Welcome to Dingo State School Numeracy Afternoon.
-
Upload
lewis-hamilton -
Category
Documents
-
view
221 -
download
1
Transcript of Welcome to Dingo State School Numeracy Afternoon.
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 6+73+3 8+922+22 22+2346+46 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 + 1Builds 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.’
7 + 4 = [ ] + 516 11 6 11 &
16
Here are the four most common student responses (Years 2-7)
Insight into misconceptions
55% 20% 10%15%
What is a typical response rate in Year 4? 6 is the correct answer.
201-198
201 - 198Jumped straight to a procedure
and got it wrong
Jumped straight to a procedure
and got it correct
Reasoned mentally Trusted
Numbers
14% 25% 61%
25% 35% 40%
28% 41% 31%
2/3
4/5
6/7
7
3 4
3
7
7 4
4 3
37 4 3
4
7
8
12 4
8
12
12 4
4 8
812 4 8
4
12
Give your child a number fact.
Can they create the related number facts?
To ensure they UNDERSTAND
Ask your child to say or draw a problem that (USES) one of these
facts
24
8 3
8
24
243
3 8
324 8 3
8
24
3
12 4
3
12
124
4 3
312 4 3
4
12LINK this to FRACTIONSEg
⅓ of 12 = 4
NUMBER FACTS STORY( drawing or oral )
A chef made 10 cakes and I ate 2 of them.
There are 8 cakes left.
RELATED FACTS EXTENDED FACTS
If I know 8 + 2 = 10 then I also know:
80 + 20 = 100100 – 20 = 80
8 + 2 = 102 + 8 = 10
10 - 8 = 210 – 2 = 8
FOUR SQUARE
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.
Ask your child to explain their strategies for adding and subtracting
Resist the temptation“ This is how you should do it”
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
1 2 3 4 5 6 7 8 9 10808 4016 32 6424 48 7256
If students are shown the links they are less likely to forget them
The x1, x2, x5 and x10 facts can provide a foundation for all
multiplication and division facts.
45
How many multiplication facts are there?
2x3 4x2 2x5 9x2 2x6 10x2 2x7 8x2 2x2
3x5 4x3 3x10 3x6 8x3 9x3 7x3 3x3
4x10 9x4 4x7 4x8 5x4 4x6 4x4
10x6 7x6 9x6 8x6 6x6
8x7 7x10 7x9 7x7
10x8 9x8 8x8
9x5 5x6 7x5 5x10 8x5 5x5
10x9 9x9
10x10
I have forgotte
n8 x 7?
I know 7x2=14
Double 14 is 28
Double 28 is 56
10 x 7 = 70Take two 7s (14) from 70
That’s 56
I know that5 x 8 = 402 x 8 = 16
40+16 = 56
What do we do if my child doesn’t know a
table fact?
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
Term 1 2007 38
1 x 9 1 x 29 1 x 379
2 x 9doubling
2 x 29 2 x 279
10 x 99 groups of 10NOT add zero
10 x 29 279 x 10
Number Facts 3X
What strategies do you use?
Term 1 2007 39
3 x 6 27 x 3 231 x 3
Number Facts 3X
(3x) double plus 1
Term 1 2007 40
3 x 6Double 6 + 612 + 6 = 18
3 x 8Double 8 + 816 + 8 = 24
What other strategies?
27 x 3Double 27 + 2754 + 27 = 81
231 x 3Double 462 + 231462+ 231 = 693
3 x 200 = 6003 x30 = 903 x 1 = 3
Number Facts 3X
Scan Think DoSee Plan Do Check
Term 1 2007 41
3 x 275
Number Facts 4X
What strategies do you use?
Term 1 2007 42
4 x 9 47 x 4 135 x 4
Number Facts 4X
(x4) Double DoubleDouble the other number, then double again.
Term 1 2007 43
4 x 6Double 6 + Double
612 + 12 = 24
4 x 9Double 9 + Double
918 + 18 = 36
What other strategies?
37 x 4Double 37 + Double
3774 + 74 = 148
135 x 4Double 135 + Double 135
270 + 270 = 540
4 x 100 = 4004 x 30 = 1204 x 5 = 20
Number Facts 4X
Scan Think DoSee Plan Do Check
Term 1 2007 44
4 x 128
Number Facts 5X
What strategies do you use?
Term 1 2007 45
5 x 6 37 x 5 135 x 3
Number Facts 5X
(x5) Multiply by 10 then half
Term 1 2007 46
5 x 610 x 6 60 ÷ 2 = 30
5 x 910 x 9 then divide 2
90 ÷ 2 = 45
What other strategies?
37 x 510 x 37 then divide 2
370 ÷ 2 = 185
135 x 510 x 135 then divide 2
1350 ÷ 2 = 675
5 x 100 = 5005 x 30 = 1505 x 5 = 25
Number Facts 5X
Scan Think DoSee Plan Do Check
Term 1 2007 47
5 x 246
Number Facts 6X
What strategies do you use?
Term 1 2007 48
6 x 7 34 x 6 267 x 6
Number Facts 6X
(x6) Multiply by 10 then half plus the number OR Double the #, then add it one more time then double again
Term 1 2007 49
6 x 7((Double 7) + 7) x 2
(14 + 7) x 221 x 2 = 42
6 x 710 x 7 then divide 2
+ 670 ÷ 2 + 6 = 42
What other strategies?
34 x 6((Double 34) + 34) x 2
(68 + 34) x 2102 x 2 = 204
34 x 610 x 34 then divide 2
+ 34340 ÷ 2 + 34 =170 + 34 = 204
267 x 6200 x 6 = 120060 x 6 = 3607 x 6 = 42
1602
Number Facts 6X
Scan Think DoSee Plan Do Check
Term 1 2007 50
6 x 262
Number Facts 7X
What strategies do you use?
Term 1 2007 51
7 x 7 24 x 7 379 x 7
Number Facts 7X
(x7) Multiply Fives strategies plus double strategies
52
7 x 77 x 10 ÷ 2 + (7 x 2)
70 ÷ 2 + 1435 + 14 = 49
8’s -1?9’s – double?
Does anyone know a better mental
strategy?
24 x 724 x 10 ÷ 2 + (24 x 2)
240 ÷ 2 + 48 168
138 x 7138 x 10 ÷ 2 + (138 x
2)1380 ÷ 2 + 276
690 + 276966
379 x 7300 x 7 = 210070 x 7 = 4909 x 7 = 63
2653
Number Facts 7X
Scan Think DoSee Plan Do Check
Term 1 2007 53
7 x 425
Number Facts 8X
What strategies do you use?
Term 1 2007 54
7 x 8 34 x 8 154 x 8
Number Facts 8X
(x8) Double + Double + DoubleWhen multiplying by 8 double the other #, double the result, and then double again.
55
6 x 8Double 6 + Double 12 +
Double 246 x 2 x 2 x 2
48
7 X 8Double 7 + Double 14 +
Double 287 x 2 x 2 x 2
56
Does anyone know a better mental strategy?
34 x 8Double 34 + Double 68 +
Double 13634 x 2 x 2 x 2 =
272
154 x 8Double 154 + Double 308
+ Double 616154 x 2 x 2 x 2
1232
278 x 8200 x 8 = 160070 x 8 = 5608x 8 = 64
2224
Number Facts 8X
Scan Think DoSee Plan Do Check
Term 1 2007 56
8 x 256
Number Facts 9X
What strategies do you use?
Term 1 2007 57
3 x 9 27 x 9 231 x 9
Number Facts 9X
(x9) Multiply by 10 then subtract the number
58
6 x 96 x 10 then take 6
60 – 6 = 54
8 x 98 x 10 then take 8
80 – 8 = 72
ROTE
34 x 934 x 10 then take 34
340 – 34 = 306
156 x 9156 x 10 then take
1561560 – 156 =
1404
456 x 9 400 x 9 = 360050 x 9 = 4506 x 9 = 54
4104
Number Facts 9X
Scan Think DoSee Plan Do Check
Term 1 2007 59
9 x 455
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