NZC - Mathematics and statistics (Phase 1)

Number structure

• subitise (recognise without counting) the number of objects in a collection of up to 5

• subitise (recognise without counting) the number of objects in a collection of up to 10, including by combining two patterns of 1–5 objects

• group objects in a collection of at least 10, subitise the number of objects in each part, and find the total number in the collection using the parts

• estimate the number of objects in a collection of less than 100, using patterns and groupings

Use a range of materials and images that represent structured and unstructured patterns and collections (e.g., dot patterns, 10s frames, dice, materials that can be grouped in 10 such as ice-block sticks).

Also use language that quantifies and compares pattern arrangements (e.g. more, less, the same, different, combine, separate).

Connect subitising to partitioning collections of objects (e.g., 6 and 2 on two dice are the same as 5 and 3 on two 10s frames).

• count forwards or backwards from any whole number between 1 and 10, and then between 1 and 20

• count forwards or backwards in 1s, 2s, and 10s from any whole number between 1 and 20, and then between 1 and 100

• count forwards or backwards in 1s, 2s, 5s, and 10s from any whole number between 1 and 100

• count forwards or backwards in 2s, 3s, 5s, and 10s from any whole number between 1 and 1,000

Use a range of materials (e.g., number lines, 100s boards, number flip charts, 1,000s books, a Slavonic abacus, ice-block stick bundles).

In general, support students to practise counting (e.g., in 2s and 5s) in short sequences (e.g., at year 3, “Count in 1s from 895 to 904; count in 2s from 90 to 110”).

Investigate short patterns in multiples of 2s, 3s, 5s, and 10s, using rhymes, songs, choral counting, the grouping of discrete objects, the recording of patterns, and picture books.

Have students practise finding 1, 10, or 100 more or less for a given number. Use materials to support students to identify numbers and patterns (e.g., 100s boards, 1,000s books).

Connect to te reo Māori to support place-value (PV) understanding (e.g., tekau mā tahi (10 and 1), toru tekau mā rua (30 and 2).

• identify, read, and write whole numbers up to at least 10

• identify, read, and write whole numbers up to at least 20, and represent them using the ten-and-ones structure of teen (11-19) and -ty (multiples of 10) numbers 
  (e.g. 17 = 10 + 7, 20 = 2 × 10)

• identify, read, and write whole numbers up to at least 100, and represent them using base 10 structure

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

Have students practise saying, reading, and writing any given number within an identified number range. Use materials to support this (e.g., number flip boards, PV flip charts and houses).

Explain that base 10 structure is based on groups of ten (ten ones form one ten, ten tens form one hundred, ten hundreds form one thousand etc.) and that both the position and value of a digit indicate the quantity it represents (e.g., 64 has 6 tens and 4 ones, 60 + 4 = 64).

Have students investigate and represent the base 10 structure of numbers using a range of materials and digital tools (e.g., 100s boards, PV houses, PV blocks, ice-block sticks, arrow cards, number fans, words, numerals).

Investigate odd and even numbers and the patterns they notice.

Connect numerals, representations of them, and language (e.g., 652 represented with PV money: “652 = 600 + 50 + 2, 6 hundreds + 5 tens + 2 ones, six hundred and fifty two”).

• compare and order whole numbers up to at least 10 and ordinal numbers (e.g., 1st, 2nd, 3rd), using words

• compare and order whole numbers up to at least 20 and ordinal numbers (e.g., 1st, 2nd, 3rd), using words or numerals and suffixes

• compare and order whole numbers up to at least 100

• compare and order whole numbers up to at least 1,000

Show the sequencing of numbers using a number line (select-numbered, marked, or empty). Change the number-line orientation from horizontal to vertical if students need support with the concepts of before and after.

Explain and use the language of comparison when demonstrating why one number is larger or smaller than another (e.g., “63 is larger than 36, as 6 tens is larger than 3 tens”).

Show how the position of digits in the PV structure helps us to order and compare two- and three-digit numbers.

• partition up to 5 objects, and then up to 10 objects, using a systematic approach and noticing patterns 

• partition and regroup up to 20 objects in different ways, using a systematic approach and noticing patterns

• partition and regroup whole numbers up to at least 100, using a systematic approach and noticing patterns
  (e.g., 10 + _ = 70, 20 + _ = 70, 30 + _ = 70)

• partition and regroup whole numbers up to at least 1,000, using a systematic approach and noticing patterns
  (e.g., 400 + 300 = _, 350 + _ = 500)

Investigate and represent the partitioning of numbers using appropriate materials for the year level – for example: 

• multilink cubes, bead strings, 10s frames, and counters, at 6 months and year 1 
• a Slavonic abacus, ice-block sticks, and PV money, at year 2 
• PV money and PV blocks, at year 3.

Connect students’ subitising with pattern understanding (at 6 months and year 1) and known groupings and facts (at years 2–3).

Explain and discuss how to systematically record the partitioning of numbers (e.g., using partitioning diagrams, tables, vertically-listed equations).

Operations

• use estimation to predict results and to check the reasonableness of calculations

• use estimation to predict results and to check the reasonableness of calculations

• use estimation to predict results and to check the reasonableness of calculations

Explain and spend time developing the concepts of: 

• estimation, using the language of ‘about’, ‘more or less’, and ‘close to’ 
• rounding, using 100s boards and number lines marked with the multiples of 10 or 100, progressing to unmarked number lines at year 3.

Have students investigate and connect practical estimation situations that involve quantities and measures (e.g., the number of balls in a box, the number of steps to the door, the length of a piece of string).

• identify the nearest ten to any whole number up to 100

• round whole numbers up to 1,000 to the nearest hundred or ten

• join and separate groups of up to a total of 10 objects by grouping and counting

• join and separate groups of up to a total of 20 objects and find the difference between groups by grouping and counting
  (e.g., 9 + 6, 7 + _ = 11)

• add and subtract numbers up to 100 without renaming
  (e.g., 53 + 21, 55 – 32)

• add and subtract numbers up to at least 100
  (e.g., 43 – 28, 37 + 18)

Explain and discuss addition and subtraction using representations, including: 

• discrete materials (counters, blocks, context items), 10s frames, and number lines (at 6 months and year 1) 
• bundles of sticks, number disks, and number lines (at year 2) 
• PV materials (PV money, blocks, and discs) and number lines (at year 3).

Connect symbols and equations with problems, using correct vocabulary (e.g., ‘add’, ‘join’, and ‘plus’ for addition). Have students practise decoding and solving word problems.

At year 3, explain and connect horizontal equations and the vertical-column method for addition and subtraction.

Demonstrate making estimates or mental calculations by connecting to place value, partitioning, and known facts.

Use a range of problem types (e.g., result, change, start-unknown).

Use worked examples and think-alouds to explain the most efficient approaches when solving problems.

Have students investigate and generalise adding 0 to or subtracting 0 from a number (at year 1) and applying the commutative property of addition (e.g., 5 + 4 = 4 + 5).

• explore addition facts up to 10 and their corresponding subtraction facts (families of facts), including doubles and halves

• recall addition facts up to 10, and explore addition facts up to 20 and their corresponding subtraction facts (families of facts), including doubles and halves

• recall addition facts up to 20 and their corresponding subtraction facts (families of facts), including doubles and halves

Use materials to investigate addition and subtraction facts (e.g., counters, 10s frames, an abacus, multilink cubes), and use part-whole diagrams to develop subtraction facts and connect to addition facts.

Explain how to record equations and families of facts, connecting with the language for each operation.

Provide a range of tasks to consolidate learning and develop fluency (e.g., physical and digital games, using families of facts and, at year 3, table grids).

• identify the relationship between skip counting and multiplication facts for 2s, 5s, and 10s

• recall multiplication and corresponding division facts for 2s, 3s, 5s, and 10s

Use a range of materials to represent skip counting and multiplication and division facts (e.g., 100s boards, choral counting, games, number lines, a Slavonic abacus, families of facts, and, at year 3, table grids).

Provide a range of tasks to consolidate learning and develop fluency.

• multiply and divide using equal grouping or counting

• multiply and divide using equal grouping or skip counting (e.g. in 2s, 5s, and 10s)

• multiply a one- or two-digit number by a one-digit number, using skip counting or known facts (e.g. 4 × 6; 2 × 23)

Represent multiplication and division problems using discrete materials, pictures, diagrams, symbols, number lines, words, equations, digital tools, and, at year 3, arrays, PV materials, and bar models.

Use correct mathematical language when discussing multiplication and division (e.g., multiply, groups of, sets of, rows of, equal groups, divide, share equally).

Have students practise decoding and solving word problems.

Connect with subitising and addition and subtraction concepts when demonstrating solving multiplication and division problems.

Explain and represent division as a sharing problem (e.g., “Share 12 marbles equally among 3 friends”) or a grouping problem (e.g., “You have 12 marbles. How many groups of 3 marbles can you make?”).

Use worked examples and think-alouds to explain the most efficient approaches when solving multiplication and division problems.

Investigate and generalise multiplying a number by 0 or 1, dividing a number by 1, dividing a number by itself, and why we cannot divide by 0 (e.g., by trying to solve 0 × _ = 5).

At year 3, explain and use the multiplicative identity (e.g., 5 × 1 = 5, 4 ÷ 1 = 4) and commutative property (e.g., 3 × 4 = 4 × 3).

Demonstrate making estimates or mental calculations by connecting to place value, partitioning, and known facts.

• divide whole numbers by a one-digit divisor with no remainders, using grouping
  (e.g. 24 ÷ 3, 32 ÷ 4)

Rational numbers

• identify and represent halves and quarters as fractions of sets and regions, using equal parts of the whole

• identify, read, write (using symbols and words), and represent halves, quarters, and eighths as fractions of sets and regions, using equal parts of the whole

• identify, read, write, and represent halves, thirds, quarters, fifths, sixths, and eighths as fractions of sets and regions, using equal parts of the whole and by positioning on a number line

Represent fractions using a range of materials – continuous (bar models, number lines), discrete (sets of objects), and digital.

Explain and reinforce that when fractions are represented symbolically: 

• the denominator is the bottom number and shows how many pieces a whole has been equally split into 
• the numerator is the top number and shows how many of those parts the fraction represents.

Have students practise saying, reading, and writing fractions in words and symbols.

Explain how to fold paper strips to create fractions of one whole. Label the parts using words and symbols, and use them to create a fraction wall for comparing and ordering fractions.

Explain that a fraction is a number that can be placed on a number line.

• directly compare two fractions involving halves, quarters, and eighths

• compare and order fractions involving halves, quarters, and eighths and identify when two fractions are equivalent

• find a half or quarter of a set using equal sharing and grouping.

• find a half and quarter of a set by identifying groups and patterns (rather than sharing by ones), and identify the whole set or shape when given a half or quarter

• find a unit fraction of a whole number (e.g., 1—3 of 15), and identify the whole set or amount when given a unit fraction (e.g. “ 1—4 of the set is 3, what is the whole set?”)

Investigate a range of practical situations using a range of representations, including materials, drawings and diagrams, and digital tools (e.g., discrete objects, bar models, paper strips for partitioning).

Make connections between: 

• symbols, words, and pictures 
• counting, subitising patterns and known groupings, and skip counting to solve problems (at years 1–2) 
• skip counting and using known addition and multiplication facts to solve problems (at year 3).

Use mathematical language to develop an understanding of fractions (e.g., numerator, denominator, shared equally, divide, partition, equal parts).

• add and subtract unit fractions with the same denominator
  (e.g. 1—8 + 1—8 + 1—8 = 3—8)

Investigate adding and subtracting fractions within familiar contexts (e.g., cutting apples into eighths or partitioning paper strips into six equal parts, and then representing addition and subtraction with these materials).

Connect representations, including symbols and equations, to drawings and materials (e.g., fraction walls, paper fraction strips), and show them on a number line.

Financial maths

• recognise and order New Zealand denominations up to $20 according to their value, make groups of 'like' denominations, and calculate their value.

• make amounts of money using one- and two-dollar coins and 5-, 10-, 20-, 50-, and 100-dollar notes.

Have students use play money (coins and notes) to represent practical financial situations.

At year 2, compare only notes with notes or cents with cents, not a mixture of them.

At year 2, investigate appropriate financial situations that involve both saving and spending.

Connect to place value, addition and subtraction, and skip counting when calculating amounts.

Equations and relationships

• solve true or false number sentences and open number sentences involving addition and subtraction of one-digit numbers, using an understanding of the equal sign
  (e.g., 2 + 5 = 3 + _, 7 – 5 = 6 – 4 (T or F?)

• solve true or false number sentences and open number sentences involving addition and subtraction of one- and two-digit numbers, using an understanding of the equal sign
  (e.g., 18 + _ = 17 + 6, 17 = 25 (T or F?)

• solve true or false number sentences and open number sentences involving addition and subtraction, using an understanding of the equal sign

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

Investigate number sentences using representations such as: 

• 10s frames and discrete materials (at years 1–2) 
• word problems with comparisons (at year 3).

At years 2–3, solve number sentences that have numbers beyond what students are using in operations, so that the emphasis is on the equal relationship, not operating.

• copy, continue, create, and describe a repeating pattern with two elements.

• copy, continue, create, and describe a repeating pattern with three elements, and identify missing elements in a pattern

• recognise and describe the unit of repeat in a repeating pattern, and use it to predict further elements using the ordinal position

• recognise, continue, and create repeating and growing patterns, and describe a rule to explain a pattern

Investigate repeating and growing patterns in a range of contexts (e.g., cultural patterns, patterns in the local environment and on everyday objects).

Use materials, sound, movement, and digital tools to represent and continue repeating and growing patterns. At years 2–3, demonstrate recording the pattern in a table.

Form generalisations when students notice that repeating patterns constructed in different ways are similar (e.g., ‘red, blue, red, blue’ and ‘hop, jump, hop, jump’ are ABAB patterns). Help students to notice the similarities and differences between patterns by recording them.

With students at year 2, generalise by using the unit of repeat and ordinal position to identify further elements in a pattern.

Use mathematical language and sentence starters to support students to explain and justify how a pattern is repeating or growing and to predict further terms.

Algorithmic thinking

• follow step-by-step instructions to complete a simple task.

• follow and give step-by-step instructions for a simple task, identifying and correcting errors as the instructions are followed.

• create and use a set of precise, step-by-step instructions for carrying out a familiar routine or task.

Represent step-by-step instructions using drawings, words, flow diagrams, and verbal instructions that form a sequence.

With students, investigate sorting unfamiliar and familiar objects according to a set of instructions, directing a person or object (e.g., through an obstacle course or maze), and following and creating a set of pictorial instructions.

Explain, justify, and show how a set of instructions is complete or incomplete, using think-alouds and prompts.

Connect a series of events from a story, narrative, or daily timetable with statements in Number, Algebra, Measurement, and Geometry.

Measuring

• estimate and use an informal unit repeatedly to measure the length, mass (weight), volume, or capacity of an object
• (e.g., 18 + _ = 17 + 6, 17 = 25 (T or F?)

• estimate and then reliably measure length, capacity, and mass (weight) using whole-number metric units (e.g., from tools with labelled markings)

Explain estimation, using the language of ‘about’, ‘more or less’, and ‘close to’ to help students reflect on what the quantity or measure might be.

Investigate practical estimating and measuring situations, using appropriate measuring tools (e.g., at year 2, balance scales, capacity containers, informal units; at year 3, rulers, measuring jugs and cups, scales).

At year 3, explain how to construct and use measurement devices, particularly rulers, measurement containers, and balance scales. Demonstrate how to accurately measure length in centimetres, mass (weight) in grams, and capacity in millilitres (at year 3).

• directly compare two objects by an attribute (e.g., length, mass (weight), capacity)

• compare the length, mass (weight), volume, or capacity of objects directly or indirectly (e.g., by comparing each of them with another object, used repeatedly)

• compare and order several objects using informal units of length, mass (weight), volume, or capacity

• compare and order objects using metric units of length, mass (weight), or capacity

Investigate practical measuring situations to compare and order objects – for example: 

• which is longer or shorter, is heaver or lighter, or holds more or less (at 6 months) 
• comparing and ordering up to three objects (at year 1) 
• explaining how identical informal units need to be used when measuring (at year 2) 
• using tools like rulers, measurement containers, and scales (at year 3).

Use mathematical language to explain and justify comparative measurement attributes (e.g., long and short; heavy, heavier, and heaviest; the same as; full and empty; more and less; wide, wider, and widest). Include descriptive te reo Māori that makes the properties of objects and shapes clear.

• turn, and describe how far an object or person has turned, using full, half, and quarter turns as benchmarks

• turn, and describe how far an object or person has turned, using full, half, quarter, and three-quarter turns as benchmarks

Investigate and explain situations involving angles as ‘how far an object or person has turned.’ Have students turn physical objects and themselves.

Connect turns with fractions (e.g., half, a quarter, three quarters).

• connect days of the week to familiar events and daily routines (e.g., the class timetable).

• identify how the passing of time is measured in years, months, weeks, days, hours 
• name and order the days of the week, and sequence events in a day using everyday language of time

• name and order the months and seasons, and describe the duration of familiar events using months, weeks, days, and hours

• identify the duration of events using years, months, weeks, days, hours, minutes, and seconds

Use visual representations to support the sequencing of events (e.g., pictorial daily timetables, calendars, day-and-month cards).

Explore estimating the duration of everyday events using minutes and seconds (e.g., “How long is it until the bell rings?”). Practise recalling a sequence of events in the past and predicting future events.

Use mathematical language to explain and justify comparisons of duration and points in time (e.g., before, after, soon, later, next, today, tomorrow, yesterday, 1st, 2nd, 3rd).

Investigate using a calendar to work out the number of days, weeks, or months until important events (e.g., the number of days until Matariki, the number of weeks until the end of term).

Explore informal ways of measuring short periods of time to identify which events last longer.

• tell the time to the hour using the language of 'o'clock'.

• tell the time to the hour and half-hour, using the language of ‘past’ and 'o'clock'

• tell the time to the hour, half-hour, and quarter past and quarter to the hour

Use digital and analogue clocks to have students practise telling the time. Connect using visual representations on an analogue clock to skip counting in 5s and fractions (a half and quarter).

Connect the ‘structure’ of duration (minutes, hours, days) to our measures of time (“There are 30 minutes in half an hour, 60 minutes in an hour”).

Identify and investigate the specific times of daily events and activities in and out of school.

Perimeter, area, and volume

• visualise, estimate, and measure the perimeter and area of 2D shapes, using informal units.

• visualise, estimate, and measure:
  • the perimeter of polygons using metric units
  • the area of 2D shapes using squares of identical size
  • the volume of rectangular prisms (cuboids) by filling them with identical 3D blocks.

Explain and demonstrate that:

• perimeter is the distance around the boundary of a 2D shape 
• area is the size of the surface of a 2D shape, or how many squares cover the surface 
• volume is the amount of 3D space a shape takes up, or how many cubes fill the shape.

Investigate familiar practical situations involving perimeter, area, and volume.

Use think-alouds to demonstrate the use of visualising to identify the appropriate attribute for a measurement task and to imagine the number of units required.

Explain the importance of using the same unit when measuring, and that there should be no gaps or overlaps around the outside (perimeter) and inside (area) of 2D shapes and in filled 3D shapes (volume).

Shapes

• identify, sort by one feature, and describe familiar 2D shapes

• identify, describe, and sort familiar 2D and 3D shapes presented in different orientations, including triangles, circles, rectangles (including squares), cubes, cylinders, and spheres

• identify, describe, and sort 2D and 3D shapes, including ovals, semicircles, polygons (e.g., hexagons, pentagons), rectangular prisms (cuboids), pyramids, hemispheres, and cones, using the attributes of shapes

• visualise, identify, compare, and sort 2D and 3D shapes, using the attributes of shapes

Make available a range of 2D and 3D shapes, including tactile shapes and materials (e.g., playdough, pipe cleaners), pictures, diagrams, and digital tools.

Investigate 2D and 3D shapes in the environment.

Use everyday language and mathematical language (including te reo Māori) to explain and justify the describing and sorting of shapes (e.g., size, corners, colour, texture, sides, angles, faces, edges, vertices, triangle/tapatoru, square/tapawhā rite, same/ōrite, different/rerekē).

Use generalisations made by students to clarify and extend understanding (e.g., “Polygons have straight sides”, “2D shapes can be identified on 3D shapes”).

• identify right angles in shapes and objects

Spatial reasoning

• compose by trial and error a target shape using smaller shapes, and decompose a shape into smaller shapes

• anticipate which smaller shapes might be used to compose a target shape, and then check by making the shape

• anticipate which smaller shapes might be used to compose and decompose a target shape, and then check by making the shape

• compose and decompose 2D shapes using the attributes of shapes (e.g., lines of symmetry), other shapes, side lengths, and angles

Make available a range of materials to compose and decompose 2D shapes (e.g., pattern blocks, attribute shapes, paper shapes, playdough, tangrams).

Use think-alouds to demonstrate anticipating how small shapes can fit into or make a new shape.

Use as target shapes: 

• shapes partitioned into smaller parts (at 6 months) 
• continuous whole shapes with no partitions (at years 1–3).

• flip, slide, and turn 2D shapes to make a pattern

• recognise lines of symmetry in patterns or pictures, and create or complete symmetrical pictures or patterns

• predict the result of a one-step transformation (reflection, translation, or rotation) on 2D shapes

Connect the informal vocabulary of flip, slide, and turn with the formal vocabulary of reflect, translate, and rotate.

Investigate practical situations (e.g., making art, paper folding, checking symmetry with mirrors) and a range of artefacts and patterns.

Pathways

• follow instructions to move to a familiar location or locate an object.

• follow and give instructions to move to a familiar location or locate an object

• follow and give instructions to move people or objects to a different location, using direction, distances (e.g., number of steps), and half and quarter turns

• follow and create a sequence of step-by-step instructions (an algorithm) for moving people or objects to a different location

Investigate ways of moving to different locations within the classroom and in other parts of the school, using simple maps at year 3.

Use picture books that emphasise positional language and movement (e.g., Scatter Cat, Bears in the Night, We’re Going on a Moa Hunt).

Use spatial language and talk frames to support giving and following instructions (e.g., near, far, next to, beside, on top, under, over, down, up, left, right, turn).

Make connections between: 

• estimating distance and bodily measures (e.g., the number of steps to the door) 
• half and quarter turns and fractions 
• following or creating instructions and algorithmic thinking.

• use pictures, diagrams, or stories to describe the positions of objects and places.

• interpret diagrams to describe the positions of objects and places in relation to other objects and places.

• interpret, draw, and use simple maps to locate objects and places relative to other objects and places.

Problem

• pose a summary investigative question about a group for which the data will have categorical variables (e.g., colour, brand), and anticipate what the data might show

• pose a summary investigative question about a group for which the data will have categorical variables, and anticipate what the data might show (e.g., which outcomes might be more frequent than others)

• pose a summary investigative question about an everyday situation, using categorical data and discrete numerical (whole number) data, identify the variable and group of interest, and anticipate what the data might show

Show, with student input, how to: 

• pose summary investigative questions about an area of interest 
• identify the variable and group of interest in investigative questions.

Plan

• plan to collect data by making observations or questioning others, and discuss how the data-gathering process might affect people

• plan survey and data-collection questions for collecting data, identify who and what the data will measure, and discuss how the data-gathering process might affect people

Pose, with student input, survey and data-collection questions that will be used to collect the data required for the investigative question.

Explain the distinction between primary and secondary data and the challenges that come with sensitive topics or questions.

Investigate how survey questions and the words within survey questions can be interpreted differently by different people.

Data

• collect categorical data for one variable

• collect categorical data for more than one variable

• collect, record, and sort data, or use secondary data sources provided by someone else

Represent data using data cards, recording sheets, and tally tables. Use data cards that represent multiple variables about an individual.

Explore investigative questions using secondary data sources.

Analysis

• create and make statements about data visualisations (e.g., pictures, graphs, dot plots) for the categorical data, giving the frequency for each category

• create and make statements about data visualisations (e.g., pictures, graphs, dot plots) for the categorical data, comparing the frequencies of categories

• create and make statements about data visualisations (e.g., pictures, graphs, dot plots, bar graphs) for the categorical and discrete numerical data

Show creating and describing data visualisations, transitioning from data cards to dot plots to bar graphs.

Represent data using data cards and picture graphs (for years 1–3), frequency tables and dot plots (for years 2–3), and bar graphs (for year 3).

Have students practise using ‘I notice’ statements that include the variable name and context when describing data visualisations.

Explain and demonstrate ‘reading the data’ and ‘reading between the data’.

Explain how to describe features of data visualisations (e.g., frequency, the least/most frequent category, modes or modal groups, highest and lowest values).

Conclusion

• choose from given options the statements that best answer the investigative question

• choose from given options the statements that best answer the investigative question, reflect on findings, and compare them with anticipated outcomes

Show, with student input, how to: 

• choose the best descriptive statements that answer an investigative question 
• collate, explain, and justify their findings to others.

Statistical literacy

• agree or disagree with others’ statements about simple data visualisations (e.g., pictures, graphs, dot plots).

• match statements made by others with features in simple data visualisations, and agree or disagree with the statements.

• identify relevant features in others' data visualisations, connect these to descriptive statements, agree or disagree with the statements, and suggest improvements to them.

Show, with student input, how to: 

• read and understand claims made by others and identify corresponding features in data visualisations 
• explain agreements or disagreements with a claim made by others.

Probability investigations

• engage in stories or games that involve chance-based situations and:
  • decide if something will happen, won’t happen, or might happen
  • identify possible and impossible outcomes (e.g., for what might happen next).

• engage in chance-based investigations about games and everyday situations to:
  • anticipate and then identify possible outcomes
  • collect and record data
  • create data visualisations for frequencies of possible outcomes (e.g., lists, pictures, graphs)
  • describe what these visualisations show
  • answer the investigative question
  • notice variations in outcomes (e.g., how often each of the numbers on a dice come up)

Investigate probability by playing games of chance using physical objects (e.g., dice, coins, spinners, pulling things out of a hat).

Explain and show how to: 

• list possible outcomes 
• visualise frequencies of outcomes 
• use the vocabulary that indicates the relative order of probabilities from impossible to certain (i.e., impossible, unlikely, possible, likely, certain).

Critical thinking in probability

• agree or disagree with the statements made by others about chance-based situations.

• explain and question statements about chance-based situations, with reference to data.

Show, with student input, how to: 

• read and understand claims made by others about chance situations 
• match statements with the relevant chance situation being described 
• explain and justify why they believe a statement is true or not.

Number

• add, plus, join 
• altogether 
• biggest, smallest 
• combine, separate 
• count 
• group 
• how many 
• in between 
• more, less
• next, before, after 
• ordinal (1^st, 2^nd, 3^rd etc.) 
• take away, minus

• count on, count back 
• digit 
• double, halve 
• equal group 
• equal part 
• fair share 
• forwards, backwards 
• fraction 
• half, quarter
• odd, even 
• partition 
• set 
• share 
• skip count 
• subtract
• sum, difference 
• whole set 

• cent, coin, dollar, note
• denominator 
• eighth 
• estimate, estimation 
• money 
• multiply, divide 
• numerator 
• place value
• quantity, amount 
• regroup

• operation 
• round 
• third, fifth, sixth
• unit fraction

Algebra

• continue 
• copy 
• next
• pattern 
• repeat

• changed, unchanged 
• element 
• equal, equivalent 
• equation
• number sentence 
• repeating pattern 
• true, false 
• unit of repeat 
• zero

• error 
• predict

• complete, incomplete 
• growing pattern 
• rule 
• sequence 
• term 

Measurement

• comparative words (long, taller, heaviest etc.) 
• full, empty 
• heavy, light 
• height
• length 
• measure, weigh 
• same as 
• short, tall, wide, large, small, big 

• capacity 
• day, week, month, year 
• days of the week 
• distance 
• earlier, later 
• hour
• morning, afternoon, evening 
• o’clock 
• starting point, end point
• weight

• area 
• full turn, half turn, quarter turn 
• half past 
• months of the year
• perimeter 
• seasons of the year
• surface
• width

• gram 
• litre, millilitre 
• measuring jug or cup
• metre, centimetre
• metric
• minute, second 
• quarter past, quarter to
• ruler 
• three-quarter turn 
• unit 
• volume 
• weighing scale, balance scale

Geometry

• flip 
• positional language (next to, above, below, under, up, down, on top of, inside etc.)
• side, corner
• size (big, small, long, short) 
• square, triangle, circle
• straight, curved, round
• turn 

• 2D shape 
• 3D or solid shape 
• cube, cylinder, sphere 
• edge, face 
• slide
• rectangle 

• direction 
• left, right 
• oval, semicircle, polygon (hexagon, pentagon), rectangular prism (cuboid), pyramid, hemisphere, cone 
• position
• symmetry, line of symmetry 
• vertex 

• location
• quadrilateral 
• reflect, reflection
• right angle 
• rotate, rotation
• transform, transformation 
• translate, translation

Statistics

• data 
• dot plot 
• information 
• most, least 
• picture graph
• survey 
• tally

• category 
• graph 
• notice 
• outcome 
• statement 
• table 
• title 

• bar graph 
• claim 
• finding 
• frequency 
• variable 

Probability

• chance 
• possible, impossible 
• will happen, won’t happen, might happen

• agree, disagree 
• anticipate 
• certain, uncertain 
• likely, unlikely
• list 

• probability