Effective Numeracy Workshop 1 Your facilitator is Marie 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

The Ministry definition: 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.”

Introductions – Get in line! Name, School, Year Level What do you already know about the Numeracy Project What are you hoping to get out of this PD session.

Time to think! 10 + 4 53 - 26 Knowledge Strategy

The Number Framework:Book One Strategies Knowledge Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Addition & Subtraction Multiplication & Division Fractions and Proportions

Strategy – your turn! There are 53 people on the bus. 26 people get off, how many people are left on the bus? 53 - 26

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 Rule Following Without Understanding Understanding is the Key 9 8 + 6 9 8 + 6 9 14 15 8 Consider reading with 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

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.

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 Level 2 Stage 6 Advanced Additive Part-Whole Level 3 Stage 7 Advanced Multiplicative Part-Whole Level 4 Stage 8 Advanced Proportional Part-Whole Level 5 Counting Strategies NZC Level 1

Advanced Multiplicative Strategies Stage 7 (NZC Level 4) Advanced Multiplicative Strategies There are 6 baskets with 24 muffins in each basket. How many muffins are there altogether?

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 Yes Can I work out the answer mentally? No calculator I mentally estimate the answer as a check Will I use pencil and paper or a calculator? I work out the answer calculator pencil No Can I work out the answer mentally? Yes

Aligning the Number Framework to the New Zealand Curriculum Stage 1 One to One Counting Stage 2 Counting from One on Materials Level One Stage 3 Counting from One by Imaging Stage 4 Advanced Counting Stage 5 Early Additive Part-Whole Level Two Stage 6 Advanced Additive Part-Whole Level Three Stage 7 Advanced Multiplicative Part-Whole Level Four Stage 8 Advanced Proportional Part-Whole Level Five

“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 7 8 2 1 3 6 TEAM A TEAM B 10 9 8 7 6 5

Numeracy Assessments

What do you remember from our first session? What is strategy? What is knowledge? What is Part-Whole thinking? Brainstorm and discuss in groups what method of assessment have they used in your current schools or in a school that you have come from. 21

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 - 15 mins)

Assessing strategy Practice In groups of 3 assess students

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 Strategies Knowledge 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 Numeral ID, Sequencing & Ordering, Grouping /Place Value, Basic facts Important pieces of information I should know instantly (i.e. within 3 seconds)

Book One: The Number Framework Number Knowledge Framework p.18 - 22 Numeral ID, Sequencing & Ordering, Grouping /Place Value, Basic Facts What Stage Am I? What do I need to learn next? I know my doubles and halves to 20 I can read and order numbers to 1000 I know how many tenths are in decimal numbers? I know my x2 x5 and x10 facts

Assessing Number Knowledge for 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 Assessment Bank 3 (AA Stage 6) This 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 3 (AA Stage 6)

What number is one more than 439 999? Question 1 What number is one more than 439 999?

What number is one less than 801 000? Question 2 What number is one less than 801 000?

Which number is the same as ? Question 3 Which number is the same as ? 48 8 3 12 4 1 3

Question 4 Write 4 as a fraction. 1 5

How many hundreds are in 35 600? Question 5 How many hundreds are in 35 600?

How many tenths are in all of the number, 5.8? Question 6 How many tenths are in all of the number, 5.8?

Question 7 15 - 8 = ?

Question 8 6 x 7 = ?

Strategies Knowledge IKAN GloSS Addition & Subtraction Multiplication & Division Fractions and Proportions Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Strategies Knowledge IKAN Formative assessment GloSS

Great we have done the numeracy assessments now what 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?

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

Number Fans p.4 Starter must link it back. What is knowledge in their teaching? Where does it fit in the framework? How may we might make the game harder? Facts to share = So you won’t have to invent new games. You can play any game. Instructions Deal the cards, two or three play. Only two put a card above their head so they cannot see. Take all the picture cards out. Important to see how knowledge is being developed. How can you develop this game in your class. Juniors can use pictures of animals or sticks. Formative thinking. Multiplication – talk about the reversible of multiplication. Place yourself on a Continuum - where would you be in this continuum one end as expert and the other as absolutely novice? Share with a partner why you placed yourself there. 47

(Taken from www.nzmaths.co.nz) 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

Now I understand the data - how do I use it for planning and teaching? Assessing Analysing data Planning Teaching Practicing / Applying

Possible Whole Class Lesson Structure Book 3: Getting Started p.13

Possible Group Lesson Structure Book 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.) Group 3 5 mins Warm Down Groups report back and share their learning

Teaching Number Knowledge Numeral Identification Sequencing and Ordering Grouping & Place Value Basic Facts

Number Knowledge Planning Units (on the wikispace)

Using Book 4 Using Book 4 Knowledge Domain Pages E Emergent (Stage 0) Number (and Fraction) Identification 2 - 10 Number (and Fraction) Sequence and Order 11 - 21 Grouping and Place Value 22 - 31 Basic Facts 32 - 38 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?

Using Book 4: Teaching Number Knowledge Number Mat p.2 Tens Frames p.2 Arrow Cards p.13 and Zap! P.26 Number Line Flips p.15 Squeeze p.15 Hundreds Board p.16 Tens and Ones p.23 Close to 100 p.24 Traffic Lights p.25 In and Out p.36 Look at the class data and find a knowledge hotspot. Use book 4 to pick an appropriate teaching activity.

A focus on basic facts Hand Game Teaching Practising Assessing Which of the basic facts activities in your classroom are focusing on teaching?

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 +

The commutative law i.e. 3 + 4 = 4 + 3 9 8 7 6 5 4 3 2 1 +

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

Addition to and with 5 (stage 2) 10 9 8 7 6 5 4 3 2 1 + 1 + 4 2 + 3 5 + 1 5 + 2 5 + 3 5 + 4 5 + 5

Groupings to 10 (Stage 3) 1 + 9 2 + 8 3 + 7 4 + 6 10 9 8 7 6 5 4 3 2 1 + 1 + 9 2 + 8 3 + 7 4 + 6

Doubles to 10 (stage 4) 1 + 1 2 + 2 3 + 3 4 + 4 5 + 5 10 9 8 7 6 5 4 3 + 1 + 1 2 + 2 3 + 3 4 + 4 5 + 5

Doubles to 20 (Stage 4) 6 + 6 7 + 7 8 + 8 9 + 9 10 + 10 10 9 8 7 6 5 4 3 2 1 + 6 + 6 7 + 7 8 + 8 9 + 9 10 + 10

Teen Numbers (stage 4) 10 9 8 7 6 5 4 3 2 1 +

Remaining facts to 10 (stage 4) 9 8 7 6 5 4 3 2 1 + 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 + 5 + 6 6 + 7 7 + 8 8 + 9 9 + 10

Facts to 20 - Add 9 (stage 5) use a thousands book or hundreds board 2 + 9 3 + 9 4 + 9 5 + 9 6 + 9 7 + 9 8 + 9 10 9 8 7 6 5 4 3 2 1 +

Remaining Facts to 20 (stage 5) ‘make the ten’ 10 9 8 7 6 5 4 3 2 1 + 3 + 8 4 + 7 4 + 8 5 + 7 5 + 8

Effectively Teaching Basic Facts Assessing Analysing data Planning Teaching Practicing / Applying

In groups number yourself 1 to 5 Practice Activities Figure It Out / Group Box with group profile Squeeze Boxes Snakes and Chances / I have Who has / jigsaws MM Flashcards Facts on a ring Slidey Cards Card Games / Salute

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

Using Student or Group Profiles

Creating an Engaging and Effective Numeracy Classroom Environment

Putting it all together – and developing an independent classroom programme.

What do you currently use as part of your independent maths programme? 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).

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

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

Any Questions?

Some things to think about The curriculum and the standards are based on students doing mathematics for 4 hours per week for 38 weeks of the year. When will your classroom programme be up and running ready for teaching in Term 1? Reflect on 3 things from this workshop that you think you will implement in your classroom?

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