The Big Picture of Numeracy

Numeracy Project Goal “To be numerate is to have the ability and inclination to use mathematics effectively – at home, at work and in the community” Published in Curriculum Update 45

Further Goals Develop multiple flexible thinking strategies Use mental and oral before written standard vertical forms Students make decisions about the smartest strategy to use on any given problem Teachers challenge children to achieve and develop a positive attitude towards learning Mathematics

Maths Strands Mathematics Strands Number and Algebra Geometry and Measurement Statistics

The Number Framework Number Knowledge Strategy

Number Framework Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Addition and Subtraction Multiplication and Division Ratios and Proportions

Numeracy Framework Each Numeracy Stage highlights key knowledge and strategy that a child should know Strong knowledge is essential for students to broaden their strategies across a full range of numbers Creates new knowledge through use Strategy Knowledge Provides the foundation for strategies

Relationship Between Knowledge and Strategy The number knowledge being developed at each level relates to the strategy at the same level

Relationship Between Knowledge and Strategy Place value and grouping and basic facts prepare a student for the next strategy stages StrategyPlace Value and Grouping and Basic Facts Stages 2-3 Addition and subtraction up to 5 Addition and subtraction with 5 Addition and subtraction up to 10 Addition and subtraction within 10 Adding and subtracting to 5 Doubles to 10 Patterns to 10 Groupings within ten Stage 4 Counting on to solve addition problems to 100 Counting back to solve subtraction problems to 100 Ten and facts Number of tens in decades Multiples that add to 100 Doubles to 20 Addition and subtraction to 10 Stage 5 Apply basic addition and subtraction facts and place value knowledge (part- whole, doubles) to solve problems

The Relationship Between Knowledge and Strategy Teachers teach knowledge at each stage before teaching strategy. Place value and basic facts knowledge and understanding comes out of strategy and then students commit these facts to memory Children need to understand the concepts behind the knowledge; e.g. our number system is based on ten

Emergent One to One Counting Counting From One (materials and Imaging) Advanced Counting Early Additive Advanced Additive Advanced Multiplicative Advanced Proportional

Our Numeracy Programme at Maungawhau School Children in the middle and senior school have workshops to address their identified learning needs (personalised learning) for Numeracy and Strand Children in the junior school are grouped according to their strategy stage using the NZ Number Framework and have personalised programmes for knowledge and basic facts

Teaching Model Teachers model and support children’s understanding using a researched teaching model i. Using materials ii. Imaging- Thinking about what would happen on the materials iii. Working only with numbers and apply the strategy to higher numbers Teachers teach to achieve next learning steps Working only with numbers Imaging Materials Using Materials

National Standards Expectations Curriculum Level Year Level After 1 Year (40 weeks) After 2 Years (80 weeks) After 3 Years (120 weeks) End of Year 4End of Year 5End of Year 6End of Year 7End of Year 8 Numeracy Stage B5P5A-6B6P6A78

Numeracy Strategy Stages  (E) Emergent  (CA) One to One Counting  (CA) Count from one on Materials  (CA) Count from one by Imaging  (AC) Advanced Counting Counting Strategies  (EA) Early Additive Part-Whole  (AA) Advanced Additive – Early Multiplicative Part-Whole  (AM) Advanced Multiplicative – Early Proportional Part Whole  (AP) Advanced Proportional Non - Counting Strategies

Strategy-Emergent Stage 0 Can you get me 7 counters from the pile please? Movie Clip 1,2,3,5,8...? The child can not consistently count a collection of objects.

Strategy- One to One Counting Stage 1 Can you get me 7 counters from the pile please? 1,2,3,4,5 6,7 The child can count a set of objects up to ten but can’t join and separate sets like =

Knowledge – Stage 0-1 Numbers to 10 The child can: Count objects to 10 Identifies numbers to 10 Writes numbers to 10 Counts forwards and backwards to 10 Knows finger patterns to 10 Orders numbers to 10 Says before and after, I more and 1 less Knows that numbers represent groups of objects Can match one to one when counting to 10

Expectations for

Strategy-Count From One on Materials Stage 2 There are 4 counters and another 4 counters. How many are there altogether? 1, 2, 3, 4, 5, 6, 7, 8 The child solves the problem by using their fingers or other materials and counts from one.

Strategy-Count From One By Imaging Stage 3 There are 4 counters and another 4 counters. How many are there altogether? Counts in head 1, 2, 3, 4, 5, 6, 7, 8 The child counts all the objects from one by imaging visual patterns of the objects in their mind.

Strategies – Stages 2-3 The child can: Addition and Subtraction Count all by using materials or imaging Multiplication and Division Solve simple problems by counting all Ratios and Proportions Solve simple problems by sharing out one by one

Number Knowledge- Stages 2-3 Numbers to 20 The child can: Count objects to 20 Identify numbers to 20 Write numbers to 20 Count forwards and backwards to 20 Order numbers to 20 Say before and after, I more and 1 less for numbers to 20 Skip count in 2s and 5s to 20 Identify half (1/2) and quarter (1/4)

Knowledge – Stages 2-3 The child knows from memory: Grouping and Place Value Groupings within 5 (4 + 1, 3+2) Groupings with 5 (5+3, 4+5) Groupings within 10 (e.g. 4+6) Basic Facts Addition and subtraction facts to 5 Doubles to 10 (3+3, 5+5)

Expectations for After Two Years

Strategy- Advanced Counting Stage 4 There are 9 counters under here and another 4 counters under there. How many are there altogether? I have 9 and 4 more. 10, 11, 12, 13. Counts on 10, 11, 12, 13. The child counts on from the larger number.

Strategy- Stage 4 Addition and Subtraction The child can: solve addition problems to 100 by counting on from the bigger number; e.g. 52+5= solve subtraction problems by counting back from the bigger number; e.g. 18-5= (-1 is 17, 16, 15….) solve problems like by skip-counting in tens Multiplication and Division solve problems that involve skip-counting in 2s, 5s and 10s Ratios and Proportions solve problems that involve skip-counting in 2s, 5s and 10s

Number Knowledge- Stage 4 Numbers to 100 The child can: Count objects to 100 Identify and write numbers to 100 Count forwards and backwards to 100 Order numbers to 100 Say before and after, I more and 1 less for numbers to 100 Skip count forwards and backwards in 2s, 5s and 10s to 100 Identify symbols and shapes for 1/2s, 1/3s, 1/4s, 1/5s

Knowledge - Stage 4 The child knows from memory: Grouping and Place Value Our number system is based on ten Groupings within 20 (14 + 6, 8+12) Groupings with 10 (10+3, 4+10) Number of tens in decades (6 tens in 60) Basic Facts Addition facts to 10 Subtraction facts to 10 Doubles to 20 (6+6, 8+8) Halves to 20 (1/2 of 12 is 6) Ten and ….facts Multiples of ten that add to 100 (60+40, 30+70)

Expectations for After Three Years

Strategy-Early Part-Whole Stage 5B There are 8 counters under there and another 6 counters under there. How many are there altogether? Bridging to Ten “I know that if I take two off the 6 and put it on the 8 it will = = 14” The child uses simple strategies such as known basic facts and doubles to solve addition and subtraction problems mentally.

Strategy- Stage 5P The child can: Addition and Subtraction apply basic facts; e.g. 8+8=16 so 58+8= 66 solve problems like 29+7= by splitting the 7 and making 30+6= solve problems like 21-4= by taking away 1 then 3. use place value to solve problems like 56+32= (5 tens and 3 tens or 50+30, 6 ones + 2 ones = 8 ones) Multiplication and Division use repeated addition; e.g. solves 6x5 by 5+5=10, =30 doubling and halving; e.g. 3x10= 30 so 6x5=30 Ratios and Proportions use repeated addition, halving and doubling to solve fractions problems

Number Knowledge- Stage 5 After 3 Years- progressing. At the End of 4 Years- achieved Numbers to 1000 The child can: Identify and write numbers to 1000 Count forwards and backwards to 1000 in 1s, 10s and 100s Order numbers to 1000 Say before and after, I more and 1 less for numbers to 1000 Skip count forwards and backwards in 2s, 3s, 5s and 10s to 100 Identify symbols for 1/2s, 1/3s, 1/4s, 1/5s, 1/10s and improper fractions Order fractions with common denominators (1/4, 2/4, ¾)

Knowledge-Stage 5 After 3 Years- progressing. At the End of 4 Years- achieved The child knows from memory: Grouping and Place Value Groupings within 100 ( , 73+27) Groupings of 2 in numbers up to 20 Groupings of 5 in numbers up to 50 Groupings of 10 that can be made from a 3 digit number The number of 100s in centuries and thousands Rounding 3 digit whole numbers to nearest 10 or 100 Basic Facts Addition facts to 20 Subtraction facts to 10 2x, 5x, 10x tables and their related division facts Multiples of 100 that add to 1000 ( )

Expectations for At the End of Year 4

Strategy- Stage 5A The child can: Addition and Subtraction Solve addition like by 59+20=79, 79+(1+5)=85 Or as = 85 Solve subtraction like 83-9 by 83-3=80, 80-6=74 Multiplication and Division Use basic multiplication and division facts to solve problems (2x, 5x, 10x) Ratios and Proportions Use basic multiplication and division facts to solve problems (2x, 5x, 10x) Use repeated halving or repeated addition

Expectations for At the End of Year 5

Advanced Part-Whole Stage 6 63 people are on the bus and 39 people get off the bus. How many people are left on the bus? I think tidy numbers would be smartest. 63 – 40 = = 24 The child can select from a wide range of strategies to solve various addition and subtraction problems mentally

Strategy – 6P The child can: Addition and Subtraction Use and explain at least two effective strategies to solve problems like and Multiplication and Division Solve problems like 20x 6 and how many twos in 48 by using multiplication and addition facts or halving and doubling Ratios and Proportions Solve problems like 4/10 of 60 by using multiplication and addition facts or halving and doubling

Knowledge- Stage 6 After 5 Years- progressing. At the End of 6 Years- achieved Numbers to 1 million The child can: Identify and writes numbers to 1 million Count forwards and backwards to 1 million in 1s, 10s, 100s and 1000s Order numbers to 1 million forwards and backwards Say 1, 10, 100, 1000 before and after, for numbers to 1 million Say forwards and backwards sequences for 1/2s, 1/4s, 1/5s and 1/10s Order decimal number sequences forwards and backwards in tenths and hundredths. Identify symbols for 1/10s, 1/100s, 1/1000s and improper fractions Order unit fractions for halves, quarters, thirds, fifths and tenths. E.g. ½, 1/3, ¼

Knowledge- Stage 6 After 5 Years- progressing. At the End of 6 Years- achieved The child instantly knows: Grouping and Place Value groupings within 1000 ( , ) groupings of 2, 3, 5 or 10 in numbers up to 100 and remainders groupings of 10 and 100 that can be made from a 4 digit number and remainder tenths and hundredths in decimals to 2 places How to round 3 digit whole numbers to nearest 10, 100 or 1000 How to round decimals with up to 2 places to the nearest whole number. Basic Facts addition and subtraction facts to 20 multiplication and division facts up to 10 times tables multiplication of basic facts with tens, hundreds, thousands

Expectations for At the End of Year 6

Strategy - 6A The child can: Addition and Subtraction Solves problems mentally by using several efficient place value strategies to solve problems like Multiplication and Division Solve multiplication problems that involve two steps for problems like 18x5 Ratios and Proportions Solve problems like 4/10 of 60 by using multiplication and division facts

Advanced Multiplicative Stage 7 There are 28 fruit trees in each row of the orchard. There are 6 rows. How many trees are there altogether? Tidy Numbers would be a smart strategy. 30 x 6 = – (2 x 6) = 168 The child can select from a wide range of strategies to solve various multiplication and division problems mentally.

Advanced Proportional Stage 8 You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool? I can see that 9:15 are both multiples of 3. I can simplify by ÷3 and get a ratio of 3:5 ?:10 = 6 The child can select from a wide range of strategies to solve challenging problems involving, decimals, fraction percentages and ratios.

Assessment Teachers use a variety of tasks (informal and formal) to form our Overall Teacher Judgements (OTJs) National Standards JAM- Junior Assessment of Maths Maths illustrations

Supporting At Home Making the most of everyday activities See the school website for activities Mathletics Maths Websites