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 StrategyPlace value and grouping and basic facts prepare a student for the next strategy stages

Strategy Place Value and Grouping and Basic Facts

Stages 2-3Addition 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 5Doubles to 10

Patterns to 10Groupings within ten

Stage 4Counting on to solve addition problems to 100Counting back to solve subtraction problems to 100

Ten and factsNumber of tens in decadesMultiples that add to 100Doubles to 20Addition and subtraction to 10

Stage 5Apply 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

EmergentOne 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 materialsii. Imaging- Thinking about what would happen on the materialsiii. Working only with numbers and apply the strategy to higher numbers

• Teachers teach to achieve next learning steps

Working only with numbers

ImagingMaterials

UsingMaterials

National Standards Expectations

Curriculum Level

1

2 3 4 5

Year Level After 1 Year(40 weeks)

After 2 Years(80 weeks)

After 3 Years(120 weeks)

End of Year 4 End of Year 5 End of Year 6 End of Year 7 End of Year 8

Numeracy Stage

2-3 4 - 5B 5P 5A-6B 6P 6A 7 8

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 4 + 3 =

Knowledge – Stage 0-1

Numbers to 10The 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 objectsCan match one to one when counting to 10

Expectations for

Strategy-Count From One on MaterialsStage 2

There are 4 counters and another 4 counters. How many are there altogether?

1, 2, 3, 4, 5, 6,

7, 8The child solves the problem by using their fingers or other materials and counts from one.

Strategy-Count From One By ImagingStage 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 imagingMultiplication and Division• Solve simple problems by counting allRatios and Proportions • Solve simple problems by sharing out one by

one

Number Knowledge- Stages 2-3

Numbers to 20The 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 CountingStage 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 SubtractionThe 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 54 +30 by skip-counting in tensMultiplication and Division• solve problems that involve skip-counting in 2s, 5s and 10sRatios and Proportions• solve problems that involve skip-counting in 2s, 5s and 10s

Number Knowledge- Stage 4

Numbers to 100The 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 ValueOur 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-WholeStage 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 =10.

10 + 4 = 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, 10+10+10=30• doubling and halving; e.g. 3x10= 30 so 6x5=30Ratios and Proportions• use repeated addition, halving and doubling to solve fractions

problems

Number Knowledge- Stage 5After 3 Years- progressing. At the End of 4 Years- achieved

Numbers to 1000The 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 5After 3 Years- progressing. At the End of 4 Years- achieved

The child knows from memory:

Grouping and Place Value• Groupings within 100 (49 + 51, 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 100Basic 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 (400+600)

Expectations for

At the End of Year 4

Strategy- Stage 5A

The child can:Addition and Subtraction• Solve addition like 59+26 by 59+20=79, 79+(1+5)=85 Or 59+26 as 60+25 = 85• Solve subtraction like 83-9 by 83-3=80, 80-6=74Multiplication 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-WholeStage 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 = 23 23 + 1 = 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 236+57 and 95-37Multiplication 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 6After 5 Years- progressing. At the End of 6 Years- achieved

Numbers to 1 millionThe 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 6After 5 Years- progressing. At the End of 6 Years- achieved

The child instantly knows:Grouping and Place Value• groupings within 1000 (498 + 502, 250+750)• 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 - 6AThe child can:

Addition and Subtraction• Solves problems mentally by using several efficient

place value strategies to solve problems like 341-75Multiplication and Division• Solve multiplication problems that involve two

steps for problems like 18x5Ratios and Proportions• Solve problems like 4/10 of 60 by using

multiplication and division facts

Advanced MultiplicativeStage 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 = 180180 – (2 x 6) = 168

The child can select from a wide range of strategies to solve various multiplication and division problems mentally.

Advanced ProportionalStage 8

You can make 9 mittensfrom 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