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


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


918 + 18 = 36



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


Term 1 2007 44

4 x 128

Number Facts 5X


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



370 ÷ 2 = 185


1350 ÷ 2 = 675

5 x 100 = 5005 x 30 = 1505 x 5 = 25

Number Facts 5X


Term 1 2007 47

5 x 246

Number Facts 6X


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


+ 670 ÷ 2 + 6 = 42


34 x 6((Double 34) + 34) x 2

(68 + 34) x 2102 x 2 = 204


+ 34340 ÷ 2 + 34 =170 + 34 = 204

267 x 6200 x 6 = 120060 x 6 = 3607 x 6 = 42

1602

Number Facts 6X


Term 1 2007 50

6 x 262

Number Facts 7X


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


Term 1 2007 53

7 x 425

Number Facts 8X


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


Term 1 2007 56

8 x 256

Number Facts 9X


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


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

Documents

Welcome to Dingo State School Numeracy Afternoon