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To Be Numerate

- Maths Information for Parents

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

Goals We want our students to

- Develop multiple flexible thinking strategies

- 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

The Big Picture of Numeracy and Maths

Maths Strands

Number

The Balance of Strand

Number 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

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.

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

Knowledge Before StrategyIt is essential that

students have sound knowledge for the strategies

they are developing e.g.

Knowledge Strategy

Stages 1-3 Numbers to 20-order, before and after Counting all to solve addition, subtraction and multiplication problems to 10

Stage 4 Numbers to 100- order, before and after Skip counting in 2s, 5s and 10s to 100 Addition and Subtraction to 100 by counting on and counting back Skip count to solve multiplication problems

Stage 5 Numbers of tens and hundreds in three digit numbers Knows 2, 5 and 10 x tables Use place value to solve addition and subtraction problems Apply simple multiplication facts to solve problems

Developmental Stage Progression

- The New Zealand Number Framework

Number Framework

Number Identification Ordering

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

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

places

Grouping and Place Value

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 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 7 groupings of all numbers up to 10 in

100 ( remainders) groupings of 10s,100s 1000s

in (up to) 7 digit numbers equivalent fractions

Basic Facts

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 6 addition subtraction facts to 20
- multiplication facts up to 10x ( some

corresponding division facts) - multiplication facts with 10s, 100s 1000s

Stages 7/8 division facts up to 10x

tables conversions (fractions/decimal/percentage

) factors, common multiples, divisibility

rules square roots

How is maths taught differently now?

Teaching Model

- Model and support childrens 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

Using EquipmentThe use of equipment is essential

when developing new strategies

- Bridging to Ten
- Happy Hundreds

Numeracy Strategy Stages

Examples of Strategies for each Stage

Emergent Stage 0

One to One Counting Stage 1

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.

Count From One By ImagingStage 3

Advanced CountingStage 4

Early Part-WholeStage 5 (Early Stage 5)

Advanced Part-WholeStage 6

Advanced MultiplicativeStage 7

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 915 are both multiples of 3.

They simplify by 3 and get a ratio of

35 ?10 6 The child can select from a wide

range of strategies to solve challenging problems

involving, decimals, fraction percentages and

ratios.

Assessing what children know

- Teachers use a variety of tasks (informal and

formal) to form our Overall Teacher Judgements

(OTJs)

- Group according to a childs strategy stage using

the New Zealand Number Framework

- Encourage children to self assess (reflect) know

and own their next learning steps. (Personalised

Learning)

National Standards

- Maths illustrations

- JAM

National Standards Expectations

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

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 sorting Giving 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.

After Two Years

Addition 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.

After Three Years

Addition/ 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 patterns Describe 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.

At the End of Year 4

Addition/ 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.

At the End of Year 5

Addition/ 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.

At the End of Year 6

Addition/ 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.

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

How can parents help?

- Developing a childs 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

Knowledge Building

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 )

- 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)

Knowledge Building cont..

- Knowing Groups of ten (Using ten frames, using

fingers, abacus, ice- block sticks)

- Recalling Doubles and Halves (ten frames,

fingers, flashcards)

- Basic addition subtraction facts to 5, then

10, then 20 (Buttons, ten frames, fingers,

flashcards, number boggle, playing cards)

Finger patterns

The Reality?

To become a Part-Whole thinker (stage 5 plus)

children need automatic recall of

- Facts to Ten (addition and subtraction)

- Doubles Facts

- Ten and .10 6 16

- Groups of ten (Place Value)

To become a Multiplicative thinker (stage 7)

children need automatic recall of

- All of the above

- The times tables

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 6013

- 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

It may surprise you

- In Stage 1-4 We focus on learning our addition

and subtraction facts to 10

- 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

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 childs next learning step.