NZC - Mathematics and statistics (Phase 2)

Number structure

• skip count from any multiple of 100, forwards or backwards in 25s and 50s

Investigate patterns in multiples, using 100s boards or 1,000s books.

Record choral counting on the board, and ask students to explain patterns and make generalisations or conjectures.

• identify, read, write, compare, and order whole numbers up to 10,000, and represent them using base 10 structure

• identify, read, write, compare, and order whole numbers up to 100,000, and represent them using base 10 structure

• identify, read, write, compare, and order whole numbers up to 1,000,000, and represent them using base 10 structure

Use marked number lines to order and compare numbers and place-value (PV) houses and materials to write and represent numbers, using base 10 structure.

Support students to: 

• practise saying, reading, and writing given numbers, including large numbers, using PV houses 
• use PV houses to generalise that multiplying by 10 moves each digit in a number one place to the left, and dividing by 10 moves each digit one place to the right.

• identify factors of numbers up to 100

• identify square numbers and factors of numbers up to 125

Represent factors of numbers using arrays or ordered lists of factor pairs.

Use multiplication charts to investigate factors, multiples, and square numbers.

Connect to students’ understanding of a square to explain and represent a square number and multiplication facts involving the same two numbers.

Operations

• use rounding, estimation, and inverse operations to predict results and to check the reasonableness of calculations

• use rounding, estimation, and inverse operations to predict results and to check the reasonableness of calculations

• use rounding, estimation, and inverse operations to predict results and to check the reasonableness of calculations

Explain how to round numbers to an appropriate value to make an estimate for a calculation.

Explain reasoning using estimation language such as ‘about’, ‘more or less', and ‘close to’.

Connect rounding with: 

• known benchmarks (e.g., doubles, halves, multiples of 10), to make estimations and check calculations 
• rounding to an appropriate unit in measurement situations.

Use number lines to support rounding, explaining how to find the midpoint between two numbers.

Explain and justify findings by connecting to estimates and other checking methods.

Use families of facts to show the connection between factors and multiples. Explain how to use families of facts to ‘work backwards’ (e.g., 7 × 8 = 56, so 56 ÷ 8 = 7).

• round whole numbers to the nearest thousand, hundred, or ten

• round whole numbers to the nearest ten thousand, thousand, hundred, or ten, and round tenths to the nearest whole number

• round whole numbers to a specified power of 10, and round tenths and hundredths to the nearest whole number or one decimal place

• add and subtract two- and three-digit numbers

• add and subtract whole numbers up to 10,000

• add and subtract any whole numbers

Explain and represent addition and subtraction using materials such as PV materials, number lines, and number discs.

Explain and connect: 

• the horizontal method and the vertical-column method of addition or subtraction 
• making estimates or mental calculations using place value, partitioning, and known facts.

Use worked examples and a range of problem types (e.g., result, change, start-unknown), using think-alouds to explain the most efficient approaches.

Have students practise decoding and solving word problems, representing them as equations.

• recall multiplication and corresponding division facts for 4s and 6s

• recall multiplication facts for 7s, 8s, and 9s and corresponding division facts

• recall multiplication facts to at least 10 × 10 and corresponding division facts.

Provide a range of tasks for students to practise and develop fluency in new and previously learned multiplication and division facts (e.g., families of facts, multiplication table grids, arrays, games).

Investigate patterns in the multiples of times tables and to generalise multiplication problems beyond recalled facts by looking for patterns.

• multiply a two-digit by one-digit number and two one-digit whole numbers
  (e.g., 23 × 5; 7 × 8)

• multiply a three-digit by one-digit number and two two-digit whole numbers
  (e.g., 245 × 6; 34 × 83)

• multiply multi-digit whole numbers
  (e.g., 54 × 112)

At year 4: 

• connect multiplication with skip counting using jumps on a number line or arrays 
• represent division using diagrams and equal sharing, connecting with known families of facts 
• generalise the distributive property of multiplication over addition (e.g., 7 × 8 = 7 × (5 + 3) = (7 × 5) + (7 × 3).

At years 5–6, represent multiplication using the area model, and make connections with place value (e.g., 34 × 7 = 30 × 7 + 4 × 7).

Explain and demonstrate: 

• the vertical-column method for division and multiplication, ensuring students understand and practise the procedure and connect with place value, known facts, and estimation 
• making estimates or mental calculations by connecting to place value, partitioning, and known facts.

Have students investigate: 

• decoding and solving word problems, representing them as equations 
• multiplication and division in measurement and proportional reasoning situations 
• multiplication to count different combinations (e.g., “If I have 4 tops and 3 pairs of shorts, how many different outfits can I make?”)

• divide up to three-digit whole number by a one-digit divisor, with no remainder
  (e.g., 65 ÷ 5)

• divide up to three-digit whole number by a one-digit divisor, with a remainder
  (e.g., 83 ÷ 5 = 16, remainder 3)

• divide up to four-digit whole number by a one-digit divisor, with a remainder
  (e.g., 198 ÷ 7; 4154 ÷ 8)

• use the order of operations rule with grouping, addition, subtraction, multiplication, and division.

Use worked examples to demonstrate a step-by-step layout with one equal sign per line.

Have students investigate: 

• decoding and solving word problems, deciding which operation to use and why 
• the distributive property of multiplication over addition and subtraction (e.g., 6 × 18 = 6 × (20 – 2) = (6 × 20) – (6 × 2).

Explain the commutative, associative, and identity properties, and justify which operations they work for and which they don’t.

Rational numbers

• identify, read, write, and represent tenths as fractions and decimals

• identify, read, write, and represent tenths and hundredths as fractions and decimals

• identify, read, write, and represent fractions, decimals (to two places), and related percentages

Represent and compare fractions, decimals, and percentages using continuous materials (double number lines, fraction walls, 100s squares).

Have students practise saying, reading, and writing decimals using decimal PV houses.

Explain and represent decimal tenths as a fraction with the denominator as 10, and percentages and decimals (to two places) as a fraction with the denominator of 100.

Investigate situations where decimals are used (e.g., in measurements at a sports day).

• compare and order tenths as fractions and decimals, and convert decimal tenths to fractions (e.g., 0.3 =3—10)

• compare and order tenths and hundredths as fractions and decimals, and convert decimal tenths and hundredths to fractions

• compare and order fractions, decimals (to two places), and percentages, and convert decimals and percentages to fractions

• divide whole numbers by 10 to make decimals

• divide whole numbers by 10 and 100 to make decimals

• multiply and divide numbers by 10 and 100 to make decimals and whole numbers (e.g., 1.3 × 10 = 13)

Use decimal PV houses to generalise that multiplying by 10 moves each digit in a number one place to the left (increasing the place value of the digit), and dividing moves each digit one place to the right (decreasing the place value of the digit).

for fractions with related denominators of 2, 4, and 8, 3 and 6, or 5 and 10:

• compare and order the fractions
• identify when two fractions are equivalent by directly comparing them,  noticing the simplest form (e.g., 3—6  = 1—2 , which is the simplest form)

for fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, or 100:

• compare and order the fractions
• identify when two fractions are equivalent

for fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, or 100:

• compare and order the fractions
• identify when two fractions are equivalent
• represent the fractions in their simplest form

Use fraction walls (equivalence materials) to represent and investigate the relationship between the denominator and numerator in a fraction and how we can use this to simplify the fraction.

Make connections with known facts such as halving and dividing by 4.

Count forwards and backwards in fractions, and place fractions on marked and unmarked number lines.

• convert (using number lines) between mixed numbers and improper fractions with denominators of 2, 3, 4, 5, 6, 8, and 10

• convert between mixed numbers and improper fractions with denominators of up to 10

• convert between mixed numbers and improper fractions

Represent improper fractions using words and materials, and place them on a number line.

At years 5–6, explain conversion as division with a remainder (e.g., 11—4 = 2 3—4 (11 divided by 4 = 2 r 3) or multiplication plus a remainder (e.g., 1 1—5 = 6—5 (1 × 5 + 1).

• find a unit fraction of a whole number, using multiplication or division facts and where the answer is a whole number (e.g., 1—5 of 40)
• identify, from a unit fraction part of a set, the whole set

• find a fraction of a whole number, using multiplication and division facts and where the answer is a whole number (e.g., 2—3 of 24)
• identify, from a fractional part of a set, the whole set

• find a fraction or percentage of a whole number where the answer is a whole number (e.g., 3—8 of 48; 30% of $150)
• identify, from a fractional part of a set, the whole set.

Use bar models, diagrams, or paper strips to represent equal parts of a whole.

At year 4, represent parts of a whole set using discrete materials to make equal groups.

At years 5–6, connect percentages and fractions of a whole to known facts and benchmarks (e.g., 25% and dividing by 4).

• add and subtract fractions with the same denominators to make up to one whole
  (e.g., 3—8 + 3—8 + 2—8 = 8—8 = 1)

• add and subtract fractions with the same denominators, including to make more than one whole.

• add and subtract fractions with the same or related denominators
  (e.g., 1—4 + 1—8)

Represent the addition and subtraction of fractions using fraction walls, number lines, and equations.

At years 4–5, explain that, when adding and subtracting fractions with the same denominator, the numerators are added or subtracted but the denominator stays the same.

At year 6, explain how to use equivalent fractions to rename fractions so that they all have the same denominator. Then add or subtract the numerators.

• add and subtract decimals to one decimal place (e.g., 1.3 + 0.2 = 1.5)

• add and subtract whole numbers and decimals to two decimal places (e.g., 32.55 – 21.21 = 11.34)

• add and subtract whole numbers and decimals to two decimal places
  (e.g., 250.11 + 135.29 = 385.4)

Explain and demonstrate both the horizontal method for representing an equation and the vertical-column method for addition or subtraction.

Investigate and connect the addition and subtraction of decimals in measurement situations.

At year 4, use number lines and decimals to add and subtract tenths, connecting tenths as fractions with tenths as decimals.

At years 5–6, connect to methods of adding and subtracting whole numbers.

• use doubling or halving to scale a quantity (e.g., to double or half a recipe)

• use known multiplication facts to scale a quantity

• use known multiplication and division facts to scale a quantity

Represent multiplicative relationships using diagrams, materials, and bar models. Use problems such as “If this recipe feeds 4 people, how much of each ingredient do we need to feed 20 people”?

Financial mathematics

• make amounts of money using dollars and cents (e.g., to make 3 dollars and 70 cents)

• represent money values in multiple ways using notes and coins

• solve problems involving purchases (e.g., ensuring they have enough money) 
• create simple financial plans (e.g., shopping lists, a family budget)

Have students practise grouping denominations and making amounts using play money, connecting with place value, skip counting, and multiplication.

Investigate authentic financial situations and represent findings using equations, spreadsheets, and tables.

• estimate and calculate the total cost and change for items costing whole-dollar amounts.

• estimate to the nearest dollar and calculate the total cost of items costing dollars and cents, and the change from the nearest ten dollars.

• calculate 10%, 25%, and 50% of whole-dollar amounts (e.g., 50% of $280).

Investigate practical situations involving calculating costs and giving change. At year 6: 

• use bar models to represent percentages of whole-dollar amounts, and connect to equivalent fractions 
• explain the procedure of dividing a whole by 10 to find 10%, 2 to find 50%, or 4 to find 25%.

Equations and relationships

• form and solve true or false number sentences and open number sentences involving multiplication and division, using an understanding of the equal sign
  e.g., 5 × __ = 20; __ ÷ 3 = 6)

• form and solve true or false number sentences and open number sentences involving all four operations
  (e.g., 674 + 56 – __ = 671)

• form and solve true or false number sentences and open number sentences involving all four operations, using an understanding of equality or inequality (e.g., 8 × 7 < 8 × 5 + 8 (T or F?)

Represent the equal sign as ‘the same as’ to demonstrate it is a symbol of equivalence.

Explain the difference between an expression (e.g., 4 × 5), an equation (e.g., 4 × 5 = 20), and an inequality (e.g., 4 × 5 < 4 × 6). Have students practise the use of equal and inequality symbols.

Investigate inverse operations to find missing numbers in equations.

• recognise and describe the rule for a growing pattern using words, tables, and diagrams, and make conjectures about further elements in the pattern

• use tables to recognise the relationship between the ordinal position and its corresponding element in a growing pattern, develop a rule for the pattern in words, and make conjectures about further elements or terms in the pattern

• use tables, XY graphs, and diagrams to recognise relationships in a linear pattern, develop a rule for the pattern in words (i.e., that there is a constant amount of change between consecutive elements or terms), and make conjectures about further elements in the pattern

Explain vocabulary in relation to patterns (e.g., ordinal, element, term, position, rule) and how to record the position and term for each element in a pattern.

Investigate visual patterns (e.g., tivaevae), making block patterns and representing patterns using pictures and materials.

Algorithmic thinking

• create and use an algorithm for generating a pattern or pathway.

• create and use an algorithm for generating a pattern, procedure, or pathway.

• create and use algorithms for making decisions that involve clear choices.

Represent a procedure as a sequence of step-by-step instructions (an algorithm). Follow the sequence by ‘acting it out’, asking students to describe and record each step.

Investigate giving directions for, or describing, the most efficient pathway on a maze or map, and sorting numbers according to a set of instructions (e.g., “Sort the odd numbers ... the multiples of 5”).

Explain and justify how a procedure has been broken into steps, the order of the steps, whether there were any errors or omissions, and, if so, how they were corrected.

At years 4–5, investigate creating a sequence of instructions (e.g., to draw a polygon or move through a maze), using digital tools or on paper. Connect with geometry when giving directions or describing pathways.

At year 5, connect algorithmic thinking to a procedure for an operation (e.g., for multiplying two numbers).

At years 5–6, investigate identifying the transformations used to create geometric patterns.

At year 6, investigate using classification diagrams to identify an object, a shape, or data based on multiple characteristics.

Measuring

• measure body parts (e.g., the arm) or familiar objects and use these as benchmarks to estimate and then measure length, mass (weight), capacity, and duration, using appropriate metric or time-based units

• estimate and then accurately measure length, mass (weight), capacity, temperature, and duration, using appropriate metric or time-based units or a combination of units

• estimate and then accurately measure length, mass (weight), capacity, temperature, and duration, using appropriate metric or time-based units or a combination of units

Investigate practical measuring situations, and have students practise the accurate use and reading of rulers, scales, timers, thermometers, and measuring jugs.

Explain and accurately measure: 

• at year 4, centimetres, metres, grams, kilograms, and litres, connecting with half units (e.g., 500 mL = 0.5 L) 
• at years 5–6, centimetres, metres, millimetres, grams, kilograms, litres, millilitres, and degrees Celsius.

Connect reading a measuring tool with rounding to the nearest given unit (e.g., 3.6 cm to the nearest cm).

Discuss the meaning of measurements in context. Explain benchmarks and prompt students to develop them (e.g., “A big step is about a metre, so roughly how long is our classroom?”)

• use appropriate units to describe length, mass (weight), capacity, and time

• use the appropriate tool for a measurement and the appropriate unit for the attribute being measured

• select and use the appropriate tool for a measurement and the appropriate unit for the attribute being measured

Explain and justify the use of appropriate metric units or tools for measuring a given attribute with the precision necessary for the problem, noting that using smaller units provides more accuracy.

• use the metric measurement system to explore relationships between units

• use the metric measurement system to explore relationships between units, including relationships represented by benchmark fractions and decimals

• convert between common metric units for length, mass (weight), and capacity, and use decimals to express parts of wholes in measurements

Explain measurement prefixes (e.g., milli-, centi-), how they connect metric units, and how they are based on powers of ten and relate to place value.

Investigate how measures can be partitioned and combined like other numbers, and how smaller units are created by equally partitioning larger units.

• recognise that angles can be measured in degrees, using 90, 180, and 360 degrees as benchmarks

• describe angles using the terms acute, right, obtuse, straight, and reflex, comparing them with benchmarks of 90, 180, and 360 degrees

• visualise, measure, and draw (to the nearest degree) the amount of turn in angles up to 360 degrees

Investigate different angles using physical and digital tools and angles in the environment, and comparing and classifying them as acute, right, reflex, or obtuse.

Make connections between angles, fractions of a circle, and turns.

At year 6, explain, demonstrate, and have students practise estimating angles and measuring and drawing them using a protractor.

• tell the time to the nearest 5 minutes, using the language of ‘minutes past the hour’ and ‘to the hour’ 

• describe the differences in duration between units of time (e.g., days and weeks, months, and years), and solve duration-of-time problems involving 'am' and 'pm' notation

• convert between units of time and solve duration-of-time problems, in both 12- and 24-hour time systems

Represent time using: 

• digital and analogue clocks (at year 4), to practise telling the time 
• analogue and digital forms (e.g., “It’s 12:45, or a quarter to one.”)

Investigate using calendars, timetables, schedules, and number lines to work out the time between two events or the duration of an event. Explore solar calendars (e.g., Roman, Gregorian) and lunar calendars (e.g., maramataka Māori, Chinese).

Explain subtracting for duration and inclusive counting (e.g., “For the number of days between now and next Tuesday, start counting from today”).

Explain relationships between the units of time (e.g., 60 seconds to the minute, 60 minutes to the hour, 24 hours in a day, 365 days in a year), and use them to convert between units of time.

Perimeter, area, and volume

• visualise, estimate, and measure:
  • the perimeter of polygons, using metric units (cm and m) 
  • the area of shapes covered with squares or half squares 
  • the volume of shapes filled with centicubes, taking note of layers and stacking.

• visualise, estimate, and calculate:
  • the perimeter of regular polygons (in m, cm, and mm) 
  • the area of shapes covered with squares or partial squares 
  • the volume of rectangular prisms filled with centicubes, taking note of layers and stacking.

• visualise, estimate, and calculate the area of rectangles and right-angled triangles (in cm² and m²) and the volume of rectangular prisms (in cm³), by applying multiplication.

Investigate practical measuring situations and connect: 

• finding area with multiplication arrays 
• finding area and volume with the commutative property of multiplication 
• how part-units can be combined using number concepts, when finding the area of a shape 
• the area of a right-angled triangle with half the area of a square.

Have students represent written methods for calculating, with clearly laid-out working.

Shapes

• identify, classify, and describe the attributes of polygons (including triangles and quadrilaterals) using properties of shapes, including line and rotational symmetry

identify, classify, and describe the attributes of:

• regular and irregular polygons, using edges, vertices, and angles
• prisms, using cross sections, faces, edges, and vertices

identify, classify, and explain similarities and differences between:

• 2D shapes, including different types of triangle
• prisms and pyramids

Use a range of 2D and 3D shapes, including tactile shapes, diagrams, student-made constructions, and digital shapes.

Investigate line and rotational symmetry using mirrors and tracing paper.

Connect to algorithmic thinking by making classification diagrams for classifying shapes.

• compare angles in 2D shapes, classifying them as equal to, smaller than, or larger than a right angle

• identify and describe parallel and perpendicular lines, including those forming the sides of polygons

• identify and describe the interior angles of triangles and quadrilaterals

Investigate interior angles using digital tools and paper shapes to generalise that the interior angles of a triangle add to 180° and those of a quadrilateral add to 360°.

Connect these understandings to ideas about right angles, straight lines, and full turns.

Spatial reasoning

• identify the 2D shapes that compose 3D shapes (e.g., a triangular prism is made from two triangles and three rectangles)

• visualise 3D shapes and connect them with nets, 2D diagrams, verbal descriptions, and the same shapes drawn from different perspectives

• visualise and draw nets for rectangular prisms

Represent 3D shapes using digital tools, sketches, blocks, and student-made constructions.

Investigate nets that will or will not fold, and match solid shapes with nets.

• visualise, predict, and identify which shape is a reflection, rotation, or translation of a given 2D shape

• resize (enlarge or reduce) a 2D shape

• visualise, create, and describe 2D geometric patterns and tessellations, using rotation, reflection, and translation and identifying the properties of shapes that do not change

Investigate using 2D shapes, squared paper, mirrors, and tracing paper to make and test conjectures about the effects of transformations.

At year 5, use a grid to scale a shape and connect the scaling with multiplication or division.

At year 6, generalise the properties of shapes that do not change when transformed (e.g., “Which properties of a square stay the same when we rotate it 90 degrees?”)

Pathways

• use grid references to identify regions and plot positions on a grid map 
• interpret and describe pathways, including those involving half and quarter turns and the distance travelled.

• interpret and create grid maps to plot positions and pathways, using grid references and directional language, including the four main compass points.

• interpret and create grid references and simple scales on maps 
  use directional language,
• including the four main compass points, turn (in degrees), and distance (in m, km) to locate and describe positions and pathways.

Investigate different types of maps (e.g., schematic, topographical, and digital maps).

Explain pathways using directional language, including te reo Māori (e.g., whakamua/forwards, whakamuri/backwards, whakamauī/to the left, whakamatau/to the right, raki/north, tonga/south, rāwhiti/east, uru/west).

Connect compass points and directional language with turns and angles, and simple scales with proportional reasoning.

Problem

• use multivariate data to investigate summary and comparison situations with categorical and discrete numerical data, by: 
  • posing an investigative question that can be answered with data 
  • making conjectures or assertions about expected findings

• use multivariate data to investigate summary, comparison, and time-series situations, by:
  • posing an investigative question that can be answered with data
  • making conjectures or assertions about expected findings

Show, with student input, how to: 

• pose summary and comparison investigative questions 
• pose time-series investigative questions (at year 6).

Connect questions to areas of interest and value to the students and their communities.

Plan

• plan how to collect primary data to support answering the investigative question, including:
  • deciding on the group of interest 
  • deciding on the variable or variables for which data will be collected 
  • taking account of ethical practices in data collection

• plan how to collect primary data or how to use provided data, including identifying the variables of interest and, for provided data: 
  • identifying who the data was collected from 
  • identifying the original investigator’s purpose for collecting the data 
  • deciding if the source is reliable (e.g., by checking if survey questions appear to be biased towards a particular point of view) 

Show, with student input, how to: 

• ask interrogative questions about sources and ethical practices 
• develop and closely examine survey or data-collection questions 
• define or establish measures for variables 
• identify ‘who, what, where, when, and how’ when using secondary datasets.

Data

• use a variety of tools to collect the data, and check for errors in it

• use a variety of tools to collect the data, check for errors in it, and correct them by re-collecting the data, if possible

• collect primary data and check for errors, and provide information about variables in secondary data (e.g., how data was collected for them and possible outcomes for them)

Show, with student input, how to: 

• use a range of representations for recording data 
• identify what errors in data look like.

Connect multiple variables for individuals, explaining that most datasets use a table design in which each row focuses on an individual and each column includes the data on multiple individuals for one variable.

Analysis

• create and describe data visualisations to make meaning from the data, with statements including the name of the variable

• create and describe data visualisations to make meaning from the data, with statements including the names of the variable and group of interest

• create and describe a variety of data visualisations to make meaning from the data, identifying features, patterns, and trends in context, and including the variable and group of interest

Show, with student input, how to: 

• represent and analyse data visualisations, creating them at first by hand and then with digital tools 
• identify the different features of data that the data visualisation reveals and how to describe them 
• read the data, and read ‘between’ the data.

Explain how different data visualisations have different features and how to describe them in context (e.g., in relation to frequency, modes, modal groups, patterns, tre

Conclusion

• choose descriptive statements that best answer the investigative question, reflecting on findings and how they compare with initial conjectures or assertions

• answer the investigative question, comparing findings with initial conjectures or assertions and their existing knowledge of the world

Show, with student input, how to: 

• choose the best descriptive statements that answer an investigative question 
• prepare their findings and explain them to others.

Statistical literacy

• check the statements that others make about data to see if they make sense, using information to clarify or correct statements where needed.

• check and, if necessary, improve the statements others make about data, including data from two or more sources.

• identify, explain, check, and, if necessary, improve features in others' data investigations (e.g., biased survey questions, misleading information or statements).

Show, with student input, how to: 

• identify misleading data visualisations, match others’ data visualisations with their statements, and check the claims made by others 
• interpret pie graphs (but not how to create them) 
• explain and justify the effectiveness of data visualisations in representing others’ findings, using interrogative questions.

Probability investigations

• engage in chance-based investigations with equally likely outcomes by: 
  • posing an investigative question 
  • anticipating and then identifying possible outcomes for the investigative question 
  • generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome 
  • creating data visualisations for possible outcomes 
  • describing what these visualisations show 
  • finding probabilities as fractions 
  • answering the investigative question 
  • reflecting on anticipated outcomes

• engage in chance-based investigations, including those with not equally likely outcomes, by: 
  • posing an investigative question 
  • anticipating and then identifying possible outcomes for the investigative question 
  • generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome 
  • creating data visualisations for possible outcomes 
  • describing what these visualisations show 
  • finding probabilities as fractions 
  • answering the investigative question 
  • reflecting on anticipated outcomes 
  • (at year 6) comparing findings from the probability experiment and associated theoretical probabilities, if the theoretical model exists

Investigate everyday chance-based situations in order to explore and experience the chance, randomness, variation, and distribution of outcomes.

Use digital tools to conduct a large number of trials in order to see what a probability estimate and probability distributions look like.

Support students to represent: 

• probability outcomes (theoretical and experimental) using lists, tables, tally charts, visualisations of distributions, words, and numbers 
• the chance of an outcome occurring using fractions, decimals, and percentages.

Connect investigative questions to outcomes and with all possible ways to get the outcomes.

Connect anticipated outcomes with theoretical and experimental distributions.

Critical thinking in probability

• agree or disagree with others’ conclusions about chance-based investigations.

• evaluate others’ statements about chance-based investigations, with justification.

• identify, explain, and check others’ statements about chance-based investigations, referring to evidence.

Show, with student input, how to: 

• match the results of chance-based investigations with statements, and check the claims in others’ investigations 
• explain and justify the statements made by others about chance-based investigations, using interrogative questions.

Number

• addend 
• convert 
• decimal 
• decimal place 
• decimal point 
• improper fraction 
• mixed number
• rename 
• scale 
• tenth

• change 
• divisor, dividend, quotient, remainder  
• factor
• hundredth 
• multiple
• product 
• proportion

• efficient 
• inverse operation 
• percentage 
• simplest form 
• square number 
• thousandth

Algebra

• conjecture 
• relationship

• algorithm 
• corresponding element 
• procedure

• constant 
• equality, inequality 
• linear pattern 
• XY graph

Measurement

• angle 
• benchmark 
• degree 
• kilogram 
• minutes past, minutes to

• a.m., p.m. 
• acute angle 
• attribute 
• degrees celsius 
• kilometre, millimetre 
• obtuse, reflex, right, or straight angle 
• timetable

• cubic centimetre, cubic metre 
• protractor 
• square centimetre, square metre

Geometry

• grid reference 
• rotational symmetry

• compass points 
• cross section 
• net 
• parallel or perpendicular line 
• perspective 
• prism 
• regular or irregular polygon 
• resize, enlarge, reduce

• centre of rotation 
• clockwise, anticlockwise 
• interior angle 
• map scale
• right-angled, equilateral, isosceles, or scalene triangle 
• tessellation

Statistics

• analysis
• assertion 
• investigative question
• conclusion

• categorical 
• data visualisation 
• discrete numerical 
• group of interest 
• source

• comparison or summary investigative question 
• feature 
• misleading 
• mode 
• primary or secondary data 
• trend

Probability

• chance-based investigation 
• equally likely outcome 
• probability experiment

• evaluate 
• not an equally likely outcome

• evidence