17th and 24th Feb

Welcome to Yandina State School

Numeracy Parent Session

Presenters: Cathy Nash , Craig Johnson, Julie Wasmund

Part 1: Making connections

In this session, we will discuss:

• The Australian Curriculum

• The importance of deep understanding

• Some common misconceptions

• Number facts

• Some activities to do with your children

By the end of this session:

• Understand a little more about the

Australian Curriculum in Mathematics

• Understand that Maths education is

concerned with more than ‘just getting the

right answer’

Quick Fire BINGO

5 8 20

2 12 18

3 9 13

4 3 6

Choose 9 random

numbers between 0

and 20 and place

them in grid

Choose 3 single

digits

Make number

sentences using

these digits to cross

out your chosen

numbers

Eg

6 + 3 = 9

( 6 x 4 ) ÷ 3 = 8

6 – 4 = 2

Australian Curriculum, Mathematics

• Goal: to prepare students for 21st Century

real-world problems, both at work and in

daily life

• We must acknowledge that the Maths

demands of the next generation may be

quite different to those of our generation...

21st Century Maths

In pairs discuss and solve

this question

Our Aim

To develop confident, creative users and

communicators of mathematics

How is Maths 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.

7 + 4 = [ ] + 5

16 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.

“But, isn't maths just about

getting the right answer?”

Would you agree or disagree with this

statement?

[ ] = 7 + 5 + 3 + 5 + 6

How would you add these numbers?

This is ‘string sum’. Sums of this type are a

focus of Year 2 and 3.

Most students can calculate that the answer

is 26…but they solve it in different ways.

Teachers look for more than just a

correct answer.

[ ] = 7 + 5 + 3 + 5 + 6

You will now see four typical student responses

to the question.

Efficient

Inefficient

Draw a continuum

as shown here.

Work with a

partner to place

each student on

this continuum.

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 + 5 + 3 + 5 + 6

Do you agree?

The longer children

rely on inefficient

methods, the harder

it becomes to shift

them to efficient

methods.

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.

Adding number plates

Digit Cards

two 2-digit numbers with the smallest

difference

two 2-digit numbers that make a total

nearest to 100

the 3rd largest 4-digit number

Choose four cards.

Arrange your cards to make:

7

3 4

3

7

7 4

4 3

3

7 4 3

4

7

8

12 4

8

12

12 4

4 8

8 12 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

24 3

3 8

3 24 8 3

8

24

3

12 4

3

12

12 4

4 3

3 12 4 3

4

12 LINK this to

FRACTIONS

Eg

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 = 100

100 – 20 = 80

8 + 2 = 10

2 + 8 = 10

10 - 8 = 2

10 – 2 = 8

FOUR SQUARE

F

O

U

R

S

Q

U

A

R

E

YEAR 1

NUMBER FACTS

STORY ( drawing or oral )

RELATED FACTS EXTENDED FACTS

FOUR SQUARE – Your turn

YEAR 1/2 8 + 4 = 12

YEAR 3/4 21 = 7 x 3

YEAR 5/6 11 x 12 =132

NUMBER FACTS

8 + 4 = 12 4 + 8 = 12

STORY ( drawing or oral )

8 dogs are in the park. 4 more dogs arrive with their owners.

Now there are 12 dogs.

RELATED FACTS

12 – 8 = 4 12 – 4 = 8

EXTENDED FACTS

80 + 40 = 120 40 + 80 = 120 120 – 80 = 40

NUMBER FACTS

3 x 7 = 21 21 = 7 x 3

STORY ( drawing or oral )

I had 3 bags of mangoes. There were 7 mangoes in each bag.

How many mangoes did I have?

RELATED FACTS

21 ÷ 3 = 7 21 ÷ 7 = 3

EXTENDED FACTS

3 x 70 = 210 2100 = 30 x 70

210 ÷ 7 = 30

NUMBER FACTS

11 x 12 = 132 12 x 11 = 132

STORY ( drawing or oral )

I had 12 cartons of eggs. There was a broken egg in each

carton. How many good eggs were there?

RELATED FACTS

132 ÷ 11 = 12 132 ÷ 12 = 11

EXTENDED FACTS

110 x 12 = 1320 1320 ÷ 11 = 120

STORY ( drawing or oral )

I had 3 loose apples and two bags of apples. Each bag had the same number of apples. I

had 13 apples altogether.

Cross Out Singles

4

4

2 6

5

12

15

3 3

12

10

5

11

6 16

15 14

Add ‘em’ Ups

Score

54

Part 2: Computation

In this session, we will discuss:

• Number facts

• The four operations

• Mental computation for addition and

subtraction

• Written methods

By the end of this session:

• Understand the importance placed on

students’ knowledge of number facts

(basic facts)

• Understand that in real world situations,

most calculations are performed mentally

• Understand the need for students to

choose and use different strategies for

adding and subtracting

RECALL RELATED EXTENDED

Model or represent this number fact Can you create a story to match this number sentence?

CALCULATE Does the question require an exact answer or an estimate?

Which is the most efficient strategy for this number sentence?

What number facts are at the core of this calculation?

5 + 7 = [ ]

7 + 5 = [ ] 12 – 7 = [ ]

5 + [ ] = 12

50 + 70 = [ ]

120 = [ ] + 70

Children need to demonstrate more than

recall of number facts alone.

Number Cups

Arrange and rearrange the cups and

counters to make number facts and related

facts.

Number Cups

Turn the cups over. Arrange and rearrange

the cups to make extended facts.

Remember this question

What number fact is central to answering

this question?

RECALL RELATED EXTENDED

Model or represent this number fact Can you create a story to match this number sentence?

CALCULATE Does the question require an exact answer or an estimate?

Which is the most efficient strategy for this number sentence?

What number facts are at the core of this calculation?

3 x 8 = 24 24 ÷ 3 = 8 24000 ÷ 3 = 8000

3 x 8000 = 24000

What is the required number fact

knowledge?

I have forgotten

8 x 7?

I know 7x2=14 Double 14 is 28 Double 28 is 56

10 x 7 = 70 Take two 7s (14)

from 70 That’s 56

I know that 5 x 8 = 40 2 x 8 = 16

40+16 = 56

What do we do if my

child doesn’t know a

table fact?

1 2 3 4 5 6 7 8 9 10 80 8 40 16 32 64 24 48 72 56

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

Discussion

Most adults were shown one way to add and

subtract, multiply and divide.

30% of Australian adults are unable to use

the procedure that was drilled into us.

Often, these adults have ‘ANXIETY’ in

situations that involve calculation.

201 - 198 Jumped

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

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.

What does Australian

Curriculum expect? • Addition and subtraction facts by Year 3

• Multiplication and division facts by Year 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

What methods do we use as

adults?

38 + 57

72 - 28

Are you smarter than a 3rd grader?

Olivia is a Year 3 student at Caloundra

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.

Nearest to 1000

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?”

Conclusion

• The goal of school Mathematics is to

prepare students for 21st Century real-

world problems, at work and in daily life.

• Maths education is concerned with more

than ‘just getting the right answer’.

• Children can be confident, creative users

and communicators of mathematics.