Knowledge overview and teaching sequence for Phase 1 (Years 0-3) 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 the first six months	During the first year	During the second year	During the third year	During the first six months	During the first year	During the second year	During the third year
Number structures	The whole numbers from 0 to 20 form a sequence. Each whole number has a unique name and numeral. The names of numbers between 13 and 19 use the ‘–teen’ suffix. Numbers in counting order are ordered from smallest to largest. Numbers can be placed on a number line to show order and magnitude. Numbers can be used to represent ordinal position in sequences (e.g. 1st, 2nd, 3rd).	The whole numbers from 0 to 100 form a sequence. The base 10 number system is organised by place value (tens and ones for two-digit numbers). The names of numbers between 20 and 99 use the ‘–ty’ suffix. Ordinal suffixes (e.g. –st, –rd, –nd, –th) can be used to represent a position in a sequence (e.g. 2nd, 3rd). Te reo Māori number naming is based on place value (e.g. rua tekau mā tahi — two 10s and 1).	The whole numbers from 0 to 120 form a sequence. The base 10 number system is organised by place value (hundreds, tens, and ones for three-digit numbers). The names of numbers between 101 and 120 use ‘one hundred and –‘ phrasing. The place value of digits helps with comparing and ordering.	The whole numbers from 0 to 1000 form a sequence. The base 10 number system is organised by place value (thousands, hundreds, tens, and ones for four-digit numbers).	Reading and writing whole numbers up to 20 Counting forwards or backwards from any whole number between 1 and 10, and then between 1 and 20 Comparing and ordering whole numbers up to 20 and ordinal numbers up to 5th, using words Locating whole numbers on a fully labelled number line	Reading and writing whole numbers up to 100, and representing them using base 10 structure Counting forwards or backwards from any whole number between 1 and 20, and then between 1 and 100 Comparing and ordering whole numbers and ordinal numbers using representations, words, or numerals, and suffixes to 100 Using te reo Māori for numbers up to 30 Locating numbers on a partially labelled number line (e.g. 17 on a number line labelled in 5s)	Reading and writing whole numbers up to 120, and representing them using base 10 structure Comparing and ordering whole numbers up to 120 Using te reo Māori for numbers up to 100 Recognising the place value of each digit in a two-digit number, and a three-digit number up to 120 Approximately locating numbers up to 120 on a partially labelled number line (e.g. 61 on a number line labelled in tens)	Reading and writing whole numbers up to 1,000, and representing them using base 10 structure Comparing and ordering whole numbers up to 1,000 Recognising the place value of each digit in a three-digit number
	Small collections can be recognised without counting. When counting collections, each object is counted once and only once (the one-to-one principle). The last number counted is the number of objects in the collection (the cardinality principle).	Counting can be organised in groups (e.g. ten ones can be renamed as one 10). The same value can be represented with different groupings (e.g. 12 is six pairs or 12 ones or one 10s and two ones).	Arranging objects into groups can help when finding their total. Groups of 10s are used to structure and count larger collections. Ten 10s can be renamed as one 100.	Groups of 10s and 100s are useful ways to structure and count large numbers. Ten 100s can be renamed as one 1,000.	Subitising (recognising without counting) the number of objects in a small collection (3–5 objects) Counting collections of up to 10 objects using one-to-one correspondence Recognising when a quantity is greater than, less than, or the same as another quantity	Subitising (recognising without counting) smaller groups of objects within a larger collection (e.g. 3 and 5 in a group of 8 objects) Counting collections of objects using one-to-one correspondence, and then by pairs, for up to 20 objects Finding the total number of objects up to 20 by grouping (using pairs, 5s, or 10s)	Finding the total number of objects up to 120 by separating them into groups (e.g. groups of ten)	Finding the total number of objects beyond 120 by first separating them into groups (e.g. groups of 10 or 100)
			Rounding to the nearest 10 depends on the value of the ones place; a number line supports this.	Rounding to the nearest 100 depends on the value of the 10s place; a number line supports this. Numbers can be rounded to support estimation before calculating.			Rounding numbers up to 120 to the nearest 10	Rounding numbers to the nearest 10 or 100 Estimating the answer to a calculation
		Counting in 2s from zero or an even number produces even numbers. Counting in 2s from an odd number produces odd numbers.	Sequences generated by counting can overlap (e.g. counting in 2s and counting in 5s overlap for numbers that are multiples of 2 and 5). Counting in 3s produces alternating patterns of odd and even numbers. Numbers ending in the digits 0, 2, 4, 6, and 8 are even and numbers ending in 1, 3, 5, 7, and 9 are odd.			Counting forwards and backwards in 2s and 10s from any whole number between 0 and 100	Counting forwards in 3s from multiples of 3s Counting forwards and backwards in 2s, 5s, and 10s from any whole number between 0 and 120 Identifying odd and even numbers up to 120	Counting forwards and backwards in 2s, 3s, 4s, 5s, and 8s from multiples of these numbers (e.g. 20, 15, 10, 5; 8, 16, 24, 32) Counting forwards and backwards in 10s and 100s from any whole number between 0 and 1000
Operations	Addition is putting parts together to find a total or whole. Subtraction is separating a number into two or more parts or finding the difference between two numbers.	Adding or subtracting 0 does not change a number (the additive identity property). Changing the order in which numbers are added does not change the result (the commutative property of addition). When subtracting numbers, the order of numbers is important (i.e. subtraction is not commutative).	Number facts can be derived from known facts using place value (e.g. 70 + 20 = 90 can be derived from 7 + 2 = 9). Addition and subtraction are inverse operations. Numbers can be added and subtracted using representations, mental strategies, known facts, and place value.	Number facts can be derived from known facts using place value (e.g. 700 + 200 = 900 can be derived from 7 + 2 = 9) Renaming (regrouping) is needed when adding or subtracting across place values. Column methods for addition and subtraction align digits in numbers by their place values.	Memorising addition and subtraction facts up to 5 (e.g. 2 + 3 = 5) Naming the number before or after a given number in the counting sequence up to 10	Memorising addition and subtraction facts up to 10, including 10 + 0 = 10 (e.g. 7 + 3 = 10) Memorising doubles and halves to 10 Naming the number before or after a given number in the counting sequence up to 20 Adding and subtracting one- and two-digit numbers up to 20, including 0 Joining and separating groups of up to 20 objects (e.g. 9 + 6, 7 + __ = 11). Adding ten to a one-digit number Solving one-step problems involving addition and subtraction using objects and pictorial representations	Memorising addition and subtraction facts up to 20 (e.g. 17 + 3 = 20) Memorising doubles and halves to 20 Adding and subtracting numbers up to 100 (e.g. 32 + 20 or 32 + 2) Adding and subtracting 3 one-digit numbers (e.g. 7 + 3 + 6). Adding 100 to a one-digit number Solving one-step addition and subtraction problems involving numbers up to 100 Solving multi-step addition and subtraction problems involving numbers up to 20	Finding the complement of a number to 100 (e.g. 34 + __ = 100) Adding and subtracting numbers up to 1000 (e.g. 329 + 3, 329 + 80, 329 − 200, 137 + 54) Solving one-step addition and subtraction problems involving numbers up to 1000 Solving multi-step addition and subtraction problems involving numbers up to 100
Operations		Multiplication involves combining equal groups. Division involves equal grouping or sharing. Counting objects in equal groups can be used to multiply (combining) or divide (sharing).	Arrays and groups can be used to represent and solve multiplication and division problems. Multiplying and dividing by 1 gives the same number (the identity property of multiplication). Multiplying by zero always results in zero (the zero property of multiplication). Two numbers can be multiplied in either order without changing the result; the same is not true when dividing (the commutative property of multiplication). Multiplication and division are inverse operations.	Multiplication can be completed by repeated addition, grouping, or using known facts, and represented using an array. Division can be completed by equal sharing, grouping, repeated subtraction, or using known facts. Dividing by zero is impossible.		Multiplying and dividing using equal grouping or counting for products and dividends within 20	Identifying the relationship between skip counting and multiplication facts for 2s, 5s, and 10s Memorising multiplication and corresponding division facts for 2s, 5s, and 10s Multiplying and dividing with products and dividends up to 100	Multiplying or dividing using equal sharing, grouping, repeated addition or subtraction, or known facts Memorising multiplication and corresponding division facts for 2s, 3s, 4s, 5s, 8s, and 10s Multiplying a one- or two-digit number by a one-digit number (e.g. 4 × 6; 2 × 23) Dividing whole numbers by a one-digit divisor with no remainders (e.g. 24 ÷ 3, 32 ÷ 4)
Rational numbers		Fractions describe parts of a whole. A whole can be divided into halves (i.e. two equal parts). A whole can be divided into quarters (i.e. four equal parts). A half means one part of a set that has been divided into two equal groups or parts. A quarter means one part of a set that has been divided into four equal groups or parts. Equal sharing means division into groups with the same number of objects in each group. Fractions of sets can be found by sharing.	The denominator of a fraction shows the total number of equal parts a whole is divided into. The numerator of a fraction shows the number of parts being counted or considered. Fractions can be named (e.g. half) or written using words and symbols. Equivalent fractions represent the same amount of the whole value (e.g. two quarters vs a half). A half is 1 of 2 equal parts, a third is 1 of 3 equal parts, and a quarter is 1 of 4 equal parts. Halves are larger than thirds, which are larger than quarters (when comparing fractions of the same whole).	Fractions can represent parts of sets, regions, measurements, and points on a number line. A unit fraction represents one part of an equally divided whole. Its numerator is 1. For unit fractions, the larger the denominator, the smaller the fraction (e.g. 1—12 < 1—6). Fractions with the same denominator can be ordered by the size of the numerator. Equivalent fractions name the same quantity and can be identified by reasoning about equal parts (e.g. 3—6 = 1—2). There are many ways to write one whole (e.g.2—2, 3—3, 4—4, 6—6 are all equivalent to 1).		Recognising and representing halves and quarters as fractions of sets, quantities, and regions, using equal parts of the whole Finding a half or quarter of a set using equal sharing and grouping Connecting 1—2 and 1—4 through halving	Recognising, reading, writing (using symbols and words), and representing halves, thirds, and quarters (1—3, 1—4, 2—4, 1—2, 2—3, 3—4) as fractions of sets, quantities, and regions, using equal parts of the whole Recognising the equivalence of 2—4 and 1—2 Directly comparing two fractions involving halves, thirds, or quarters	Reading, writing, and representing fractions of sets, quantities, and measurements on a number line, and of regions, using small denominators Counting in unit fractions up to 1 Comparing unit fractions with denominators up to 12 Comparing non-unit fractions with the same denominator up to 12 Identifying when two fractions are equivalent, using representations
				When adding or subtracting fractions with the same denominator, the denominators remain unchanged, and the numerators are combined. Subtraction of fractions with the same denominator represents taking away parts of equal size.				Adding and subtracting fractions with the same denominator within a whole (e.g. 1—8 + 2—8 + 3—8 = 6—8)
			The size of the whole can be determined if a fractional part is known (e.g. if 1—2 = 5, then the whole is 10).	The relationship between part and whole is multiplicative, not additive.			Finding a half, quarter, or third of a set by identifying groups and patterns (rather than sharing by ones) Finding a whole when given a 1—2, 1—3, or 1—4 of a length, shape, or set of objects or quantities	Finding a unit fraction of a whole number by connecting to division (e.g.1—3 of 15 is found by 15 ÷ 3) Finding the whole when given a unit fraction by connecting to repeated addition or multiplication (e.g. if 1—4 of a set is 3, the whole set is 4 × 3 = 12)
Financial mathematics		New Zealand coins and notes have different values.	New Zealand coins and notes can be ordered and grouped to find the total value.	New Zealand currency is a decimal system of dollars made up of 100 cents. Finding the total cost and giving change with money involves addition and subtraction.		Recognising and knowing the value of New Zealand denominations of currency (i.e, coins and notes)	Recognising and ordering New Zealand denominations according to their value, making groups of 'like' denominations, and calculating their value Combining denominations of currency (either all notes or all coins) to make a particular value	Representing currency values of mixed dollars and cents without using decimal notation (e.g. $2 and 50 cents) Making amounts of money using one- and two-dollar coins and 5-, 10-, 20-, 50-, and 100-dollar notes Using addition and subtraction to give change

Algebra

	Knowledge The facts, concepts, principles, and theories to teach				Practices The skills, strategies, and applications to teach
	During the first six months	During the first year	During the second year	During the third year	During the first six months	During the first year	During the second year	During the third year
Equations and Relationships		The symbols + and - represent addition and subtraction, and the equal sign shows that two sides of an equation represent the same quantity. An open number sentence is a statement that contains an unknown value.	The symbols × and ÷ represent multiplication and division in number sentences.			Completing open number sentences involving addition and subtraction of one-digit numbers (e.g. 2 + 5 = 3 + __) Checking the truth of number sentences involving addition and subtraction of one-digit numbers (e.g. 7 − 5 = 6 − 4, true or false?)	Checking the truth of number sentences involving direct comparisons of whole numbers up to 120 (e.g. 16 > 60, true or false?) Checking the truth of number sentences and completing open number sentences involving addition, subtraction, multiplication, or division using tens frames, discrete materials, or number lines (e.g. 18 + __ = 17 + 6, 6 ÷ __ = 2, 2 + 2 + 2 = 3 × 2, true or false?)	Checking the truth of number sentences involving direct comparisons of whole numbers up to 1,000 (e.g. 313 < 330, true or false?) Checking the truth of number sentences and completing open number sentences involving addition, subtraction, multiplication, or division (e.g. 217 − __ = 105, 12 ÷ 3 = 5 − 2,true or false?)
			Numbers can be compared using “greater than” (>), “less than” (<), and equals (=).
	Patterns are made up of elements (including numeric or spatial elements) in a sequence governed by a rule, and they arise in a range of situations (e.g. cultural patterns, patterns in the local environment, patterns on everyday objects). Ordinal numbers (e.g. 1st, 2nd, 3rd) can be used to describe the elements in a sequence. Repeating patterns have a repeating group of elements called the unit of repeat. A missing element can be predicted from other elements in the pattern.			A growing number pattern is a sequence of numbers that increase or decrease from one term to the next due to a consistent rule.	Copying, continuing, creating, and describing a repeating pattern with two elements (e.g. cat, dog, cat, dog, ____, ____) Using ordinal numbers up to 5th place to describe position in a sequence	Copying, continuing, creating, and describing a repeating pattern with three elements Identifying missing elements in a pattern (e.g. red, green, blue, red, _____, blue)	Recognising and describing the unit of repeat in a repeating pattern, and using the unit of repeat and ordinal position in a repeating pattern to predict further elements (e.g. ACDC in the pattern ACDCACDCACDC)	Recognising, continuing, and creating growing number patterns

Measurement

	Knowledge The facts, concepts, principles, and theories to teach				Practices The skills, strategies, and applications to teach
	During the first six months	During the first year	During the second year	During the third year	During the first six months	During the first year	During the second year	During the third year
Measuring	Length is the distance between two points. Weight is how heavy something feels. Capacity is the maximum amount of liquid a container can hold.		Standard measuring units are universally agreed and commonly used units for making measurements that enable people to communicate clearly. Measuring tools are usually marked with standard units to ensure consistent measurements of properties such as length, mass (weight), and capacity. When measuring length, area, or volume, the measurement units must remain the same and there must be no gaps or overlaps between them.	Systems of measurement have a history; different cultures use different approaches (e.g. measurement in te ao Māori is based on the human body and natural relationships).	Directly comparing two objects by an attribute (e.g. length, mass (weight), capacity)	Comparing the length, mass (weight), or capacity of objects directly or indirectly (e.g. by comparing each of them with another reference object, used repeatedly) Using comparative language for lengths and heights (longer, shorter, taller) and mass (heavier, lighter)	Estimating and using an informal unit repeatedly to measure the length, mass (weight), or capacity of an object Comparing and ordering several objects using informal units of length, mass (weight), or capacity Estimating and measuring length (cm), mass (g), and capacity (mL), using tools with labelled markings and whole-number metric units	Estimating and measuring length (cm and m), mass (g and kg), and capacity (mL and L), using tools with labelled markings and whole-number metric units Comparing and ordering objects using whole-number metric units of length, mass, or capacity
			The distance around the boundary of a 2D shape gives its perimeter. A polygon is a 2D straight-edged shape where the sides connect to form a closed shape.	Perimeter is the sum of the lengths of sides of a 2D shape. Area is the measure of a region's size on a surface.			Measuring the perimeter of polygon using metric units
								Measuring the area of rectangles using squares of equal size
			A turn is a rotation around a point. A turn can be directional and is described using clockwise (to the right) and anticlockwise (to the left).				Turning an object or person and describing how far they have turned, using full, half, quarter, and three-quarter turns as benchmarks
	The weekdays are Monday through Friday. The weekend consists of the days Saturday and Sunday.	Time can be measured in a range of units: years, months, weeks, days, hours, minutes, and seconds. Time is measured using clocks, which can be analogue or digital. A sequence of events can be described using everyday language (e.g. before, after, tomorrow, yesterday, next, and last). The parts of the day include morning, midday, noon, afternoon, evening, night, and midnight.	Duration is the length of time between the start and end of an event.		Connecting days of the week to familiar events and daily routines (e.g. via the class timetable) Naming and ordering the days of the week, including naming the day before and the day after	Telling the time on analogue and digital clocks to the hour, using the language of 'o'clock' Selecting appropriate units of time to communicate approximate durations in years, months, weeks, days, hours, minutes, or seconds Sequencing events in a day using everyday language of time (e.g. after, before, earlier, later, tomorrow, yesterday, the day after, next)	Naming and ordering the months and seasons Describing durations of familiar events using years, months, weeks, and days, or hours, minutes and seconds Telling the time on analogue and digital clocks to the hour, half-hour, and quarter-hour, using the language of ‘past’ and 'o'clock' Naming the month before and the month after Using ordinal numbers to identify months of the year	Identifying the duration of events using years, months, weeks, days, hours, minutes, and seconds Telling the time on analogue and digital clocks to the nearest 5 minutes and the nearest minute, using the language of minutes past the hour and to the hour Describing the differences in duration between units of time (e.g. days vs weeks, months vs years)
			There are 60 minutes in an hour. There are 30 minutes in half an hour.	There are 15 minutes in a quarter of an hour. There are 60 seconds in a minute. There are 24 hours in a day, 365 days in a year, and 366 days in a leap year. There are 52 weeks in a year. A leap year occurs every 4 years. Months are approximately four weeks long; the specific number of days in each month varies. Larger durations of time can be measured in decades (10 years), centuries (100 years), and millennia (1,000 years).

Geometry

	Knowledge The facts, concepts, principles, and theories to teach				Practices The skills, strategies, and applications to teach
	During the first six months	During the first year	During the second year	During the third year	During the first six months	During the first year	During the second year	During the third year
Shapes	2D shapes have attributes such as size, colour, sides, angles, and corners that can be observed and described using geometric language. Shapes have the same name despite their colour or size.	3D shapes have attributes such as size, colour, faces, edges, and vertices that can be observed and described using geometric language.	Te reo Māori supports identifying shape attributes (e.g. triangle \| tapatoru, square \| tapawhā rite, same \| ōrite, different \| rerekē).	A regular polygon is a two-dimensional shape with all sides of equal length and all interior angles of equal measure.	Identifying, sorting by one attribute, and describing familiar 2D shapes, including triangles, circles, and rectangles (including squares)	Identifying, describing, and sorting by one attribute familiar 2D and 3D shapes presented in different orientations, including cubes, cylinders, and spheres	Identifying, describing, visualising, and sorting 2D and 3D shapes, including ovals, semicircles, polygons (e.g. hexagons, pentagons), rectangular prisms (cuboids), pyramids, and cones, using the attributes of shapes	Identifying, describing, visualising and sorting regular polygons with up to 10 sides
Spatial Reasoning		Shapes can be composed from smaller shapes or decomposed into smaller shapes.	Shapes can flip (reflect), turn (rotate), slide (translate), and be used to create patterns.	A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts. Line symmetry is where one half of an object or shape is a mirror image of the other half, across a line of symmetry.		Composing a compound shape using smaller shapes by trial and error, and decomposing a shape into smaller shapes	Flipping, sliding, and turning 2D shapes to make a pattern or compose a shape	Recognising lines of symmetry in patterns or pictures, and creating or completing symmetrical patterns or pictures
Pathways	Spatial language can be used for giving and following instructions (e.g. near, far, next to, beside, on top, under, over, down, up, left, right, turn).	The position of a location can be described relative to another location, including a known environmental feature.	Paths can be described using sequenced instructions for moving or locating an object (e.g. for moving to another part of the school).	Directions such as forward, left, and right depend on the orientation of the observer.	Following instructions to move to a familiar location or locate an object		Following and giving instructions to move to a different location, using direction, distances (e.g. number of steps), and half and quarter turns	Following and creating a sequence of step-by-step instructions for moving people or objects to a different location, including half and quarter turns and the distance to be travelled
						Using positional language to describe the position and movement of objects (e.g. above, below, left, right, in-front, behind, top, bottom, inside, outside, on, under, next to)
		Maps are 2D representations of places in the world showing the view from above with symbols to show locations and landmarks.		Cardinal directions are the four principal points of a magnetic compass: north, east, south and west.		Using pictures, diagrams, or stories to describe the positions of objects and places.	Interpreting diagrams to describe the positions of objects and places in relation to other objects and places.	Using simple maps to locate objects and places relative to other objects and places.

Statistics

	Knowledge The facts, concepts, principles, and theories to teach				Practices The skills, strategies, and applications to teach
	During the first six months	During the first year	During the second year	During the third year	During the first six months	During the first year	During the second year	During the third year
Developing knowledge from data		Data is information collected about the world. A variable refers to an attribute being studied (e.g. colour, height, age of children). A categorical variable (e.g. colour, brand) classifies objects into groups (categories). Categorical data can be counted.		A numerical variable in data is a number that is a measure or a count.		Collecting categorical data for an investigative question with limited categories (e.g. Do students in our class have one foot longer than the other?) Recording data using tally charts	Collecting categorical data for an investigative question with limited categories (e.g. What are the favourite pets of students in our class?) Sorting categorical data into categories and considering if “other” should be a category for sorting rare responses Recording data using tally charts	Collecting categorical data and sorting the responses Collecting numerical data by asking an investigative question with a response that is a count or a discrete measurement (i.e. a whole number) (e.g. How many teeth have been lost by the students in our class? What are the shoe sizes in the class?)
Visualisation of data		Data visualisations are representations (including picture graphs) of all available values for a variable that show the frequency for each value. Picture graphs use a consistent image for each value; across the categories each image has the same height (for a vertical chart).	Data visualisations are representations (including picture graphs and dot plots) of all available values for a variable that show the frequency for each value. Dot plots represent each data point with a dot of the same size.	Data visualisations are representations (including dot plots and bar graphs) of all available values for a variable that show the frequency for each value. In a bar graph, each bar corresponds to a category or number, and the height of the bar (for a vertical chart) or the length (for a horizontal chart) directly corresponds to the frequency of the category or number.		Creating picture graphs for categorical data	Creating data visualisations for categorical data	Creating data visualisations for categorical and numerical data
Interpretation of data		Data visualisations are representations that help reveal the story of a set of data.				Describing a picture graph by giving the frequency for each category Answering questions about a picture graph, including which category has the most or least items	Describing data visualisations using the variable name and the context and giving the frequency for each category Answering questions about data visualisations, including which category has the most or least items	Describing data visualisations using the variable name and the context and giving the frequency for each category or number Answering questions about data visualisations, including which category has the most or least items and questions involving operations (e.g. How many teeth did our class lose in total?)

The language of Mathematics and Statistics for Years 0–3

	At six months Students will be taught the following words:	Year 1 Students will be taught the following new words:	Year 2 Students will be taught the following new words:	Year 3 Students will be taught the following new words:
Number	1st, 2nd, 3^rd, 4^th, 5^th add, plus, join between combine compare, order count group how many, total, all together largest, smallest more, less next, before, after number line pair subtract, separate, take away, minus same.	digit equal group equal part forwards, backwards fraction, half, quarter, whole set sum, difference tally.	cent, coin, dollar, note denominator double, halve, third estimate, estimation even, odd money multiply, divide numerator place value round (a number) skip count quantity, amount times whole set.	change equivalent fraction fifth, sixth, eighth renaming unit fraction.
Algebra	continue copy pattern repeat.	changed, unchanged element equal, number sentence repeating pattern true, false unit of repeat.	greater than, less than predict.	complete, incomplete growing pattern rule sequence visualize.
Measurement	comparative and superlative words (long, taller, heaviest etc.) days of the week, weekend full, empty heavy, light height high, low length measure, weigh same as short, tall, wide, large, small, big weight.	analogue, digital tomorrow, yesterday, next, last capacity day, week, month, year distance distant, far, near, close earlier, later heavier, longer, shorter hour, minute, second morning, midday, noon, afternoon, evening, midnight o’clock starting point, end point.	anti-clockwise, clockwise full turn, half turn, quarter turn half past months of the year polygon seasons of the year shallow, deep, depth, width surface turn.	a.m, p.m area decade, century, millennia gram litre, millilitre measuring jug or cup metre, centimetre metric leap year perimeter quarter past, quarter to ruler three-quarter turn unit volume weighing scale, balance scale.
Geometry	flip positional language (beside, next to, above, below, under, up, down, on top of, inside, outside, in front of, behind.) line side, corner size (big, small, long, short) square, triangle, circle straight, curved, round turn.	2D shape 3D or solid shape cube, cylinder, sphere map middle, centre slide rectangle.	angle direction edge, face, vertex left, right oval, semicircle, polygon (hexagon, pentagon), rectangular prism (cuboid), pyramid, cone position	horizontal, vertical location north, east, south, west reflect, reflection regular right angle rotate, rotation symmetry, line of symmetry transform, transformation translate, translation.
Statistics		category data, data visualisation frequency most, least picture graph variable, numerical, categorical.	dot plot.	bar graph context.

Mathematics and Statistics Years 0–10 Glossary

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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NZC - Mathematics and statistics Phase 1 (Years 0–3)

Number

Knowledge

Practices

During the first six months

During the first year

During the second year

During the third year

During the first six months

During the first year

During the second year

During the third year

Number structures

Operations

Rational numbers

Financial mathematics

Algebra

Knowledge

Practices

During the first six months

During the first year

During the second year

During the third year

During the first six months

During the first year

During the second year

During the third year

Equations and Relationships

Measurement

Knowledge

Practices

During the first six months

During the first year

During the second year

During the third year

During the first six months

During the first year

During the second year

During the third year

Measuring

Geometry

Knowledge

Practices

During the first six months

During the first year

During the second year

During the third year

During the first six months

During the first year

During the second year

During the third year

Shapes

Spatial Reasoning

Pathways

Statistics

Knowledge

Practices

During the first six months

During the first year

During the second year

During the third year

During the first six months

During the first year

During the second year

During the third year

Developing knowledge from data

Visualisation of data

Interpretation of data

The language of Mathematics and Statistics for Years 0–3

At six months

Year 1

Year 2

Year 3

Number

Algebra

Measurement

Geometry

Statistics

Links to mathematics and statistics supports and resources:

Infosheet – Mathematics and Statistics Learning Area Years 0-10