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## To Be Numerate

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Title: To Be Numerate

1
To Be Numerate
• Maths Information for Parents

2
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

3
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

4
The Big Picture of Numeracy and Maths
5
Maths Strands
6
Number
7
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
8
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.

9
Knowledge and Strategy
• Knowledge
• Number Identification
• Number Sequence and Order
• Grouping and Place Value
• Basic Facts
• Strategy Three domains
• Multiplication and Division
• Ratios and Proportions

10
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
11
Developmental Stage Progression
• The New Zealand Number Framework

12
Number Framework
13
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

14
Grouping and Place Value
Stages 1- 3 within 5, with 5, within 10,
patterns to10.
Stage 4 groupings with 10 and 20, number
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
15
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,
• 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
16
How is maths taught differently now?
17
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

18
Using EquipmentThe use of equipment is essential
when developing new strategies
• Bridging to Ten
• Happy Hundreds

19
Numeracy Strategy Stages
20
Examples of Strategies for each Stage
21
Emergent Stage 0
22
One to One Counting Stage 1
23
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.
24
Count From One By ImagingStage 3
25
26
Early Part-WholeStage 5 (Early Stage 5)
27
28
29
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.
30
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)

31
National Standards
• Maths illustrations
• JAM

32
National Standards Expectations
33
National Standardsare based on all areas of the
Maths Curriculum
• Number and Algebra
• - Knowledge
• -Multiplication and Division
• -Ratios and Proportions (Fractions)
• -Patterning (Algebra)
• Geometry and Measurement
• Statistics

34
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.
35
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.
36
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.
37
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.
38
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.
39
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.
40
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

41
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

42
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)

43
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)

44
Finger patterns
45
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

46
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

47
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

48
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.