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NZC - Mathematics and statistics Phase 3 (Years 7–8)

Knowledge overview and teaching sequence for Phase 3 (Years 7-8) of the Mathematics and Statistics Learning Area. From 1 January 2026 this content is part of the statement of official policy relating to teaching, learning, and assessment of Mathematics and Statistics in all English medium state and state-integrated schools in New Zealand.

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Knowledge overview and teaching sequence for Phase 3 (Years 7-8) of the Mathematics and Statistics Learning Area. From 1 January 2026 this content is part of the statement of official policy relating to teaching, learning, and assessment of Mathematics and Statistics in all English medium state and state-integrated schools in New Zealand.

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Number

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

During Year 7

During Year 8

During Year 7

During Year 8

Number structures and operations

  • In our number system each place value is a power of 10, and this continues infinitely.
  • Repeated multiplication can be expressed using exponent notation with positive exponents.
  • An exponent means ‘raising to the power of’ (e.g. 52 is 5 raised to the power of 2 or 5 to the second power).
  • Expanded form uses powers of 10 to indicate place value.
  • In our number system, each place value is a power of 10, and this continues infinitely to the left and right.
  • Repeated division can be expressed using exponent notation with negative exponents.
  • Decimals can be represented using negative exponents (i.e. negative powers of ten).
  • Reading, writing comparing, and ordering whole numbers using powers of 10 (e.g. 10,000 = 104, 1000 < 104)
  • Representing numbers in expanded form using powers of 10 (e.g. 34,506 = 3 × 104 + 4 × 103 + 5 × 102 + 6)
  • Reading, writing comparing, and ordering whole numbers and decimals using positive and negative powers of 10
  • Representing whole numbers and decimals in expanded form using powers of 10 
  • (e.g. 3.61 = 3 × 101 + 6 × 10−1 + 1 × 10−2)
  • Representing negative powers of 10 as a fraction and a decimal, and vice-versa (e.g. 0.01 = 1—100 = 10−2)
  • Whole numbers greater than zero are either prime, composite, or the number 1.
    • A prime number has exactly two distinct factors: 1 and the number itself.
    • A composite number has more than two distinct factors.
    • 1 is neither prime nor composite.
  • The highest common factor (HCF) of two numbers is the greatest number that is a factor of both the numbers.
  • The least common multiple (LCM) of two numbers is the smallest number that they are both factors of.
  • Each composite number can be represented as a unique product of prime factors and summarised with exponent notation.
  • Using exponents and identifying square roots for square numbers up to at least 144
  • Using radicals (√) to represent square roots
  • Using divisibility rules to identify numbers that are divisible by 2, 3, 4, 5, 6, 8, 9, and 10
  • Identifying prime numbers to 100
  • Finding the highest common factor (HCF) of two numbers under 100, and finding the least common multiple (LCM) of two numbers under 10
  • Using exponents and identifying cube roots for cube numbers up to at least 125
  • Using radicals (√ and 3√) to represent square and cube roots
  • Evaluating square and cube roots for perfect squares and cubes and using a calculator to approximate them for other numbers
  • Representing composite numbers as products of their prime factors, using exponents to summarise repeated factors (e.g. 36 = 2 × 2 × 3 × 3 × 3 = 22 × 33)
  • The number system extends infinitely, including into negative numbers, and can be represented with a number line.
  • Integers are all the whole numbers, including positive whole numbers, negative whole numbers, and zero.
  • Every number has an additive inverse, and their sum is zero (e.g. −5 and 5 are additive inverses; −5 + 5 = 0 and 5 + −5 = 0).
  • Locating integers on a number line
  • Ordering whole negative and positive numbers using a number line
  • Identifying the additive inverse of any number
  • Representing addition and subtraction of integers using a number line
  • Using negative numbers to solve problems in a range of contexts, including the measurement of temperature and finance
  • Locating negative and positive numbers on a number line
  • Comparing and ordering negative and positive numbers using a number line (e.g. −3.4 < −3)
  • Evaluating expressions involving negative numbers, addition, and subtraction (e.g. 3 + −7)
  • Rounding, estimation, and using benchmarks support comparing numbers and checking whether findings are reasonable.
  • Division can result in a remainder expressed as a whole number, fraction, or decimal.
  • Using rounding and estimation to predict results and to check the reasonableness of calculations (e.g. 0.73 + 0.8 + 0.999 must be less than 3 since each are close to but less than 1)
  • Rounding whole numbers to any specified power of 10, and rounding decimals to the nearest whole number, tenth, or hundredth
  • Multiplying whole numbers
  • Dividing whole numbers by one- or two-digit divisors (e.g. 327 ÷ 5 = 65.4 or 652—5)
  • Using rounding, estimation, and benchmarks to predict results and to check the reasonableness of calculations (e.g. 14.7 × 5 must be between 14 × 5 = 70 and 15 × 5 = 75)
  • Rounding whole numbers to any specified power of 10, and rounding decimals to the nearest whole number, tenth, hundredth, or thousandth
  • Multiplying and dividing whole numbers (e.g. 327 ÷ 15 = 21.8 or 214—5)
  • In expressions that have more than one operation, the order of operations is important; operations are done as follows:
    1. operations grouped inside brackets
    2. exponents such as squaring and cubing
    3. multiplication and division, from left to right
    4. addition and subtraction, from left to right.
  • A mnemonic, such as GEMA: grouped, exponents, multiplicative (× and ÷), and additive (+ and −) can be used to remember the order of operations.
  • Evaluating expressions using the order of operations
  • Evaluating expressions with integers, using the order of operations
  • A fraction can describe a proportional relationship between two amounts.
  • Every fraction can be represented by an infinite set of equivalent fractions that occupy the same point on the number line.
  • Fractions can be converted to decimals using division, and the result can be:
    • a terminating decimal (e.g. 5—16 = 0.3125)
    • repeating and infinite decimal (e.g. 7—3 = 2.3., 1—7 = 0.142857)
    • non-repeating and infinite decimal (e.g. √2 = 1.414213...).
  • In the simplest form of a fraction, the numerator and denominator do not share a common factor.
  • Scaling by powers of 10 and using number facts supports multiplication with decimals.
  • Multiplying a whole number by a fraction and finding that fraction of that whole number have the same result.
  • Percentages are decimal fractions with denominators of 100; they are represented using the percent symbol %.
  • The product of two fractions can be found by multiplying the numerators and multiplying the denominators.
  • Percentages can be used to proportionally increase or decrease a quantity.
  • Ratios can be used to describe proportional relationships and unequal division of a whole.
  • Ratios, fractions, and percentages can all represent proportional relationships between two quantities.
  • Identifying, reading, writing, and representing fractions, decimals, and percentages
  • Comparing, ordering, and converting between fractions, decimals, and percentages
  • Finding equivalent fractions and representing fractions in their simplest form 
  • Adding and subtracting fractions, including improper fractions and mixed numbers, and representing the answer in its simplest form
  • Adding and subtracting decimals
  • Multiplying and dividing numbers by powers of 10
  • Multiplying whole numbers by fractions and representing the answer in its simplest form
  • Multiplying decimals by whole numbers (e.g. 0.7 × 5 and 0.7 × 50, which both relate to knowing 7 × 5 = 35)
  • Dividing fractions by whole numbers and representing the answer in its simplest form
  • Dividing a whole number by a unit fraction
  • Finding a fraction of a whole number (e.g. 5—3 of 186)
  • Finding a whole amount when given a fraction (e.g. 5—4 of the set is 85, what is the whole set?)
  • Finding common percentages of whole numbers
  • Finding the whole (100%) when given a percentage (e.g. 40% is 28)
  • Using proportional reasoning to explore multiplicative relationships between quantities (e.g. “If there are 3 red for every 7 blue balls, how many balls are there altogether when there are 18 red balls?”)
  • Multiplying whole numbers by fractions, including by improper fractions, by mixed numbers, and by first converting to an improper fraction
  • Multiplying fractions and representing the answer in its simplest form
  • Multiplying and dividing numbers by powers of 10 
  • Multiplying positive decimals (e.g. 2.3 × 45)
  • Finding a fraction of a whole number, including when the result is a mixed number or improper fraction (e.g. for 2—5 of 42, 2—5 × 42 = 84—5 = 164—5 )
  • Finding a whole amount when given a fraction, including when the whole set is a mixed number or improper fraction (e.g. if 8 is 3—5 of a set, 8 × 5—3 = 131—3 )
  • Finding percentages of whole numbers
  • Finding the whole (100%) when given a percentage (e.g. 3% is 27)
  • Identifying percentage equivalence in calculations (e.g. 45% of 20 is equal to 20% of 45)
  • Dividing a quantity into two parts, given the part:part or part:whole ratio
  • Expressing the division of quantity into two parts as a ratio

Financial mathematics

  • Solutions to problems involving New Zealand currency are rounded to two decimal places.
  • Cash payments in New Zealand are rounded up or down to the nearest 10 cents.
  • Calculating the total cost and change for a transaction involving any amount of money
  • Applying percentage discounts to whole dollar amounts (e.g. in a 20%-off sale)
  • Creating and comparing weekly, monthly, and yearly finance plans (e.g. for saving plans, phone plans, budgets, and ‘buy now, pay later’ services)
  • Applying percentage discounts (e.g. a 35% discount on $180 will give a new price of $180 − (0.35 × $180) = $117)

Algebra

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

During Year 7

During Year 8

During Year 7

During Year 8

Equations and relationships

  • A variable can be used to represent:
    • an unknown number, often in formulae (e.g. s in s2)
    • a quantity that can vary or change (e.g. y = 3x + 4; A = bh)
    • a specific unknown value to be solved (e.g. 3a = 18).
  • The solution to an equation satisfies that equation.
  • Equations can be rearranged using inverse operations (e.g. addition and subtraction, multiplication and division). 
  • Solutions to equations can be checked using substitution.
  • Equations can be solved through trial and error, but this can be an inefficient method.
  • Forming and solving one- and two-step linear equations with integer solutions (e.g. t + 7 = 12, 5s + 3 = 18)
  • Checking the truth of and completing number sentences involving all four operations and including the use of inequalities (e.g. 0.8 × 12 ≤ 8 × 0.5 + 8, true or false?)
  • Forming and solving linear equations with rational solutions (e.g. t + 7 = 6.5, 5s + 9 = −18)
  • Forming and solving linear inequalities and representing the solution on a number line (e.g. t − 3 ≥ −5)
  • Using substitution to find the value of an expression or formula (e.g. calculating w + 12 given w = 4)
  • Algebra has its own specialised notation to express relationships and operations concisely, including:
    • 3b in place of b + b + b, 3 × b, and b × 3
    • b in place of 1b
    • ab in place of a × b or b × a (in alphabetical order)
    • a2 in place of a × a, a3 in place of a × a × a
    • a—b in place of a ÷ b and a × 1—b
    • a in place of a1
    • 1 in place of a—a when a ≠ 0.
  • The distributive, commutative, and associative laws are true for all real numbers.
  • Algebraic expressions can be presented in many different ways including fully factorised, partially factorised, and fully expanded forms.
  • Rearranging known formulae using one or two steps (e.g. making w the subject of A = lw)
  • Simplifying expressions involving any of the four operations by collecting like terms (e.g. 3a + a + a = 5a, 3b − 2b = b)
  • Rearranging known formulae using one or two steps
  • Simplifying algebraic expressions involving sums, products, differences, and single brackets, and collecting like terms (e.g. 2(x + 3) + 1 = 2x + 6 + 1 = 2x + 7)
  • Factorising simple algebraic expressions (e.g. 5x − 35 = 5(x − 7))
  • A coordinate plane extends to 4 quadrants that meet at the origin (0, 0).
  • Linear patterns have a constant increase or decrease, can be described by the rule t = a × n + d, and can be graphed as a straight line on a coordinate plane.
  • Identifying and plotting points in the four quadrants of the coordinate plane, using ordered pairs and values from a table
  • Using tables, graphs in the coordinate plane, and diagrams to recognise the relationship between the ordinal position and its corresponding element in a linear pattern, develop a rule for the pattern in words, and make conjectures about further elements in the pattern
  • Identifying the constant increase or decrease in a linear pattern, using variables and algebraic notation to represent the rule in an equation, and using the equation to make conjectures

  • Investigating the patterns of triangular numbers, square numbers, and cube numbers, extending the patterns, creating tables of values, and plotting the values on the coordinate plane

Measurement

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

During Year 7

During Year 8

During Year 7

During Year 8

Measuring

  • Liquids can be measured by capacity and by volume; there are standard conversions between measurements, in particular 1 mL = 1 cm3, 1L = 1000 cm3, and 1 m3 = 1000 L.
  • Selecting and using an appropriate base measure (e.g. metre, gram, litre) within the metric system, along with a prefix (e.g. kilo–, centi–) to show the size of units
  • Estimating and measuring length, area, volume, capacity, mass (weight), temperature, time, and angle, using appropriate units
  • Converting between metric units of area (mm2, cm2, m2, and km2) and volume (mm3, cm3 and m3)
  • Converting between different volume units (cm3, m3, mL, L)
  • Area is a two-dimensional measure, so its units are squared (e.g. cm2).
  • Volume is a three-dimensional measure, so its units are cubed (e.g. cm3).
  • Formulae represent the relationship between measurements and can be used to determine unknown measurements from known measurements.
  • Shapes can be decomposed or recomposed to help find their measurements (e.g. their perimeters, areas, and volumes).
  • Measurement formulae for perimeter are:
    • for a square: P = 4l
    • for a rectangle: P = 2(l + w).
  • Measurement formulae for area are:
    • for a triangle: A = 1—2bh or A = bh—2
    • for a square: A = l2
    • for a rectangle: A = lw or A = bh.
  • Measurement formulae for volume are:
    • for a cube: V = l3
    • for a rectangular prism: V = lwh.
  • The area of a parallelogram is given by A = bh.
  • The area of a trapezium is given by A = 1—2(a + b)h or A = (a + b)h—2.
  • The volume of a triangular prism is given by V = 1—2bhl.
  • Using formulae to find unknown measurements related to perimeter (e.g. the length of the unknown sides of a square given its perimeter, the length of an unknown side in a composite shape given its perimeter)
  • Using formulae to find unknown measurements related to area (e.g. the base of a triangle given its area and height, the area of a figure composed of a triangle and rectangle, given side lengths)
  • Using formulae to find unknown measurements related to volume (e.g. the dimensions of a cube given its volume, the volume of a rectangular prism given side lengths)
  • Calculating the area of a parallelogram and a trapezium
  • Calculating the area of a shape, given some lengths and its perimeter, and vice versa
  • Calculating lengths of quadrilaterals, given their area and other sufficient information
  • Calculating the volume of triangular prisms
  • Calculating the volume of composite figures made up of cubes, rectangular prisms, and/or triangular prisms
  • Duration questions can involve fractions of time and converting between units of time.
  • Reading, interpreting, and using timetables and charts that present information about duration
  • Reading, interpreting, and using timetables, charts and results that present information about duration.
  • Converting times to a given unit (e.g. hours and minutes to minutes)

Geometry

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

During Year 7

During Year 8

During Year 7

During Year 8

Shapes

  • Triangles can be categorised by their angles.
    • An acute triangle has three acute angles.
    • A right triangle has one right angle.
    • An obtuse triangle has one obtuse angle.
  • Triangles can also be categorised by their sides.
    • An equilateral triangle has three equal-length sides.
    • An isosceles triangle has at least two equal-length sides.
    • A scalene triangle has different measures for each side length.
  • All angles in an equilateral triangle are 60°.
  • The base angles (opposite the equal sides) of an isosceles triangle are equal. 
  • The radius is the distance from the outside of a circle to the centre.
  • The diameter is the length of a line through the centre of a circle that touches opposite points on the edge of the circle.
  • The circumference is the distance around a circle.
  • Classifying triangles by both their angle and side properties
  • Identifying and describing the parts of a circle: the radius, diameter, and circumference

Spatial reasoning

  • The sum of the exterior angles of a polygon is 360°.
  • In a regular polygon, all exterior angles are the same; an exterior angle can be found by subtracting the interior angle from 180° or by dividing 360° by the number of sides.
  • The interior angle sum of a triangle is 180°; for a quadrilateral, it is 360°. 
  • The interior angle sum of any polygon can be found using the formula 180(n−2)°, where n represents the total number of sides.
  • Transforming 2D shapes in the coordinate plane by a single translation, reflection across a given mirror line, or a rotation about a given point by a multiple of 90 degrees
  • Identifying the 2D shapes that compose 3D shapes
  • Drawing nets for prisms and pyramids
  • Transforming 2D shapes on the coordinate plane, including composite shapes, by a combination of translations, reflections, rotations, and scaling by any factor
  • Reasoning about unknown angles in situations involving perpendicular lines, parallel lines, and transversals
  • Solving for an unknown angle in a diagram by setting up and solving a multi-step equation based on supplementary, complementary, vertical, and adjacent angle relationships
  • Proving that the interior angle sum of a triangle is 180°, and generalising a rule for the interior angle sum and exterior angles for any polygon
  • Reasoning about unknown angles in situations involving internal and external angles of polygons

Pathways

  • A map’s scale is the ratio between a distance on the map and the corresponding distance in the physical world.
  • Interpreting and communicating the location of positions and pathways using coordinates, angle measures, and the eight main and halfway compass points (e.g. NE, which is 45° E from N)
  • Using map scales, compass points, distance, and turn to interpret and communicate positions and pathways in coordinate systems and grid reference systems

Statistics

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

During Year 7

During Year 8

During Year 7

During Year 8

Developing knowledge from data

  • A variable is an attribute or measurement of the people or objects being studied.
    • A categorical variable classifies objects or individuals into groups.
    • Discrete numerical variables are counted.
    • Continuous numerical variables are measured.
  • The response to a statistical question can be summarised by a measure of central tendency.
    • The mean is the average of numerical data.
    • The median is the middle value for sorted numerical data.
    • The mode is the data value with the highest frequency for categorical data or discrete numerical data.
  • The response to a statistical question can be summarised by the range as a measure of spread. The range for numerical data is the highest value minus the lowest value.
  • Planning and collecting data in order to respond to a statistical question (e.g. Are our feet the same length?)
  • Calculating the mean, median, and mode for numerical data
  • Calculating the range for numerical data

Visualisation of data

  • Categorical data can be visualised through dot plots and bar graphs.
  • Paired categorical variables can be visualised through a stacked bar graph or a clustered bar graph.
  • Bivariate time-series data can be visualised through a time-series graph.
  • A good data visualisation should allow viewers to discern the variable or variables and who the data was collected from, and then, depending on the type of visualisation, additional information such as units for numerical variables, frequency, proportions, patterns, and trends.
  • Outliers are individual data points that are very much bigger or smaller than most of the data points.
  • Outliers skew the mean value for a data set towards themselves, but not the median value.
  • Outliers are not necessarily an error, as there are some events that occur rarely in many situations.
  • For a given set of data, choosing and constructing an appropriate data visualisation according to the data type (e.g. a dot plot, bar graph, time-series graph)
  • Noticing and explaining outliers in a given set of data

Interpretation of data

  • The response to a statistical question includes findings that are summarised and interpreted in context and using evidence. 
  • The tapering sides of a data visualisation are known as tails and may taper at the same rate, producing a symmetrical shape, or an uneven rate, producing a skewed shape.
    • In positively skewed data, the right-tail tapers more slowly than the left tail.
    • In negatively skewed data, the left tail tapers more slowly than the right tail.
  • Interpreting a data visualisation includes describing its variables and their units, the context for the data, and the visualisation’s key features:
    • its shape (e.g. the number of peaks, and whether the shape is symmetrical or skewed)
    • its central tendency (where the middle of the data lies, as indicated visually by the centre of the visualisation and numerically by the median)
    • its spread (how spread the data is from the minimum to the maximum value, and the numerical value of the range)
    • other features depending on the type of data and the data visualisation (e.g. the least and most frequent categories in categorical data, trends for time-series data).
  • A graph that is missing parts (e.g. title, axis labels, axis scales) or has errors may have been made to be misleading or to hide information.
  • Responding to statistical questions by calculating an appropriate measure of central tendency and range for a variety of data tables and data visualisations
  • Interpreting data visualisations, including those from contemporary media
  • Identifying when a data visualisation cannot be interpreted accurately due to missing information
  • Identifying outliers by eye and taking them into account when using range as a measure of spread

Probability

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

During Year 7

During Year 8

During Year 7

During Year 8

Experimental probability

  • Some chance-based situations, such as rolling a weighted die, can only be explored through probability experiments.
  • Results from sets of repeated trials for the same experiment may vary.
  • The Law of Large Numbers states that as the number of trials in a chance experiment increases, the experimental probability will approach the experiment’s theoretical probability.
  • The estimated probability of an event from an experiment is the number of times the event happens divided by the total number of trials in the experiment (i.e. the relative frequency for that event).
  • Carrying out a chance experiment and calculating the experimental probability of each outcome
  • Comparing experimental probability (using at least 30 trials) to theoretical probability, and explaining why they differ and how increasing the number of trials reduces this difference
  • Carrying out chance experiments of at least 100 trials and comparing the experimental probability of each individual outcome to its theoretical probability, in order to demonstrate the Law of Large Numbers

Theoretical probability

  • Lists, tables, and tree diagrams are useful systematic methods for generating all possible outcomes.
  • If all possible outcomes are assumed to be equally likely, the probability of an event is number of ways the event can happen—total number of possible outcomes.
  • Probabilities can be expressed as a fraction or decimal between 0 and 1, or as a percentage between 0% and 100%.
  • An event is a subset of the sample space and thus can be a single outcome or a combination of outcomes.
  • The probability of an event and its complement add to 1.
  • Calculating probabilities for events as decimals, fractions, and percentages
  • Comparing the likelihood of different events
  • Calculating probabilities for complementary events

The language of Mathematics and Statistics for Years 7–8

Year 7

Students will be taught the following new words:

Year 8

Students will be taught the following new words:

Number

  • associative
  • benchmark
  • brackets
  • commutative
  • discount
  • distributive
  • divisibility rule
  • evaluating expressions
  • expanded form
  • exponent, power
  • GEMA.
  • highest common factor (HCF)
  • integer 
  • least common multiple (LCM)
  • order of operations
  • negative
  • prime numbers, composite numbers
  • radicals
  • repeating and non-repeating decimals
  • round up or round down (finance)
  • square root
  • terminating decimals.
  • budget
  • cube number
  • cube root
  • negative exponent
  • prime factors
  • ratio.

Algebra

  • algebraic notation
  • expanded form
  • formulae
  • like terms
  • linear equation
  • linear patterns.
  • ordered pairs 
  • origin
  • rearrange
  • substitution
  • variable
  • value.
  • algebraic expression
  • factorised form, factorising
  • simplifying expression
  • triangular numbers.

Measurement

  • angles (complementary, supplementary, vertical, adjacent)
  • composite shape.
  • duration 
  • recompose.
  • deriving (formulae).

Geometry

  • base angles
  • equilateral, isosceles, scalene triangle.
  • exterior angle and interior angle.
  • grid reference
  • radius, diameter, circumference.
  • scale (map).

Statistics

  • central tendency 
  • median, mode.
  • outlier 
  • skewed data (positively, negatively), tapering and tails.

Probability

  • complements / complementary event
  • experimental or theoretical probability
  • estimated probability.
  • law of large numbers 
  • relative frequency.
  • tree diagrams
  • weighted die.

Word or phrase

Description

Abstraction

The process of identifying and extracting the fundamental structures, patterns, or properties of a mathematical or statistical concept, detaching it from its original context to create a more general idea.

Additive identity

Zero will not change the value when added to a number. For example, 16 + 0 = 16.

Algebraic expression

A single mathematical expression that can be a number or a variable that may or may not have exponents, or combinations of these that is written as products or quotients. Examples include 8, x2, 8x2, 8—x2, or 32a7m—bc4.

Algorithm

A set of step-by-step instructions to perform a computation.

Arithmetically (growing pattern)

A description of a pattern that grows when each term increases or decreases by adding or subtracting a constant value.         

Associative property

A property of operation where three or more numbers can be added or multiplied in any grouping without changing the result. For example, (4 + 3) + 7 = 4 + (3 + 7) because 7 + 7 = 4 + 10, and (4 × 3) × 5 = 4 × (3 × 5).

Attribute

A geometric characteristic or feature of an object or common feature of a group of objects — such as size, shape, colour, number of sides.

Base ten

Our number value system with ten digit symbols (0-9); the place value of a digit in a number depends on its position; as we move to the left, each column is worth ten times more, with zero used as a placeholder; to the right, the system continues past the ones’ column, to create decimals (tenths, hundredths, thousandths); the decimal point marks the column immediately to the right as the tenths column.    

Benchmarks

A reference point that we can use for comparison or estimation. For example, “My finger is about one centimetre wide.”

Bivariate data

Bivariate data is data in a set that has two variables for each subject.

Categorical variables

A variable that classifies objects or individuals into groups or categories. For example, hair colour, breed of dog.

Chance

The likelihood that an outcome will occur.

Claim

A statement of interpretation drawn from mathematical or statistical data.

Coefficient

In an algebraic term, the coefficient is the number that multiplies the variable. For example, in the term 3y, 3 is the coefficient.

Commutative property

A property of operations where numbers can be added or multiplied in any order without changing the result. For example, 5 + 6 = 6 + 5 or 7 × 8 = 8 × 7.

Compose, decompose, recompose

Compose is to make a shape using other shapes. Decompose is to break a shape into other shapes. Recompose is to form the broken pieces of a shape into its original shape.

Conditional probabilities

The possibility of an event or outcome happening, based on the existence of a previous event or outcome.

Conjecture

A mathematical or statistical statement whose truth or otherwise is yet to be determined through analysis or computation.

Constant

A fixed value or a specific unchanging number in an equation, function, or expression.

Data

A collection of facts, numbers, or information; the individual values of which are often the results of an experiment or observations.

Data collection methods

Questions asked to get the data; carefully posed to ensure that the data will help to answer the intended investigative question.

Data visualisations

A graphical, tabular, or pictorial representation of information or data.

Discrete materials

Separate objects that can be counted and grouped. For example, counters or ice block sticks.

Discrete numerical variables

Variables that can be counted and have a limited range of possibilities. For example, number of students in each team or the result of rolling a die.

Distribution

In mathematics, distribution describes spreading terms out equally across an expression; in statistics, distribution describes how data values are spread across the range of values collected.

Element (in a repeating pattern)

In a repeating pattern, an element is the repeating core.
In a growing pattern, an element is a section of the pattern. For example, in the Fibonacci sequence 1, 1, 2, 3, 5, 8, the next element is the sum of the previous two elements (5 + 8 = 13).

Equation

A number statement that contains an equal sign. The expressions on either side of the equal sign have the same value (are equal).

Equivalent fractions

Fractions that represent the same value or number. For example, 1—2, 2—4, 3—6, and 4—8 are equivalent fractions because they represent the same number.

Estimate

A rough judgement of quantity, value, or number. In statistics, an assessment of the value of an existing, but unknown, quantity. In probability, an estimate is the probability that results from the outcome of an experiment

Event

One or more outcomes from a probability activity, situation, or experiment.

Evidence

Information, findings, data that support (prove) a statement or argument.

Expression

Two or more terms involving numbers and/or variables connected by operations. Expressions do not include an equal or inequality sign.

Function

The expression or equation which describes the relationship between two variables, where every x value has a unique y value. This can be written using mathematical notation or shown as a graph in the XY plane.

Geometrically

A description of a pattern that grows when each term increases or decreases by multiplying or dividing a constant value.  

Group of interest

Who the data is collected from in a statistics investigation.

Growing pattern

A pattern where there is a constant increase or decrease between each term. For example, 5, 10, 15, 20.

Inequality

A mathematical statement in which one number or expression is greater or less than another.

Inference

Making a conclusion based on evidence and reasoning.

Informal unit

A non-standard unit used to measure. For example, blocks, pens, fingers. The informal units used should all be the same size.

Inverse operations

The opposite operation, so addition is inverse to subtraction, and multiplication is inverse to division. They are useful to check calculations. For example, to check 4 × 5 = 20, we can see if 20 ÷ 5 = 4.

Investigative question

A question that guides inquiry in an investigative study.

Irrational number

A real number that cannot be expressed as a ratio of two integers. Examples are π and √4.

Justify

Use previously accepted statements and mathematical reasoning, evidence, or proof to explain statements about a conjecture.

Number sentence

An equation or inequality expressed using numbers and mathematical symbols. For example, 10 + 10 = 3 + 7 + 5 + 5.

Ordinal

The numerical position of the element in the sequence. For example, first, second, third, and so on.

Orientation

The angle at which an object is positioned.

Outcome

A possible result of a trial of a probability activity or a situation involving an element of chance.

Population

Group of individuals, items, or data used for an investigative study.

Primary data

Data collected first-hand for a specific purpose. For example, a survey, experiment, or interview. (See also Secondary data).

Probability experiment

A test that can be carried out multiple times in the same way (trials). The outcome of each trial is recorded.

Quantifying

Expressing a quantity using numbers.

Question
  • Investigative
  • Interrogative
  • Survey
  • Data Collection
  • Analysis (Analytical Question)

Rational number

A real number that can be expressed as a ratio of two integers. This includes integers, decimals, and fractions.

Rationalise

The process of eliminating roots or imaginary numbers from the denominator of a fraction.

Reasoning

Analysing a situation and using mathematical and statistical methods to arrive at a finding or conclusion.

Reciprocal

The inverse of a number or function, also known as the multiplicative inverse, for example, the reciprocal of 3—x is x—3.

Relative frequency

The number of times an event occurs divided by the total number of possible outcomes.

Repeating pattern

A pattern containing a 'unit of repeat'. For example, red, green, blue, red, green, blue.

Secondary data

Data collected by someone else, or a process, and/or obtained from another source. For example, online, books, other researchers. (See also Primary data).

Similarity

This is used to describe figures that have the same features, but different sizes. For example, two triangles both having angles of 40°, 60° and 80° but different side lengths.

Subitise

Instantly recognise the number of items in an arrangement without counting.

Tangible and intangible

Tangible is an object that can be touched. For example, a group of blocks. Intangible is a quality or measurement that cannot be touched. For example, colour or length.

Term (in a pattern)

One of the numbers in a pattern or sequence. For example, for 2, 4, 6, 8, the second term is 4.

Theoretical probability

A calculation of how likely an event is to occur in a situation involving chance.

Uncertainty

In probability, when the chance of an event occurring is unknown.

Unit of repeat

The part of a repeating pattern that repeats. The part is made up of several elements.

Variables (statistics and algebra)

A property or quantity that can take on different values. In statistics, a variable represents characteristics that may vary among individuals or over time. In algebra, a variable typically represents an unknown value or a quantity that can change within a given context.

Variation

The differences seen in the values of a property for different individuals or at different times.

Visualisation

The process of creating a mental or visual representation of data, concepts, or ideas. It can involve mentally imagining or manipulating information or visually representing data.

Links to mathematics and statistics supports and resources:

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