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## Effective Numeracy Workshop 1 Your facilitator is Marie Hirst

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**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**Year Level**Favorite subject to teach Country of Birth 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.”**Knowledge**Strategy Time to think! 10 + 4 53 - 26**Knowledge**Strategies Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Addition & Subtraction Multiplication & Division Fractions and Proportions The Number Framework:Book One**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, ……..**9 8**+ 6 9 8 + 6 Rule Following Without Understanding Understanding is the Key 9 14 15 8 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.**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?**Yes**I work out the answer Can I work out the answer mentally? No calculator pencil Will I use pencil and paper or a calculator? I work out the answer I work out the answer I mentally estimate the answer as a check The written form**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**TEAM A**10 9 8 7 6 5 4 2 3 1 Bowl A Fact (Bk 4 p35) TEAM B 10 9 8 7 6 5 4 2 3 1**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?**Knowledge**Strategies Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Addition & Subtraction Multiplication & Division Fractions and Proportions The Number Frameworks**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? • 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**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 Assessment**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 4 (AM Stage 7)**Which number is the same as ?**1 3 5 5 3 2 3 12 20 4 6 Question 1**1**2 4 8 50 100 8 17 3 6 Question 2 Which fraction does not equal ?**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.**Knowledge**Strategies Addition & Subtraction Multiplication & Division Fractions and Proportions Number Identification Number Sequence and Order Grouping and Place Value Basic Facts IKAN Formative assessment GloSS Formative 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 will you group your children?**How many maths groups will you have? How many children will be in each group? How many groups will you teach a day? How long will you spend with 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**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? 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.