Transcript Parent Workshop 2014 September Numeracy 1

Welcome to
Dingo State School
Numeracy
Afternoon
Our Aim
•
Help children feel confident when
working mathematically …
How is mathematics education
different for this generation?
Previously we
were taught
mainly facts
and
procedures.
Lessons were
about practise
and recall
Lessons ensure
students have
deep and
connected
understandings.
Students are
expected to
explain, reason
and justify.
In the Australian Curriculum,
we expect students to have:
• Understanding
• (connecting, representing, identifying, describing, interpreting,
sorting, …)
• Fluency
• (calculating, recognising, choosing, recalling, manipulating, …)
• Problem solving
• (applying, designing, planning, checking, imagining, …)
• Reasoning
• (explaining, justifying, comparing and contrasting, inferring,
deducing, proving, …)
“But, I wasn’t good at Maths”
When we focus too much on facts and
procedures, students may develop
misconceptions and inefficient
methods.
This quite often leads to maths anxiety,
disengagement and poorer
performance in all subjects that
require mathematics.
Going mental first
• Mental computation and estimation
account for approximately 80% of the
calculations we do in real life
• Using a calculator 15-18% of the time
• Paper and pencil methods 3-5% of the
time
Most adults were not taught mental
computation methods.
Discussion
• 30% of Australian adults are
unable to use the procedure that
was drilled into us.
• Most adults were shown one way
to add and subtract, multiply and
divide.
• Often, these adults have
‘ANXIETY’ in situations that
involve calculation
Counting and Subitising
The counting principles
•Each object must be counted only
once
•Numbers must be said once
•Arrangement of objects does not
affect how many there are in the
collection
•The last number said tells how many
in the collection
Key Terms
•Rainbow Facts or friends of 10
•Doubles
•Near doubles
•Subitising
•Partitioning
•Compensating
•Jumping
Key Terms
•Rainbow Facts or friends of 10
Key Terms
•Doubles
•Near doubles
2+2
3+3
22+22
46+46
6+7
8+9
22+23
46+47
Counting and Subitising
Subitising
•Students recognise numbers at a glance
•Familiar with collections or arrangements
such as dice patterns
•Seeing smaller parts within collections
Subitising assists students to quantify
collections and build whole-part
relationships and an understanding of
decimal numbers.
Partitioning
•Breaking a number up into smaller
numbers, usually hundreds, tens and
ones.
156
•100 + 50 + 6
•50 + 50 + 50 + 6
9731
•9000 + 700 + 30 + 1
Builds fluency and flexibility of thinking
[ ]=7+5+3+5+6
How would you add these numbers?
[ ]=7+5+3+5+6
Child A adds in order: 7,5,3,5 and then 6 (counting all on her
fingers)
Child B says ‘7 and 3 make 10’, ‘5 and 5 make 10’ and ‘6 more
is 26’
Child C says ‘5+5 = 10’ , then ‘6 + 3 = 9’, ‘so that’s 19’. He then
counts on 7 more
Child D takes 2 from 7 and adds it the 3 to make 4 lots of 5.
She says, ‘Four fives are 20. 20 and 6 more is 26.’
Insight into misconceptions
7+4=[ ]+5
16
11
6
11 & 16
55%
20%
15%
10%
Here are the four most common student
responses (Years 2-7)
What is a typical response rate in Year 4?
6 is the correct answer.
201-198
201 - 198
Jumped straight
to a procedure
and got it wrong
Jumped straight
to a procedure
and got it correct
Reasoned
mentally
Trusted
Numbers
2/3
14%
25%
61%
4/5
25%
35%
40%
6/7
28%
41%
31%
Give your child a
number fact.
7
8
3
4
7
4
7
4
3
4
7
7
3
3
3
4
Can they create the
related number facts?
12
4
To
12 ensure they
8
4
UNDERSTAND
12
4
8
Ask your child to say or
12 a problem
draw
8 4that
(USES) one of these
12
facts
4 8
24
8
8
3
24
24
3
3
3
8
3
8
12
24
24
8
3
LINK this to
FRACTIONS
Eg
⅓ of 12 = 4
3
4
12
12
4
4
3
3
4
12
12
4
3
FOUR SQUARE
NUMBER FACTS
8 + 2 = 10
2 + 8 = 10
RELATED FACTS
10 - 8 = 2
10 – 2 = 8
STORY
( drawing or oral )
A chef made 10 cakes and I ate
2 of them. There are 8 cakes
left.
EXTENDED FACTS
If I know 8 + 2 = 10
then I also know:
80 + 20 = 100
100 – 20 = 80
What methods do we use as
adults?
38 + 57
72 - 28
JUMP- addition & subtraction
SPLIT: addition & subtraction
Students must be confident and flexible with Place
Value concepts to assist with mental computation.
Left to right adding and subtracting
• Students and adults naturally use left to
right thinking for mental calculations.
• Left to right written methods connect to
students’ mental strategies.
Compensating
38 + 57
72 - 28
What does Australian
Curriculum expect?
• Addition and subtraction facts by Year 3
• Multiplication and division facts by Year
3/4
• A greater focus on mental methods to
prepare students for real world
situations
• A range of written methods (not just the
one method)
• Students to choose methods and
strategies to suit individual problems
How can you help at home?
•Talk about ways that you use to add
and subtract mentally.
•Practise number facts in game
situations.
•Don’t expect your children to
naturally add and subtract like you
do.
•Let your children discuss their ways
for adding and subtracting with you.
Resist the temptation
“ This is how you should do it”
Ask your child to explain their
strategies for adding and subtracting
Ask your child for an estimate before
they calculate the exact answer
Ask “Is that answer reasonable?”
Adding number plates
Other Ideas
• Play board games with dice, spinners,
dominoes and cards.
• Cook with the kids, scales, measuring
cups and timers etc.
• Smarties or any sweets are great for
counting large numbers, sharing…..
• Family bar of chocolate is great for
fractions
• Shopping or travel challenges. How long,
How much
If students are shown the links they are
less likely to forget them
1
8
2
3
16
24
4
32
5
6
7
8
9
40
48
56
64
72
The x1, x2, x5 and x10 facts can
provide a foundation for all
multiplication and division facts.
10
80
10x10
How many multiplication facts are there?
10x9
9x9
10x8
9x8
8x8
8x7
7x10
7x9
7x7
10x6
7x6
9x6
8x6
6x6
9x5
5x6
7x5
5x10
8x5
5x5
4x10
9x4
4x7
4x8
5x4
4x6
4x4
3x5
4x3
3x10
3x6
8x3
9x3
7x3
3x3
4x2
2x5
9x2
2x6
10x2
2x7
8x2
2x2
45
2x3
What do we do if my
child doesn’t know a
table fact?
I have
forgotten
8 x 7?
I know 7x2=14
Double 14 is 28
Double 28 is 56
I know that
5 x 8 = 40
2 x 8 = 16
40+16 = 56
10 x 7 = 70
Take two 7s (14)
from 70
That’s 56
Teaching Number Facts
What is more important.
To know your number facts or to
understand strategies to solve
number facts?
37
You need to know the basics
1’s 2’ 10s
1x9
1 x 29
1 x 379
2x9
doubling
2 x 29
2 x 279
10 x 9
9 groups of
10
NOT add
zero
10 x 29
279 x 10
Term 1 2007
38
Number Facts 3X
What strategies do you use?
3x6
27 x 3
Term 1 2007
231 x 3
39
Number Facts 3X
(3x) double plus 1
3x6
Double 6 + 6
12 + 6 = 18
3x8
Double 8 + 8
16 + 8 = 24
What other
strategies?
27 x 3
Double 27 + 27
54 + 27 = 81
231 x 3
Double 462 + 231
462+ 231 = 693
3 x 200 = 600
3 x30 = 90
3x1=
3
Term 1 2007
40
Number Facts 3X
Scan Think Do
See Plan Do Check
3 x 275
Term 1 2007
41
Number Facts 4X
What strategies do you use?
4x9
47 x 4
Term 1 2007
135 x 4
42
Number Facts 4X
(x4) Double Double
Double the other number, then double again.
4x6
Double 6 + Double 6
12 + 12 = 24
4x9
Double 9 + Double 9
18 + 18 = 36
What other
strategies?
37 x 4
Double 37 + Double
37
74 + 74 = 148
135 x 4
Double 135 + Double
135
270 + 270 = 540
4 x 100 = 400
4 x 30 = 120
4x5=
20
Term 1 2007
43
Number Facts 4X
Scan Think Do
See Plan Do Check
4 x 128
Term 1 2007
44
Number Facts 5X
What strategies do you use?
5x6
37 x 5
Term 1 2007
135 x 3
45
Number Facts 5X
(x5) Multiply by 10 then half
5x6
10 x 6 60 ÷ 2 = 30
5x9
10 x 9 then divide 2
90 ÷ 2 = 45
What other
strategies?
37 x 5
10 x 37 then divide 2
370 ÷ 2 = 185
135 x 5
10 x 135 then divide 2
1350 ÷ 2 = 675
5 x 100 = 500
5 x 30 = 150
5x5=
25
Term 1 2007
46
Number Facts 5X
Scan Think Do
See Plan Do Check
5 x 246
Term 1 2007
47
Number Facts 6X
What strategies do you use?
6x7
34 x 6
Term 1 2007
267 x 6
48
Number Facts 6X
(x6)
Multiply by 10 then half plus the number OR
Double the #, then add it one more time then double again
6x7
((Double 7) + 7) x 2
(14 + 7) x 2
21 x 2 = 42
6 x7
10 x 7 then divide 2
+6
70 ÷ 2 + 6 = 42
What other
strategies?
34 x 6
((Double 34) + 34) x
2
(68 + 34) x 2
102 x 2 = 204
34 x 6
10 x 34 then divide 2
+ 34
340 ÷ 2 + 34 =
170 + 34 = 204
267 x 6
200 x 6 = 1200
60 x 6 = 360
7x6=
42
1602
Term 1 2007
49
Number Facts 6X
Scan Think Do
See Plan Do Check
6 x 262
Term 1 2007
50
Number Facts 7X
What strategies do you use?
7x7
24 x 7
Term 1 2007
379 x 7
51
Number Facts 7X
(x7) Multiply Fives strategies plus double strategies
7x7
7 x 10 ÷ 2 + (7 x 2)
70 ÷ 2 + 14
35 + 14 = 49
8’s -1?
9’s – double?
Does anyone know a
better mental
strategy?
24 x 7
24 x 10 ÷ 2 + (24 x
2)
240 ÷ 2 + 48
168
138 x 7
138 x 10 ÷ 2 + (138
x 2)
1380 ÷ 2 + 276
690 + 276
966
379 x 7
300 x 7 = 2100
70 x 7 = 490
9x7=
63
2653
52
Number Facts 7X
Scan Think Do
See Plan Do Check
7 x 425
Term 1 2007
53
Number Facts 8X
What strategies do you use?
7x8
34 x 8
Term 1 2007
154 x 8
54
Number Facts 8X
(x8) Double + Double + Double
When multiplying by 8 double the other #, double the result, and then
double again.
6x8
Double 6 + Double 12 +
Double 24
6x2x2x2
48
7X8
Double 7 + Double 14 +
Double 28
7x2x2x2
56
Does anyone know a
better mental strategy?
34 x 8
Double 34 + Double 68 +
Double 136
34 x 2 x 2 x 2 =
272
154 x 8
Double 154 + Double 308
+ Double 616
154 x 2 x 2 x 2
1232
278 x 8
200 x 8 = 1600
70 x 8 = 560
8x 8 =
64
2224
55
Number Facts 8X
Scan Think Do
See Plan Do Check
8 x 256
Term 1 2007
56
Number Facts 9X
What strategies do you use?
3x9
27 x 9
Term 1 2007
231 x 9
57
Number Facts 9X
(x9) Multiply by 10 then subtract the number
6x9
6 x 10 then take 6
60 – 6 = 54
8x9
8 x 10 then take 8
80 – 8 = 72
ROTE
34 x 9
34 x 10 then take 34
340 – 34 =
306
156 x 9
156 x 10 then take
156
1560 – 156 =
1404
456 x 9
400 x 9 = 3600
50 x 9 = 450
6x9 =
54
4104
58
Number Facts 9X
Scan Think Do
See Plan Do Check
9 x 455
Term 1 2007
59
Double Digit Multiplication
What aspects of learning
multiplication are the
most important?
60
By the end of primary
27 x 33 =
Trusting the numbers
In order for our students to do
this they must TRUST the
numbers.
Thank you
62
Cheers