Many of the mathematics ARBs can support teachers with decisions they need to make around the 2009 National Standards progressions. They can provide evidence of learning that can contribute to establishing their overall teacher judgements (OTJ).
Mathematics ARB items have been developed around curriculum levels and are generally trialled with groups of students. The data from the trials provides the difficulty level, i.e., how hard it was for the trial students to get the correct answer. However, it is the strategies that students use to complete tasks that indicate where they are on the National Standards progressions, rather than the ARB item or the difficulty level. An ARB item at one curriculum level could be used to identify a range of curriculum levels related to the standards.
For example students might answer questions on a level 3 item about addition. The strategies that students use can indicate which step on the National Standard progression they are working at:
 advanced counting strategies suggest curriculum level 1 (specifically Year 2)
 early additive strategies suggest curriculum level 2
 advanced additive/early multiplicative strategies suggest curriculum level 3
 advanced multiplicative /early proportional strategies suggest curriculum level 4.
The term [early] is used to indicate the earlier year level of the standard (Years 3, 5 and 7) . For example an assessment statement at level 3 that has [early] following it indicates that the statement is appropriate for a Year 5 level.
These mathematics assessment resources from the ARBs have been mapped to the key foci from the 2009 National Standards Mathematics progressions. The statements provided in the National Standards selector are an interpretation of the standards with a link to ARB items that can be used to provide evidence relating to the standard at that level.
Click on the Curriculum area and Curriculum level to view the description of the National Standards step and related ARB resources.
 apply countingall strategies
 apply countingon, countingback, skipcounting, and simple grouping strategies to combine or partition whole numbers
 use equal sharing and symmetry to find fractions of sets, shapes, and quantities
 count all item in a set [early]
 use counting on strategies or skip counting strategies to solve simple addition and subtraction problems:
 Addition:
 Subtraction:
[early] Apply basic addition facts and knowledge of place value and symmetry to:
 combine or partition whole numbers;
 find fractions of sets, shapes, and quantities.
Apply basic addition and subtraction facts, simple multiplication facts, and knowledge of place value and symmetry to:
 combine or partition whole numbers;
 find fractions of sets, shapes, and quantities.
Addition/Subtraction (Combine or Partitioning)
 add and subtract 2digit whole numbers (involving simple recombining) using addition basic facts and simple place value knowledge [early] or start to use partwhole strategies (such as place value partitioning):

Addition: Party balloons  Adding and subtracting more numbers  Going on a picnic  Spending at the shop  Buying some things  The right money  Counting money  Solving maths problems  The same total  A few coins  Adding coins  Change from $10  Different dollars  Spending pocket money  How much change?  Cover up II  Number line addition and subtraction  Seeds and cards  Cover up  Number line addition  Estimating addition  Lemons, library and sports  Adding sweets

Subtraction: Easy or harder subtractions  Party balloons  Adding and subtracting more numbers  Going on a picnic  Spending at the shop  Buying some things  Solving more maths problems  Showing change  Change from $10  Spending pocket money  Working out change  How much change?  Going on camp  Cover up II  Number line addition and subtraction  Seeds and cards  Cover up  Lemons, library and sports
Multiplication/Division (Combine or Partitioning)
 use symmetry to partition small sets of objects: or grouping diagrams [early]
 use simple basic facts knowledge to solve multiplication and division problems
 use additive strategies (such as repeated addition/subtraction, deriving from known basic facts: How many are there?
 Multiplication:
 Division:
Fractions of sets, shapes and quantities
 start to partition ("chunk") to find simple unit fractions (halves, thirds, quarters, fifths, and tenths).
 Partitioning sets and shapes:
 involve finding half of small quantities (under 20) without using sets [early] or use basic facts knowledge and simple additive strategies (such as repeated addition) to find fractions of small quantities (e.g., finding 1/4 of 12 can involve recognising that 3 + 3 + 3 + 3 = 12).
 Fractions as operators:
*The resource Fractions and sets could be used without the sets provided as evidence of students ability to find fractions of quantities (fractions as operators).
 combine or partition whole numbers;
 find fractions of sets, shapes, and quantities.
 combine or partition whole numbers, including performing mixed operations and using addition and subtraction as inverse operations;
 find fractions of sets, shapes, and quantities.
Addition/Subtraction (Combine or Partitioning)
 add and subtract 2 and 3digit numbers that involve recombining and use partwhole strategies such as place value partitioning, tidy numbers, rounding and compensation [early];
 use a range of different and more sophisticated partwhole strategies and larger 3digit numbers that involve multiple recombining;
 utilise the inverse relationship of addition and subtraction (reversibility or complementary addition);

Addition: Collecting beads  Making a cake  Some maths problems  Solving maths problems  Saving for a pet  Estimating with addition  Student answers  Number line addition and subtraction III  Estimating addition  Number line addition II  Estimating with addition III  City populations  Estimate these II  Fruit shop profit  Temperature changes  Bank account  Packing cherries  Sharing fruit and vegetables  At the canteen  School swimming sports  Art show  Tests and marks  Sharing Jelly beans  Keep fit programme  Buying groceries  Knock the can  Buying books II  Fruit and vegetables

Subtraction: Easy or harder subtractions  Collecting beads  Making a cake  Buses, games and trains  Solving more maths problems  How much farther?  Going on camp  Number line subtraction II  Student answers  Number line addition and subtraction III  City populations  Temperature changes  Bank account  Cans of fruit drink  At the canteen  Art show  Tests and marks  Sharing Jelly beans  Keep fit programme  Buying groceries  Close to a half  Subtraction wheel  Fruit and vegetables  MP3 Player
Multiplication/Division (Combine or Partitioning)
 use multiplicative strategies such as doubling and halving* [early], combining place value partitioning with basic facts, rounding and adjustment (such as compensation), and derived basic facts:

Multiplication: Saving money  Gardening at home  How many are there?  School garden  Lemonade and muffins  Buying Christmas presents  Using doubling and halving II  Using doubling and halving  Halving and doubling  Estimating stamps, money and pinecones  Estimate these II  Rock wall  Packing cherries  Cans of fruit drink  Soccer season  Town hall concert  Counting sheep  School swimming sports  Buying books  Cleaning windows  The price of flour  Powerful twenty five  Food fractions II  Packing food for the hāngi  MP3 Player

Divsion: Saving money  How many are there?  Cough medicine  How many groups? II  Equal sharing III  Estimating stamps, money and pinecones  Packing cherries  Give aways  Cans of fruit drink  Dividing with remainder  Sharing fruit and vegetables  Town hall concert  No remainder  Counting sheep  Buying books  Art show  Sharing Jelly beans  Fish shop  The price of flour  Powerful twenty five  MP3 Player
*The resources Using doubling and halving and Using doubling and halving II explore the use of the doubling and halving strategy.
Fractions of sets shapes and quantities
 partition sets and shapes into common fraction parts. Partitioning sets and shapes:
 identify the fraction part: Partwhole fractions:
 use additive (such as repeated addition) and simple multiplicative strategies (repeated halving) to find common fractions of quantities (e.g., 1/4 of 60, 1/2 of 60 is 30, and 1/2 of 30 is 15) [early] or start to use multiplication and division facts, and simple multiplicative strategies to find common fractions of quantities (e.g., for 1/4 of 24, involve recognising that 4 lots of 6 make 24, so 1/4 of 24 is 6;

Fractions of sets, shapes and quantities: Shading fractions of sets and shapes  Farm fractions  Buying Christmas presents  Building percentages  Fractions and sets  Fraction Soup  Toy holiday  Fractions of money  Money fractions  Counters and fractions  Hungry shark  Sam the clown  Cookie monster  Soccer season  Sharing Easter eggs  Model car fractions  Food fractions II  Food fractions  Fruit Salad
 apply additive strategies to decimals;
 balance positive and negative amounts.
 use multiplication and division as inverse operations on whole numbers;
 apply additive strategies flexibly to decimals and integers.
Addition/Subtraction (Combine or Partitioning)
 a broad range of additive partwhole strategies (tidy numbers, place value knowledge, compensation) to solve decimal addition problems [early]: Bus prices  How much farther?;

solving addition and subtraction:
 Addition with decimals:
 negative numbers Water level  Changing temperatures  TV game show  International time difference II;
 fractions Adding and subtracting fractions (questions a & b)  Eating fractions of cake;
 whole numbers: Number line addition and subtraction II can be used to show addition and subtraction strategies on number line;

Addition: Collecting beads  Bus prices  Buying more CDs and DVDs  Buying some gear  Comparing prices  Weighing for the post  Estimating with addition  Number line addition and subtraction II  Estimating addition II  Estimating in sport  Estimating sums of money  Estimating scores and crowds  Who is estimating? Addition  Estimating farm animals  City populations  Estimate the menu  Estimate these  Indoor cricket scores  House points  Buying electricity  Temperature changes  Sharing fruit and vegetables  Which bottle size?  Checking the bank account  Buying vegetables  Distances between resorts  TV game show  Changing temperatures  Water level

Subtraction: Collecting beads  Buying more CDs and DVDs  How much farther?  Number line addition and subtraction II  Estimating people  City populations  House points  Temperature changes  More marbles  Checking the bank account  Buying vegetables  Distances between resorts  Close to a half  Close to one  TV game show  Changing temperatures  Water level
Multiplication/Division (Combine or Partitioning)

a broad range of additive and multiplicative strategies (such as partitioning both factors, and multiplicative reversibility) to solve maths problems involving:

whole numbers: Estimation involving multiplication: Estimating multiplication  Estimating sweets II  How I estimate: Multiplication  Estimating sweets  Estimating in sport  Estimating food numbers  Estimating bags and boxes  Estimating stamps  Who is estimating? Multiplication  Estimate the menu  Estimate these  Estimating sweets and buses  Estimating lots
 ratio: Show how many

fractions
Students can work out the simplest form of fractions (equivalent fractions):  Finding fractions of quantities:
 percentages: finding a range of percentages of quantities:
 Multiplication with decimals:

Multiplication: Buying more CDs and DVDs  Comparing prices  On the job  Estimating multiplication  Estimating sweets II  Lengths of the pool  Computer printing  Working out the weight  How I estimate: Multiplication  Estimating sweets  Estimating in sport  Estimating food numbers  Estimating bags and boxes  Estimating stamps  Who is estimating? Multiplication  Making necklaces  Estimate the menu  Estimate these  Estimating sweets and buses  Indoor cricket scores  Buying electricity  Building a fence  Estimating lots  Which bottle size?  Buying CDs and DVDs  Buying vegetables  Powerful twenty five  TV game show  Strategy
 Division:

whole numbers: Estimation involving multiplication:
Note: using multiplication as the inverse of division and vice versa is evidence of multiplication at level 4.
 continue sequential patterns and number patterns based on ones.
 create and continue sequential patterns by identifying the unit of repeat
 continue number patterns based on ones, twos, fives, and tens.
 continue repeated patterns [early] or create and continue repeated patterns and identify the unit of repeat
 create and continue number patterns
 create and continue sequential patterns with one or two variables by identifying the unit of repeat;
 continue spatial patterns and number patterns based on simple addition or subtraction.
 create and continue, and give the rule for sequential patterns with two variables;
 continue spatial patterns and number patterns based on repeated addition or subtraction
At level 2 look for evidence that students can ...
 continue a simple repeating pattern and can identify the repeated part [early] or continue the pattern and describe how simple patterns with two variable (features such as shading and shape) repeats:
 continue a simple spatial or number pattern that is increasing by a simple addition of subtraction (sequential) rule [early]: or continue patterns with more complex sequential rules (more complex addition or subtraction) for spatial and number patterns:
* The resource Missing shapes has both types of repeating patterns.
+ some resources also ask students to identify/describe rules (early level 3) but these are very simple sequential rules (early/level 2).
 create, continue, and predict further members of sequential patterns with two variables;
 describe spatial and number patterns, using rules that involve spatial features, repeated addition or subtraction, and simple multiplication.
 determine members of sequential patterns, given their ordinal positions;

describe spatial and number patterns, using:
 tables and graphs;
 rules that involve spatial features, repeated addition or subtraction, and simple multiplication.
At level 3 look for evidence that students can ...
 continue repeating patterns, identify the repeating part, and predict the shapes for given ordinal positions (e.g., what the 35th shape would look like):

continue patterns with more complex sequential rules (more complex addition or subtraction), and describe the sequential rule for the pattern: Stick patterns and rules II  Missing numbers and rules  Stick patterns and rules  Continue the patterns  Making stick patterns II  Making more stick patterns  Missing numbers II  Making stick patterns  Block patterns II  Making triangle patterns II  Pyramid pattern  Fish patterns  Matchstick patterns II  Bike hire  Patterns and rules II  Patterns and rules III  Stacking cans

describe spatial and number patterns giving a sequential/recursive rule:
spatial patterns:Stick patterns and rules II  Stick patterns and rules  Making stick patterns II  Making more stick patterns  Dot patterns  Making stick patterns  Block patterns II  Block patterns  Making triangle patterns II  Pyramid pattern  Fish patterns  Patterns with counters  Matchstick patterns II  Cross pattern  House patterns  Patterns with X and O  Chair and table patterns  Stacking cansnumber patterns:Missing numbers and rules  Continue the patterns II  Machines with rules  Missing numbers II  Different rules  Number machines II  Block patterns  Making triangle patterns II  Bike hire  Patterns and rules  Multiplication rules  Patterns and rules II  Addition rules  Patterns and rules III
Note: if a student describes a pattern using a functional (direct) rule this may be evidence that they are operating at Algebra, early Level 4 for Patterns and relationships (e.g., Repeating bead patterns)

find and represent relationships in spatial and number patterns, using:
 tables and graphs;
 general rules for linear relationships.

find and represent relationships in spatial and number patterns, using:
 tables and graphs;
 equations for linear relationships;
 recursive rules for nonlinear relationships;
 apply inverse operations to simple linear relationships.
At level 4 look for evidence that students can ...

continue patterns and identify functional/direct rules for given spatial and number patterns [early]: Stick patterns and rules II  Stick patterns and rules  Making stick patterns II  Making more stick patterns  Repeating bead patterns II  Machines with rules  Number machines II  Repeating bead patterns  Bike hire  Necklace patterns  Cross pattern  Patterns with X and O  Multiplication rules
 represent patterns in tables or on appropriate graphs:

use a functional/direct rule to find any given members of the pattern: functional rules: Stick patterns and rules  Making more stick patterns  Building patterns  Diamond patterns  Matchstick patterns III  Diamond patterns II  Black and white triangle patterns  Beehive patterns  Foreign currency exchange  Cross pattern  Number machines  Knitting needles  Measurement table  Tables and chairs  Matchstick patterns  Grid triangles

compare the lengths, areas, volumes or capacities, and weights of objects directly
 compare the lengths, areas, volumes or capacities, and weights of objects and the durations of events, using selfchosen units of measurement
 measure the lengths, areas, volumes or capacities, and weights of objects and the duration of events, using linear wholenumber scales and applying basic addition facts to standard units.
 measure the lengths, areas, volumes or capacities, weights, and temperatures of objects and the duration of events, reading scales to the nearest whole number and applying addition, subtraction, and simple multiplication facts to standard units.
At level 2 look for evidence that students can ...
Length
 measure a length with a scale to the nearest whole number:
Area
 measure area of shapes using whole unit squares:
Volume/capacity
 compare the volume/capacity of objects to a given standard unit measure:
 measure the volume of objects using whole cubed units;
Temperature

compare the temperature of objects/situations:
Weight

compare the weight of objects to a given standard unit measure:
Time
 measure (analogue and digital) time to the nearest half/quarter hour:
 add and subtract time problems to the nearest half hour:
 add and subtract time problems involving days, weeks and months:
* Looking at length, weight, and capacity can be used as evidence for length, capacity and weight.
 measure time and the attributes of objects choosing appropriate standar units and working with them to the nearest tenth;
 mesure time and the attributes of objects, choosing appropriate standard units;
 use arrays to find the areas of rectangles and the volumes of cuboids, given wholenumber dimensions
At level 3 look for evidence that students can ...
Length
 measure length using a given unit of measurement or :

measure length to the nearest half unit of measurement [early] or nearest tenth of a unit of measurement: Measuring toy planes  Coin trail  Estimating height and length  Units of measurement II  Matching units of length  How many centimetres?  Inches and centimetres  Millimetre, centimetre, metre or kilometre?  Cutting the door down  Five swimmers  Five dolls  Units of measurement  Packing sweets  Making chocolate gift packs  Units of measurement III
Area

measure area of shapes using an array (multiplication of lengths) or unit squares and half measures: Correcting mistakes  Area of shapes II  Unit square area  Making different rectangles  Area of four shapes  Making the largest perimeter  Working out area  Rectangular area  Setting up tables  Packing boxes  Total area  Area and perimeter  Area of two shapes  How many Xs cover Y  Triangle areas  Packing sweets
Note: solving array problems may also indicate evidence for early multiplicative strategies;
Volume/capacity
 measure volume of objects using cubed units and half measures:
 identify capacities of everday containers:
Temperature

measure temperature on a scale to the nearest tenth of a unit:
Weight

measure weight on a scale to the nearest tenth of a unit:
Time
 measure (analogue and digital) time: Writing time differently  A farmer's day  Camp timetable II;
 add and subtract analogue and digital time problems:
Units of measurement
 select appropriate units of measurement for time and the attributes of objects [early]:.
 measure time and the attributes of objects, using metric and other standard measures;
 make simple conversions between units, using whole numbers;
 use side or edge lengths to find the perimeters and areas of rectangles and parallelograms and the volumes of cuboids, given wholenumber dimensions.
 use metric and other standard measures;
 make simple conversions between units, using decimals;
 use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
At level 4 look for evidence that students can ...
Length/perimeter

calculate length and perimeter of shapes/objects: Correcting mistakes  Perimeter and length  Measuring perimeters  Area and perimeter of four shapes  Smallest perimeter  Making the largest perimeter  Same area, different lengths  Making road signs  Changing perimeter  Garden perimeter  Using cubes  Extending the patio  Using string lines  Fencing the field  Finding the perimeter  Measuring the extension  Finding area and perimeter  How big is the school hall?  Calculating the perimeter  Fencing paddocks
 Note: solving perimeter problems may also indicate evidence for additive strategies (Number and Algebra, Level 2/3/4).
Area

calculate area of shapes/objects: Correcting mistakes  Area of shapes II  Measuring tapa cloth  Sending envelopes  Area and perimeter of four shapes  Soccer and netball  Area of the section II  Smallest perimeter  Making the largest perimeter  Total area  Same area, different lengths  Island area  How many blocks?  The Danish flag  Making road signs  Changing perimeter  Measuring the extension  Finding area and perimeter  How big is the school hall?
Note: solving area problems may also indicate evidence for early multiplicative strategies (Number and Algebra, Level 3).
Volume

measure volume of objects with whole number [early] or decimal measures: Estimating the room  Holding millilitres  Different capacities  Volume and capacity  Packing chocolate  How many blocks?  Using cubes  Dripping Tap
Note: solving volume problems may also indicate evidence for advanced multiplicative strategies (early Number and Algebra, Level 4).
Temperature

measure temperature on a scale including negative numbers: Changing temperatures II;
Note: using temperature may also indicate evidence for dealing with negative amounts (early Number and Algebra, Level 4).
Weight

measure weight on a scale to the nearest tenth of a unit:
Angle

measure the angle of shapes or object in degrees:
Time
 measure (analogue and digital) time (including tenth of a second);
 add and subtract analogue and digital time problems:
Units of measurement

convert between different whole number [early]: Different sized capacities  Sending soccer balls  How many minutes between?  Holding millilitres  Changing weights  Different weights  Different capacities  Using orange juice  Dripping Tap
or different decimal units of measurement:
*The resource The Danish flag can provide evidence of students' ability to calculate perimeter and area of a complex shape (Level 4).
+The resource Estimating the room can provide evidence of students' ability to measure (estimate) width, height and length as well as volume at level 4.

sort objects and shapes by a single feature and describe the feature, using everyday language
 sort objects and shapes by different features and describe the features, using mathematical language
[early]
 sort objects and two and threedimensional shapes by their features, identifying categories within categories.
 sort objects and two and threedimensional shapes by two features simultaneously;
 create nets for cubes.
Shapes
 can sort shapes based on two features:
Nets
 create a net for a cubes:
 sort two and threedimensional shapes, considering the presence and/or absence of features simultaneously and justifying the decisions made;
 create nets for rectangular prisms;
 draw plan, front, and side views of objects.
 sort two and threedimensional shapes (including prisms), considering given properties simultaneously and justifying the decisions made;
 identify nets for rectangular prisms;
 draw or make objects, given their plan, front, and side views.
Shapes
Nets
 identify and create nets for rectangular prisms:
Views
 draw different views of 3dimensional shapes/objects:
 make a 3dimensional shape from given views:
 sort two and threedimensional shapes into classes, defining properties and justifying the decisions made;
 create or identify nets for rectangular prisms and other simple solids;
 draw plan, front, side, and perspective views of objects.
 sort two and threedimensional shapes into classes, considering the relationships between the classes and justifying the decisions made;
 create or identify nets for rectangular prisms and other simple solids, given particular requirements;
 draw or make objects, given their plan, front, and side views or their perspective views.
Shapes
Nets
 create nets for rectangular prisms or identify nets for rectangular prisms: Matching nets II  Net of an open box;
Views
 draw different views of complex 3dimensional objects: Different views II  Different views;
 draw perspective views (isometric) of 3dimensional objects: Drawing 3d shapes  Drawing isometric shapes;
 make a 3dimensional shape from given views: Making a shape.

represent reﬂections and translations by creating patterns
 represent reflections and translations by creating and describing patterns
 represent reflections, translations, and rotations by creating and describing patterns.
 represent and describe the symmetries of a shape.
At level 2 look for evidence that students can ...
 reflect, translate or rotate shapes to make a pattern and/or describe how a pattern was made:
 show, identify and describe aspects of symmetry of a shape:
 represent and describe the results of reflection, rotation, and translation on shapes.
 represent and describe the results of reflection, rotation, and translation on shapes or patterns.
At level 3 look for evidence that students can ...

show and describe the result of transformations upon given shapes and patterns: Animal transformations  Showing transformations  Doing transformations  Drawing lines of symmetry  Reflecting on words II  Transforming patterns IV  Transforming frogs  Some kind of transformation  Still looks the same  Rotated patterns  Matching shapes and transformations  Combining triangle reflections  Reflecting shapes  Reflecting figures
 Identify and describe the transformations that have produced given shapes or patterns.
 Identify and describe the features of shapes or patterns that change or do not change under transformation.
At level 4 look for evidence that students can ...

describe the transformations that have changed a shape or pattern: Transforming Patterns II  Transforming traffic lights  Reflecting shapes II  Rotating shapes  Figure the pattern  Enlarging shapes II  Finding the angle of rotation  Transformation or not?  Reflecting on words  How much of a full turn?  How many times?  More reflections  Star symmetry  Reflection, rotation or translation  Reflecting the number 5  Transformation properties
 identify how an enlargement transformations has changed a shape or pattern:
 identify shapes or patterns and how they change or remain under transformation:

describe personal locations and give directions, using everyday language.
 describe personal locations and give directions, using steps and half or quarterturns.
[early]
 describe personal locations and give directions, using wholenumber measures and half or quarterturns.
 describe personal locations and give directions, using simple maps
Position and orientation
At level 2 look for evidence that students can ...
 give personal locations and directions (including left, right, forward and backwards, and half and quarter turns) [early]:
 describe locations of places or objects on simple maps:
 describe locations and give directions, using grid references and points of the compass.
 describe locations and give directions, using grid references, turns, and points of the compass.
Position and orientation
At early level 3 look for evidence that students can ...
 use grid references or compass points (North, South, East, West) for directions and a standard measures for distance:
 use grid references or compass points and turns:
 describe locations and give directions, using grid references, simple scales, turns, and points of the compass.
 describe locations and give directions, using scales, bearings, and coordinates.
Position and orientation
At level 4 look for evidence that students can ...
 use simple scale [early]:
 use more detailed compass points (including NE, SE, NW, SW):
 use more complex scales;
 use coordinates;

investigate questions by using the statistical enquiry cycle (with support), gathering, displaying, and/or counting category data.
 investigate questions by using the statistical enquiry cycle (with support), gathering, displaying, and/or identifying similarities and differences in category data
 describe the likelihoods of outcomes for a simple situation involving chance, using everyday language.
 gather and display category and simple wholenumber data;
 interpret displays in context.
 gather and display category and simple wholenumber data;
 interpret results in context.
Statistical enquiry cycle
 pose simple questions (with support) to investigate given situations [early]: Favourites II  Teresa and the tuck shop;
 plan how to conduct a statistical investigation: Healthy plants;
Gather and display data
 construct simple graphs or tables with some scaffolding [early]: Tomato plants  Types of fruit  Marbles graph  Party food  Pupil ages  Food groups  Coloured sticks  Colour of shapes  Feeding the pets;
 construct simple graphs or tables independently: Foods I like  Choosing a sport;
 produce stemandleaf graphs (with scaffolding indicates at or above Year 4): Teachers' ages  Birth months II;
Analyse and interpret data
 identifying simple individual features of graphs and tables such as the most common (mode) or least common frequencies [early]: Phone calls  Zoo animals  Harry's happy chart  Favourite ice creams;
 identifying features of graphs and tables including comparisons between different parts of a graph or a table: Tomato plants  Aeroplane arrivals  Bar chart findings  Favourite ice creams;
 interpreting stemandleaf graphs of familiar scenarios indicated at or above Level 2: Extended family ages.
 gather, display, and identify patterns in category and wholenumber data;
 interpret results in context.
 gather or access multivariate category and wholenumber data;
 sort data into categories or intervals, display it in different ways, and identify patterns;
 interpret results in context, accepting that samples vary.
Statistical enquiry cycle
 pose a simple question to investigate, plan who to sample, and how to collect and display the data: Sport on TV;
Gather and display data
 construct graphs or tables of category or whole number data, including dot plots with category data, or scaffolded stemandleaf graphs [early]: Marine fish  Lunch food;
 construct graphs or tables of category or whole number data, including multivariate graphs, dot plots with whole number data, or stemandleaf graphs: Science test results  Icecream flavours  Waiting time;
Analyse and interpret data
 make comparisons within a graph or table including comparing frequencies in different categories [early]: Wickets in cricket  Sun hats  Hair colour;
 make comparisons within or between graphs or tables including combining or comparing frequencies in different categories and identifying or using the sample size: Common words  Hours of sunshine  Sports on TV  Fireworks  Truck stop  How many pets?;
 interpret and make comparisons of stemandleaf graphs indicates student at Level 3: Throwing a ball  Student heights.
[early]
investigate summary, comparison, and relationship questions by using the statistical enquiry cycle:
 gather or access multivariate category and measurement data;
 sort data and display it in multiple ways, identifying patterns and variations;
 interpret results in context, accepting that samples vary and have no effect on one another.
investigate summary, comparison, and relationship questions by using the statistical enquiry cycle:
 gather or access multivariate category, measurement, and timeseries data;
 sort data and display it in multiple ways, identifying patterns, variations, relationships, and trends and using ideas about middle and spread where appropriate;
 interpret results in context, identifying factors that produce uncertainty.
Statistical enquiry cycle
 pose questions to investigate, planning who to sample, and how to collect and display the data [early]
 identify the correct order of steps for a statistical investigation, and critique and extend questions to put in a survey: Sliding, spinning, tumbling  Birth months I  Creating scales II  Healthy tomato plants  Shoe colours  Takeaway survey;
Gather and display data

construct graphs or tables of category, whole number or measurement data, including multivariate data (with scaffolding) [early]: Sports played  Letters to houses  Water temperature  Maths test scores  Teenagers time for tasks  House sales  Assignment marks  Nutrition in foods  Softball throws  Birth dates  Pie sales  TV favourites  Women's marathon  Colours of cars I  NZ population  Picking peaches  Number of deaths  Showing data using graphs  Typing rates  Making pie charts  Employment data  Sunshine hours II  Word lengths  World softball scores  College students' heights  Soft drinks  Eye colour  School tests  Newspaper delivery  Paua divingTables: Healthy tomato plants  School rubbish II  Table of shapes  Tidy desks; Pie graphs: Soft drinks  Word lengths  Making pie charts; Histograms: Women's marathon;
 construct graphs or tables of category, whole number or measurement data, including multivariate or time series data: Tables Right or left; Pie graphs (with scaffolding). TV favourites;

construct graphs with composite or bivariate: Letters to houses  Maths test scores  Teenagers time for tasks  Assignment marks  Softball throws  Colours of cars I  NZ population  Showing data using graphsAssignment marks  Maths test scores;
 construct graphs with timeseries data: Typing rates  Number of deaths;
Analyse and interpret data
 interpreting simple features of tables or graphs, pie graphs and the simple [early] distributions in tables and graphs [early]: People and their pets  Eyes and hair colour  Olympic Games  Kauri trees  Cleaning the beach II;
 interpreting features of bivariate tables or graphs, composite graphs:

interpreting features of timeseries graphs: Bank balances  Unemployment rate  Food prices  Monthly rainfall  Pocket money II  Desert road closureSliding cubes  Sentence length  People and their pets  Letters to houses  Pocket money II  Food prices  Boys' weights  Bank balances;
 using ideas of the middle and spread of distributions: Sunshine hours  Basketball averages  Softball  Test scores II  Cross country race  Netball and archery  Time to get to school.
 describe the likelihoods of outcomes for a simple situation involving chance, using everyday language.
Probability
 compare and explain the likelihoods of outcomes for a simple situation involving chance.
 compare and explain the likelihoods of outcomes for a simple situation involving chance, acknowledging uncertainty.
Probability

identify the most likely outcomes for probability situations involving counting small numbers of objects [early] or identify the most likely outcomes for probability situations involving frequency or area models of probability, explaining their reasoning or acknowledging uncertainty: Spin a surprise  Clothing combinations I  Sandwich combinations  Friends combinations  Possible events  Snack food combinations  Sandwich combinations II  Grab bag  Is it possible?  Toy bag  Lunchtime combinations  Different spinnersSpinner probabilities  Spin a surprise;
 describe the probabilities for simple events using everyday language [early] or describe the probabilities for events using everyday language including area models: Possible events  Different spinners.
 order the likelihoods of outcomes for simple situations involving chance, experimenting or listing all possible outcomes
 order the likelihoods of outcomes for situations involving chance, considering experimental results and models of all possible outcomes.
Probability
 order probability for simple situations of chance [early]: Fruit in school  Hot air balloon  Marble bag;
 order probabilities for simple situations of chance with frequency or area models. Nuka Island  Spinner chances  Counters in bag  Favourite All Black  Snakes and ladders  Roll a prize;
Combinations
At level 3 look for evidence of:
 list all the outcomes of the combination of two independent events [early]: Lunchtime combinations  Clothing combinations IV  Sandwich combinations;
 list all the outcomes of the combination of two or more independent events: Clothing combinations V  Clothing combinations II  Racing car combos  Dice combinations II  Yum Takeaways;
 use simple multiplicative models to find all possible outcomes of events: Combinations of marbles  Clothing combinations III.
 order the likelihoods of outcomes for situations involving chance, checking for consistency between experimental results and models of all possible outcomes.
 express as fractions the likelihoods of outcomes for situations involving chance, checking for consistency between experimental results and models of all possible outcomes.
Probability
 order the probability of given outcomes [early] or with with justification: Spinner for a board
 express as fractions the likelihoods of outcomes for situations involving chance:
 perform experiments to test probability predictions:
Combinations
 identify all combinations using models of all outcomes, including tree diagrams of two [early] or three independent outcomes:
 identify all combinations using tree diagrams