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: 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

The Big Picture of Numeracy and Maths

Maths Strands MATHEMATICS (Balance shifts as students progress) Number and Algebra Geometry and Measurement Statistics

Number NUMBER FRAMEWORK Number Knowledge Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Strategy Addition and Subtraction Multiplication and Division Proportions and Ratios

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: StagesTime Spent on Number and Algebra Time spend on other strands (Geometry and Measurement, Statistics) 1-480%20% 570%30% 660%40% 750%

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. StrategyKnowledge Creates new knowledge through use Provides the foundation for strategies

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 Strategy It is essential that students have sound knowledge for the strategies they are developing; e.g. KnowledgeStrategy 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 KNOWLEDGE Number Identification Number Sequence and Order Basic Facts Grouping and Place Value

Number Identification & Ordering Stages & decimals to 3 places Stages Stages Stage & ½, 1/3, ¼, 1/5 Stage & improper fractions

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- 3within 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 7groupings of all numbers up to 10 in 100 (& remainders) groupings of 10s,100s &1000s in (up to) 7 digit numbers equivalent fractions

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- 3addition 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 7/8division 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 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 Imaging Materials Using Materials

Using Equipment The use of equipment is essential when developing new strategies Bridging to Ten Happy Hundreds

Numeracy Strategy Stages  Emergent  One to One Counting  Count from one on Materials  Count from one by Imaging  Advanced Counting Counting Strategies  Early Additive Part-Whole  Advanced Additive Part-Whole  Advanced Multiplicative  Advanced Proportional Non - Counting Strategies

Examples of Strategies for each Stage

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.

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 =

Count From One on Materials Stage 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 Imaging Stage 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.

Advanced Counting Stage 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 =

Early Part-Whole Stage 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 = 15 The child uses simple strategies to solve addition and subtraction problems mentally

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

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? 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.

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)

National Standards JAM Maths illustrations

National Standards Expectations

National Standards are 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 AdditionSolve simple addition problems to 10 by counting all the objects by using materials or imaging SubtractionSolve simple subtraction problems to 10 by counting all the objects by using materials or imaging MultiplicationSolve simple multiplication problems to 10 by counting all the objects by using materials or imaging AlgebraCopy simple patterns and identify what comes next. MeasurementCompare lengths, weights, volumes, areas by direct comparison GeometrySort objects by choosing a feature and explain their sorting Giving simple directions (forwards, backwards, left, right) StatisticsSort objects into groups; e.g. animals and make simple statements- identify how many of each, what there is the most of.

After Two Years AdditionSolve simple addition problems to 100 by counting on from the bigger number SubtractionSolve simple subtraction problems to 100 by counting back MultiplicationSolve simple multiplication problems by skip-counting FractionsSolve simple problems by equal sharing or halving (shapes and quantities) AlgebraContinue simple patterns and identify how they repeat. MeasurementCompare lengths, areas, weights, volumes using self-chosen units GeometrySort objects and shapes by different features and describe the features. Describe personal locations, give directions (how many steps, half and quarter turns) StatisticsWith 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 MultiplicationSolve simple multiplication problems by repeated addition FractionsFind fractions of sets, shapes and quantities by using known facts AlgebraCreate and continue sequential patterns- spatial and number based on simple addition and subtraction. MeasurementMeasure lengths, areas, weights, volumes, duration of events using linear whole number scales and applying basic facts GeometrySort 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) StatisticsWith 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 FractionsFind fractions of sets, shapes and quantities by using known multiplication facts AlgebraCreate 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 GeometrySort 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 StatisticsIndependently, 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 FractionsFind fractions of sets, shapes and quantities by applying additive and simple multiplicative strategies and knowledge of symmetry AlgebraCreate, 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. GeometrySort 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. StatisticsIndependently, 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 FractionsFind fractions of sets, shapes and quantities by applying additive and simple multiplicative strategies AlgebraDescribe 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. GeometrySort 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. StatisticsIndependently, 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 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

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 )

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)

Finger patterns

The Reality? Doubles Facts Ten and … = 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)

It may surprise you to know…. Algorithms are okay but only when… A student shows an understanding of how they work e.g involves renaming 73 as 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 or They also know other strategies they can use They are achieving at Stage 6

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

Support Material –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.