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To Be Numerate ……

Maths Information for Parents

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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:

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Goals – We want our students to:

Use mental strategies and confidently explain orally before written standard vertical forms

Use a range of strategies and make decisions about using the most effective strategy to work out any given problem.

Achieve and develop a positive attitude towards learning mathematics while enjoying the challenge of problem solving

Develop multiple flexible thinking strategies

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The Big Picture of Numeracy and Maths

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Maths Strands

MATHEMATICS(Balance shifts

as students progress)

Number and Algebra

Geometry and Measurement

Statistics

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Number

NUMBERFRAMEWORK

Number Knowledge Strategy

Number Identification

Number Sequence and Order

Grouping and Place Value

Basic FactsAddition

and Subtraction

Multiplicationand

Division

Proportionsand

Ratios

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The Balance of StrandNumber and Algebra is the most important strand.

The balance shifts as students progress through the stages. A guide to this is:

Stages Time Spent on Number and Algebra

Time spend on other strands (Geometry and Measurement, Statistics)

1-4 80% 20%

5 70% 30%

6 60% 40%

7 50% 50%

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The NZ 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.

Strategy Knowledge

Creates new knowledge through use

Provides the foundation for strategies

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Knowledge and Strategy• Knowledge – • Number Identification • Number Sequence and Order • Grouping and Place Value • Basic Facts

• Strategy – Three domains• Addition and Subtraction • Multiplication and Division• Ratios and Proportions

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Knowledge Before StrategyIt is essential that students have sound knowledge for

the strategies they are developing; e.g.

Knowledge Strategy

Stages 1-3Numbers to 20-order, before and after

Counting all to solve addition, subtraction and multiplication problems to 10

Stage 4Numbers to 100- order, before and afterSkip counting in 2s, 5s and 10s to 100

Addition and Subtraction to 100 by counting on and counting backSkip count to solve multiplication problems

Stage 5Numbers of tens and hundreds in three digit numbersKnows 2, 5 and 10 x tables

Use place value to solve addition and subtraction problemsApply simple multiplication facts to solve problems

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Developmental Stage Progression

The New Zealand Number Framework

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Number Framework

NUMBERKNOWLEDGE

Number Identification

Number Sequence and Order

Basic FactsGrouping and Place Value

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Number Identification & Ordering

Stages 6 - 8 1- 1 000 000 &decimals to 3 places

Stages 0-1 1-10

Stages 2-3 1-20

Stage 4 1-100 & ½, 1/3, ¼, 1/5

Stage 5 1-1000 & improper fractions

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Grouping and Place Value

Stages 6 groupings within 1000, groupings of 2, 3, 5 and 10 in 100, groupings of 2, 3, 5, & 10 in 4 digit numbers (& remainders)tenths and hundredths in decimals to (2 places)

Stages 1- 3 within 5, with 5, within 10, patterns to10.

Stage 4 groupings with 10 and 20, number of tens in decades

Stage 5 groupings within 100, groups of 10s, 100s & 1000s in 4 digit numbers

Stages 7 groupings of all numbers up to 10 in 100 (& remainders)groupings of 10s,100s &1000s in (up to) 7 digit numbersequivalent fractions

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Basic Facts

Stages 6 addition & subtraction facts to 20

multiplication facts up to 10x (& some corresponding division facts)

multiplication facts with 10s, 100s & 1000s

Stages1- 3 addition and subtraction facts to 5, doubles to 10

Stage 4 addition and subtraction facts to 10, doubles to 20, ten and facts, multiples of ten that add to 100

Stage 5 addition facts to 20, subtraction facts to10, 2x, 5x and 10x timetables, hundreds that add to 1000

Stages 7/8 division facts up to 10x tablesconversions (fractions/decimal/percentage) factors, common multiples, divisibility rules & square roots

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How is maths taught differently now?

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Teaching Model• Model and support children’s

understanding using a researched teaching model

• Steps for when a new strategy is introduced

i. Using materials ii. Thinking about what would happen on the materials iii. Working only on numbers and applying strategy to higher numbers

• Teach to achieve next learning steps Working only with numbers

ImagingMaterials

UsingMaterials

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The use of equipment is essential when developing new strategies

Bridging to Ten

Happy Hundreds

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Numeracy Strategy StagesEmergent One to One CountingCount from one on Materials Count from one by ImagingAdvanced Counting

Counting Strategies

Early Additive Part-WholeAdvanced Additive Part-WholeAdvanced MultiplicativeAdvanced Proportional

Non - Counting Strategies

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Examples of Strategies for each Stage

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Emergent Stage 0

Can you get me 7 counters from the pile please?

1,2,3,5,8...?

The child can not consistently count a collection of objects.

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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 =

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Count From One on MaterialsStage 2

There are 4 counters and another 3 counters. How many are there altogether?

1,2,3,4,5,6,7

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

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Count From One By ImagingStage 3

There are 4 counters and another 3 counters. How many are there altogether? Counts in head

1,2,3,4,5,67 The child counts all the objects from one by imaging visual patterns of the objects in their mind.

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Advanced CountingStage 4

There are 9 counters under there and another 4 counters under there. How many are there altogether? Counts on 9, 10, 11, 12, 13.

The child counts on from the largest number.

To be achieving at Stage 4 a child needs to be able to solve problems such as

49 + 4 =

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Early Part-WholeStage 5 (Early Stage 5)

There are 9 counters under there and another 6 counters under there. How many are there altogether?

Take one off the 6 and put it on the 9 it =10 so 10 + 5 = 15

The child uses simple strategies to solve addition and subtraction problems

mentally

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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

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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.

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Advanced ProportionalStage 8

You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool? The child sees that 9:15 are both

multiples of 3. They 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.

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Assessing what children know

Group according to a child’s strategy stage using the New Zealand Number Framework

Encourage children to self assess (reflect) know and own their next learning steps. (Personalised Learning)

Teachers use a variety of tasks (informal and formal) to form our Overall Teacher Judgements (OTJs)

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National Standards

• JAM

• Maths illustrations

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National Standards Expectations

Curriculum Level

1 2 3 4 5

Year Level After 1 year (40 wks)

After 2 year (80 wks)

After 3 year (120 wks)

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 5P 5A 6P 6A 7 8

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National Standardsare based on all areas of the

Maths Curriculum• Number and Algebra

- Knowledge

-Addition/ Subtraction

-Multiplication and Division

-Ratios and Proportions (Fractions)

-Patterning (Algebra)• Geometry and Measurement• Statistics

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After One Year

Addition Solve simple addition problems to 10 by counting all the objects by using materials or imaging

Subtraction Solve simple subtraction problems to 10 by counting all the objects by using materials or imaging

Multiplication Solve simple multiplication problems to 10 by counting all the objects by using materials or imaging

Algebra Copy simple patterns and identify what comes next.

Measurement Compare lengths, weights, volumes, areas by direct comparison

Geometry Sort objects by choosing a feature and explain their sortingGiving simple directions (forwards, backwards, left, right)

Statistics Sort objects into groups; e.g. animals and make simple statements- identify how many of each, what there is the most of.

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After Two YearsAddition Solve simple addition problems to 100 by counting on from the bigger

number

Subtraction Solve simple subtraction problems to 100 by counting back

Multiplication Solve simple multiplication problems by skip-counting

Fractions Solve simple problems by equal sharing or halving (shapes and quantities)

Algebra Continue simple patterns and identify how they repeat.

Measurement Compare lengths, areas, weights, volumes using self-chosen units

Geometry Sort objects and shapes by different features and describe the features.Describe personal locations, give directions (how many steps, half and quarter turns)

Statistics With support, investigate questions, collect data and display. Identify similarities and differences. Make comparisons.Probability -Identify possible outcomes of events. What is more/less likely to happen.

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After Three YearsAddition/Subtraction

Solve addition and subtraction problems by applying basic facts, knowledge of place value to combine and partitioning whole numbers

Multiplication Solve simple multiplication problems by repeated addition

Fractions Find fractions of sets, shapes and quantities by using known facts

Algebra Create and continue sequential patterns- spatial and number based on simple addition and subtraction.

Measurement Measure lengths, areas, weights, volumes, duration of events using linear whole number scales and applying basic facts

Geometry Sort objects and 2D and 3D shapes by their features and identify categories within categories. Show reflection, translation and rotation by creating and describing patternsDescribe personal locations, give directions (using whole measures- metres, half and quarter turns)

Statistics With support, investigate questions, collect data and display. Interpret displays in context.Probability- Compare and explain the likelihood of outcomes.

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At the End of Year 4Addition/Subtraction/Multiplication

Solve problems by applying addition, subtraction and simple multiplication facts, knowledge of place value and symmetry to combine and partition whole numbers

Fractions Find fractions of sets, shapes and quantities by using known multiplication facts

Algebra Create and continue spatial and number patterns based on repeated addition or subtraction.

Measure-ment

Measure lengths, areas, weights, volumes, duration of events reading to nearest whole number and applying basic addition, subtraction and simple multiplication facts to standard units

Geometry Sort objects and 2D and 3D shapes by their using two features simultaneously. Describe the symmetries of a shape. Create nets for cubes.Describe personal locations, give directions using simple maps

Statistics Independently, investigate questions, gather and display data. Interpret displays in context.Probability- Compare and explain the likelihood of outcomes involving chance.

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At the End of Year 5Addition/Subtraction/Multiplication

Solve problems by applying additive and simple multiplicative strategies and knowledge of symmetry to combine or partition whole numbers

Fractions Find fractions of sets, shapes and quantities by applying additive and simple multiplicative strategies and knowledge of symmetry

Algebra Create, continue and predict further members of sequential patterns with two variables. Use rules that involve spatial features, repeated addition or subtraction and simple multiplication.

Measure-ment

Measure time and the attributes of objects choosing appropriate standard units to nearest tenth.

Geometry Sort 2D and 3D shapes, consider features simultaneously and justify their decisions. Describe the symmetries of a shape. Create nets for rectangular prisms. Drawing plans, side and front views.Describe personal locations, give directions using grid references and points on a compass.

Statistics Independently, investigate questions, gather, display and identify patterns in data. Interpret displays in context.Probability- Order the likelihoods of outcomes involving chance. List all possibilities.

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At the End of Year 6Addition/Subtraction/Multiplication

Solve problems by applying additive and simple multiplicative strategies (including mixed operations) to combine or partition whole numbers

Fractions Find fractions of sets, shapes and quantities by applying additive and simple multiplicative strategies

Algebra Describe spatial number patterns using tables and graphs, rules that involve spatial features, repeated addition, subtraction and simple multiplication.

Measure-ment

Measure time and the attributes of objects choosing appropriate standard units.

Geometry Sort 2D and 3D shapes, consider features simultaneously and justify their decisions. Describe the symmetries of a shape. Draw or make objects given their plan, side and front views.Describe personal locations, give directions using grid references, turns and points on a compass.

Statistics Independently, investigate questions, gather or access multivariate data. Interpret displays in context.Probability- Order the likelihoods of outcomes involving chance.

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How do we cater for individual learning needs in Maths?

• Using a variety of assessments and analyse data

• Grouping and teaching according to learning needs

• Individual Learning Goals

• Cross grouping in the middle and senior classes

• Personalised Learning Programmes

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How can parents help?

Developing a child’s knowledge is a key to their success and development in mathematics

This is the perfect area for you to help and support your child at home

Knowledge lists for each stage and activities are on our school website

Encourage your child to spend 10 minutes a day or 3x 20 minutes a week on Mathletics

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Knowledge Building

Numbers before and after(Letter boxes, say a number, use a number line, use number cards, write a number down, ladder game, keyboard numbers, using dice)

Identifying numbers(Letter boxes, number plates, speed signs, how many km to go, number cards, combine numbers, odometers, metres)

Ordering numbers(Number cards, write some numbers down, cut up calendars)

These activities can be used at all levels – just use different range of numbers for different levels

Counting(cars, shells on beach, pegs, run around the house, how many steps you walk, count backwards, start from different numbers, skip counting groups of objects; e.g. pairs of shoes )

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Knowledge Building cont..

Basic addition & subtraction facts to 5, then 10, then 20 (Buttons, ten frames, fingers, flashcards, number boggle, playing cards)

Recalling Doubles and Halves (ten frames, fingers, flashcards)

Knowing Groups of ten (Using ten frames, using fingers, abacus, ice- block sticks)

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Finger patterns

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The Reality?

Doubles Facts Ten and ….10 + 6 = 16 Groups of ten (Place Value)

To become a Part-Whole thinker (stage 5 plus) children need automatic recall of…

All of the above The times tables

To become a Multiplicative thinker (stage 7) children need automatic recall of …

Facts to Ten (addition and subtraction)

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It may surprise you to know….Algorithms are okay but only when… A student shows an understanding of how they work

e.g. 73 - 59 involves renaming 73 as 60+13

A student reaches end of Stage 6 It is an effective method for the problem posed.

e.g. Try working out this out as an algorithm

10004 or 199

- 9998 + 99

They also know other strategies they can use They are achieving at Stage 6

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It may surprise you…

At Stage 3-4: We focus on developing understanding of multiplication and division (not learning the multiplication & division facts)

At Stage 5 Students learn addition facts to 20 & subtraction facts to 10

2x, 5x and 10x multiplication facts

In Stage 1-4: We focus on learning our addition and subtraction facts to 10

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Support Material• www.nzmaths.co.nz/families

– Video, Maths at Our House (cooking, maps, shopping, newspapers)

– Number Knowledge Activities (games, activities and flashcards)

School Website:

Knowledge Lists

Knowledge activities

• Student-led conferences/reports: It will identify you child’s next learning step.