effective numeracy workshop 1 your facilitator is marie hirst

Effective Numeracy Workshop 1

Your facilitator isMarie Hirst

Objectives

• Become familiar with the New Zealand Number Frameworks and how they relate to the Curriculum.

• Know how to use GloSS and IKAN numeracy assessment tools and analyse the data to inform future teaching and learning.

• Become familiar with numeracy resources including the www.nzmaths.co.nz website

Year Level

Country of Birth

Favorite subject to

teach

Familiarity with teaching numeracy (0-10)

Introductions – Get in line!

• Name, School,

• What do you already know about the Numeracy Project

• What are you hoping to get out of this PD session.

Are Ma and Pa numerate?

The Ministry definition:

“To be numerate is to have the ability and inclination to use mathematics effectively- at home, at work and in the community.”

Time to think!

10 + 4

53 - 26

Knowledge

Strategy

The Number Framework:Book One

StrategiesKnowledge

Number Identification

Number Sequence and Order

Grouping and Place Value

Basic Facts

Addition & Subtraction

Multiplication & Division

Fractions and Proportions

53 - 26

Strategy – your turn!

There are 53 people on the bus. 26 people get off, how many people are left on the

bus?

Exploring Strategy

It’s not just if I get the answer right.

It’s how I solved it that’s important

Consider 4 children solving 99 + 5

A did 99 + 1 100 + 4 104

B did 99, 100, 101, 102, 103, 104

C did 9 + 5 = 14, put down the 4 carry the 1…..

D did 1, 2, 3, 4, 5, 6, ……..

Understanding is the Key

9 8

+ 6

9 8

+ 6149 815

Rule Following Without Understanding

Consider reading without comprehension or cooking without a recipe!

The NZ Number Framework Stage 1 One to One Counting

Stage 2 Counting from One on Materials

Stage 3 Counting from One by Imaging

Stage 4 Advanced Counting

Stage 5 Early Additive Part-Whole

Stage 6 Advanced Additive Part-Whole

Stage 7 Advanced Multiplicative Part-Whole

Stage 8 Advanced Proportional Part-Whole

Counting Strategies

Grouping Strategies

The NZ Number Framework Stage 1 One to One Counting

Stage 2 Counting from One on Materials

Stage 3 Counting from One by Imaging

Stage 4 Advanced Counting

Stage 5 Early Additive Part-Whole NZC Level 2

Stage 6 Advanced Additive Part-Whole NZC Level 3

Stage 7 Advanced Multiplicative Part-Whole NZC Level 4

Stage 8 Advanced Proportional Part-Whole NZC Level 5

Counting Strategies

NZC Level 1

Part-whole Strategies

Book One: The Number Framework

Strategy Framework pages 15-17

Where did the framework come from?

Lets take a look at some children on different stages of the strategy number framework.

There are 6 baskets with 24 muffins in each basket. How many muffins are there altogether?

Stage 7 (NZC Level 4)

Advanced Multiplicative Strategies

Stage 8 (NZC Level 5)Advanced Proportional Strategies

It takes 10 balls of wool to make 15 beanies. How many balls of wool does it take to make 6 beanies?

The written form

I mentally estimate the

answer as a check

Will I use pencil and paper or a

calculator?

I work out the answer

I work out the answer

calculatorpencil

No

Can I work out the answer mentally?

I work out the answer

Yes

The NZ Number Framework Stage 1 One to One Counting

Stage 2 Counting from One on Materials

Stage 3 Counting from One by Imaging

Stage 4 Advanced Counting

Stage 5 Early Additive Part-Whole NZC Level 2

Stage 6 Advanced Additive Part-Whole NZC Level 3

Stage 7 Advanced Multiplicative Part-Whole NZC Level 4

Stage 8 Advanced Proportional Part-Whole NZC Level 5

Counting Strategies

NZC Level 1

Part-whole Strategies

“Success doesn’t come from the way you think it does,…

it comes from the way you think!”

Schuler

Bowl A Fact (Bk 4 p35)

10 9

5 4

78

2

1

3

6

TEAM A

10 9

5 4

78

2

1

3

6

TEAM B

Numeracy Assessments

What do you remember from our first session?

What is strategy?

What is knowledge?

What is Part-Whole thinking?

Assessing Strategy using GloSS

• Assesses strategies for solving add/sub, mult/div and proportions problems against the number framework.

• There are 5 different versions of the GloSS assessment on nzmaths.co.nz (H, I, J, K, L)

• One-on-one oral interview with each child. (should take between 5 - 20 mins)

Assessing strategy Practice

In groups of 3 assess students

N.B. Write questions on the

form first!

What does a GloSS stage mean?

Harry solved 8 + 5 by going 5 + 5 + 3 = 13

- What does this mean? What stage is he?

- Is this an instructional or an achieved stage?

- Use his thinking to solve 7 + 9

- What may be his next learning step?

Curriculum Expectations

The Number Frameworks

StrategiesKnowledge

Number Identification

Number Sequence and Order

Grouping and Place Value

Basic Facts

Addition & Subtraction

Multiplication & Division

Fractions and Proportions

Knowledge & Strategy are equally important

29 + 7 = 36

Strategy: I did 29 + 1 = 30 then 30 + 6 = 36

What knowledge did I need?

Exploring Number Knowledge

Important pieces of information I should

know instantly(i.e. within 3

seconds)

Numeral ID, Sequencing & Ordering, Grouping /Place Value, Basic facts

Book One: The Number FrameworkNumber Knowledge Framework p.18 - 22

What Stage Am I? What do I need to learn next?

•Basic Facts: I know my doubles and halves to 20•Numeral ID: I can read and order numbers to 1000•Place Value: I know how many tenths are in decimal numbers?•Basic Facts: I know my x2 x5 and x10 facts

Numeral ID, Sequencing & Ordering, Grouping /Place Value, Basic Facts

Assessing Number Knowledgefor Stages 0-3 : Oral Interview(1) Start counting from 1. Stop at 32.

(2) Count backwards from 10. Stop at zero.

(3) Count backwards from 23. Stop at 11.

Show each number (on card). For each number ask:

What is this number? What number comes after this?

What number comes before this?

(4) 1 (5) 5 (6) 9 (7) 12

(8) 19 (9) 14 (10) 31 (10) 80

(11) 100 (12) 409 (13) 870

Look for confusions between

‘teen’ and ‘ty’

Assessing Number knowledge for stages 4+ using IKAN on nzmaths

IKAN AssessmentThis is a knowledge test so the questions come then go quite quickly.The questions start easy then get harder.Try to answer as many questions as you can but if they get too hard read a book quietly.

Bank 4 (AM Stage 7)

Question 1

Which number is the same as ?

1

35

53

23

1220

46

Question 2

Which fraction does not equal ?

12

48

50100

817

36

Question 3

Which decimal is bigger, 0.639 or 0.84?

Question 4

Which decimal is smaller, 2.7 or

1.987?

Question 5

How many hundredths are in all of 3.04?

Question 6

63 ÷ 9 = ?

Question 7

÷ 7 = 6?What number divided by

seven gives six?

Question 8

Write all the factors of 81.

Addition & Subtraction

Multiplication & Division

Fractions and Proportions

Number Identification

Number Sequence and Order

Grouping and Place Value

Basic Facts

StrategiesKnowledge

IKANFormative assessment

GloSSFormative assessment

Great we have done the numeracy assessments now

what?

You don’t do an assessment you use an assessment!!

Effective Teaching Cycle

Assessing

Analysing data

Planning

Teaching

Practicing / Applying

Analysing numeracy data• Look at Harry’s completed GLoSS and IKAN

recording form.• Collate his data onto the class summary grid.

• What does this tell you about Harry?

•Any correlation between strategy and knowledge?

•What range of abilities is there in the class - How do these relate to expectations?

•How might you group your students for teaching?

•Any common knowledge gaps for whole class teaching?

How long will you spend with each

group?

How will you group your children?

How many groups will you teach a day?

How many maths groups will you

have?How many children will be in

each group?

Lesson Structures (Book 3 p.12)Whole class, ability groups, mixed-ability groups, individual

Problem Solving

Legs in the barn(Taken from www.nzmaths.co.nz)

One third of the animals in the barn are chickens. The rest are pigs. There are 20 legs in

all. How many pigs are there?

4

Solution: Now if 80% of the class plays tennis, 20% don’t play tennis. This 20% must be part of the golf players. So they play golf but not tennis. This means that the remaining 50% play both tennis and golf.

Problem Solving from nzmaths

Tennis and Golf Players (Level 4)In a class in the school down the road,

everyone plays tennis or golf or both. In fact 80% play tennis and 70% play golf. What

percentage plays both games?

Number Fans p.4

Assessing

Analysing data

Planning

Teaching

Practicing / Applying

Now I understand the data - how do I use it for planning and teaching?

Teaching Number Knowledge

Numeral Identification

Sequencing and Ordering

Grouping & Place Value

Basic Facts

Number Knowledge Planning Units (on the wikispace)

Using Book 4Knowledge Domain Pages

Number (and Fraction) Identification

2 - 10

Number (and Fraction) Sequence and Order

11 - 21

Grouping and Place Value 22 - 31

Basic Facts 32 - 38

Using Book 4

E Emergent (Stage 0)

CA Count All (Stages 1,2,3)

AC Advanced Counting (Stage 4)

EA Early Additive (Stage 5)

AA Advanced Additive (Stage 6)

AM Advanced Multiplicative (Stage 7)

AP Advanced Proportional (Stage 8)

Thousands Book, Book 4 p.16

• What is the learning intention?• Which stages is it appropriate for?• What equipment is needed (any MM?)• How could you adapt / extend the activity?• Could it be used for whole class, group

teaching, or adapted for independent work?

• Choose an activity. • Practice • Share with another group

Using Book 4: Teaching Number Knowledge

Y1-3Number Mat p.2Tens Frames p.2Thousands Book p.16Tens and Ones p.23

Y4-6Arrow Cards p.13 Zap! P.26Number Line Flips p.15Squeeze p.15Traffic Lights p.25Close to 100 p.24

Y7-8Zap p.26Close to 100 p.24In and Out p.36Reading Decimal Fractions P.8Who Gets More? P.20Multiplication Madness p.36

Hand Game

Teaching Practising Assessing

Which of the basic facts activities in your classroom are focusing on teaching?

A focus on basic facts

+

Study this grid

What was + ?

• While you were studying the grid what were you looking for?

Teaching Basic Addition Facts to 20

An adaptation of work by Peter Hughes

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9

The commutative lawi.e. 3 + 4 = 4 + 3

+ 0 + 19

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9

Addition to and with 5 (stage 2)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

1 + 4

2 + 3

5 + 1

5 + 2

5 + 3

5 + 4

5 + 5

Groupings to 10 (Stage 3)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

1 + 9

2 + 8

3 + 7

4 + 6

Doubles to 10 (stage 4)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

1 + 1

2 + 2

3 + 3

4 + 4

5 + 5

Doubles to 20 (Stage 4)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

6 + 6

7 + 7

8 + 8

9 + 9

10 + 10

Teen Numbers (stage 4)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

Remaining facts to 10 (stage 4)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

2 + 4

2 + 6

2 + 7

3 + 4

3 + 6

Facts to 20 - Near Doubles (Stage 5)

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

5 + 6

6 + 7

7 + 8

8 + 9

9 + 10

Facts to 20 - Add 9 (stage 5)use a thousands book or hundreds board

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

2 + 9

3 + 9

4 + 9

5 + 9

6 + 9

7 + 9

8 + 9

Remaining Facts to 20 (stage 5)‘make the ten’

10

9

8

7

6

5

4

3

2

1

0

+ 0 1 2 3 4 5 6 7 8 9 10

3 + 8

4 + 7

4 + 8

5 + 7

5 + 8

Assessing

Analysing data

Planning

Teaching

Practicing / Applying

Effectively Teaching Basic Facts

In groups number yourself 1 to 5

1. Figure It Out / Group Box with group profile2. Squeezy Boxes3. Snakes and Chances / Jigsaws4. MM Flashcards / Facts on a ring 5. Slidey Cards/ basic facts flips6. Card Games / Salute

Practice Activities

Putting it all together – and developing an

independent classroom programme.

Possible Whole Class Lesson StructureBook 3: Getting Started p.13

10 mins

Whole class

Whole class teaching (Number knowledge)

30-45 mins

Group 1 Teacher (Strategy or Knowledge)Practice

Group 2 Activity (Problem Solving, Games, Investigations etc.)

Teacher (Strategy or Knowledge)

Group 3 PracticeActivity (Problem Solving, Games, Investigations etc.)

5 mins

Warm Down

Groups report back and share their learning

Possible Group Lesson StructureBook 3: Getting Started p.13

Independent Activity• Group box with targeted maths activities/games

• Problem Solving (from nzmaths website / Figure It Out, etc

• Strand maintenance

• Bookwork (Textbooks, Figure It Out, worksheets etc).

• Computer: (CD Roms, Digital Learning Objects, create powerpoint)

• Other resources (e.g.Think Tank, Pearson Independent Cards),

• Learning Centres; (e.g basic facts, investigations, logical thinking)

• Juniors: Tactile (e.g.mobilo, playdough etc).

What do you currently use as part of your independent maths

programme?

Weekly Plan ExampleWeekly Planning Template Book 3: Getting Started p.24

Communicating with the student what they can do and what their next steps

are.

Using Student or Group Profiles (nzmaths or wiki)

www.nzmaths.co.nz/

Effective Numeracy teaching is about…

Students

– thinking mathematically rather than remembering mathematical rules.

Teachers

– using the number framework to identify where a student is at and develop next steps.

– using concrete material to develop a greater conceptual understanding of number properties

– developing pedagogical content knowledge to effectively address misconceptions.

It is not about…

• Groups• Games• Number

Although all three of these may be part of successful implementation…

Objectives of this workshop• Become familiar with the New Zealand Number Frameworks

and how they relate to the Curriculum.

• Know how to use GloSS and IKAN numeracy assessment tools and analyse the data to inform future teaching and learning.

• Become familiar with numeracy resources including the nzmaths website

• Next 3 workshops: content workshops focusing on: Addition/Subtraction, Multiplication/Division, and Proportions

Any Questions?

A final thought

We all get heavier as we get older, as there’s a lot more information in our

heads!

Our Cluster Wiki Space:http://mathsleadteachers.wikispaces.com

National Maths Website:

www.nzmaths.co.nz