 ÷ 8 = 60
3680 ÷ 8 =
1840 ÷ 4 =
920 ÷ 2 = 460
Tidy Numbers
Algorithm
4000 ÷ 8 = 500
500 - (320 ÷ 8)=
3680
500 - 40 = 460
13 x 16 (Cross Products)
13 x 16
10
6
10
100
60
3
30
18
The algorithm is essentially the
same as this place value method
16
x 13
18
30
60
100
208
16
x 13
48
160
208
13 x 16 = 100+60+30+18 = 208
10
6
100
60
30
18
10
3
0.7 x 1.3 = 0.91
1
0.7
0.7
0.3
0.21
Sums and Products
Product
42
product
6
7
13
sum
15
3
5
8
sum
Stage 7(Level 4)
•Explore further activities and key ideas at
this stage
•Discuss planning and independent work for
this stage
Multiplying by 11
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.
In Class Visits
Do you remember Richard - the
first winner from survivor?