Foundation Number and Algebra Essential Learnings with Proficiencies

Transcription

1 Content Descriptions NUMBER AND PLACE VALUE (F-8) Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond Subitise small collections of objects Compare, order and make correspondences between collections, initially to 20, and explain reasoning Represent practical situations to model addition and subtraction Represent practical situations to model sharing MONEY AND FINANCIAL MATHEMATICS Represent simple, everyday financial situations involving money PATTERNS AND ALGEBRA (F-10) Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings Follow a short sequence of instructions Foundation Number and Algebra Essential Learnings with Proficiencies Know the names of the numbers (F) Count orally forwards and backwards (initially to and from 20) (F) Counting from any starting point to and beyond 20 (F) Understand and connect names, numerals and quantities (U) Understand that there are patterns in the way numbers are said (U) Match the names to the numbers and quantities (F) Understand and connecting names, numerals and quantities (U) Understand that objects must be only counted once use of oneone correspondence Subitise up to 10 (F) Understand and connecting names, numerals and quantities (U) Use one-to-one correspondence to identify when two sets are equal in size and when one set is larger than another. Compare larger and smaller of two numbers (R) Order 3 or more numbers with explanation (R) Fluent in counting numbers in sequences readily, continuing patterns, and comparing objects directly to 20 by 1s Reason by explaining comparisons of quantities, creating patterns, and explain processes for indirect comparisons Understand and use terms such as first and second to indicate ordinal position in a sequence. To tenth(u) Real world (authentic) problems modelling addition and subtraction (U) Represent the problem using pictures, numbers or words (F) Convert between pictures, numbers and words (story problems) (PS) Problem Solve using materials to model authentic problems, sort objects, use familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer Use materials to model addition and subtraction of subtraction by the aggregation (grouping together) and disaggregation (moving apart) of objects. They add and subtract by counting forward and backward using the numbers from 0 to 20. Real world (authentic) problems modelling sharing (U) Use a range of practical strategies for sharing small groups of numbers, such as visual displays or concrete materials (U) Use verbal action stories to model situations that involve sharing (U) Use toy money to pay for goods in play situations (U) Sort and classify objects with justification of the classification (U) Copy patterns with explanation of the repeating elements two elements (F) Continue patterns with explanation of the repeating elements (F) Create patterns with explanation of the repeating elements (R) Be Fluent when counting numbers in sequences readily, continuing patterns, and comparing objects directly (F) Reason when explaining comparisons of quantities, creating patterns, and explain processes for indirect comparisons (R) use of drawn simple symbols in place of objects; for example, B for boy Carry out a specified sequence of actions to move an object from one location to another (PS) Play a simple rule-based game moving a specified number of places according to the result on a die in a chance-based game (U) 0.5 Foundation may, for example: Match individual objects with counting sequences up to and back from 10. Connect number names and numerals with sets of up to 10 elements. Order the first, second and third elements of a set. Use counting strategies to solve problems that involve comparing, combining and separating these sets. Copy and create simple patterns. Standard F.0 Match individual objects with counting sequences up to and back from 20. Connect number names and numerals with sets of up to 20 elements. Estimate the size of these sets (of up to 20). Order the first 10 elements of a set. Use counting strategies to solve problems that involve comparing, combining and separating these sets. Represent, continue and create simple patterns.

2 Content Descriptions USING UNITS OF MEASUREMENT (F-10) Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language Compare and order the duration of events using the everyday language of time Connect days of the week to familiar events and actions SHAPE (F-7) Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment LOCATION AND TRANSFORMATION (F-7) Foundation Measurement and Geometry Essential Learnings with Proficiencies Compare longer, shorter, same and explain reasoning (R) Compare heavier, lighter, same and explain reasoning (R) Compare which holds more, less or same and explain reasoning (R) Be Fluent in comparing objects directly (F) Reason by explaining comparisons of quantities and explaining processes for indirect comparison of measurement (R) Use suitable language when comparing objects (U) Know and use the language of time (F) Use of a clock to determine the hour o clock Compare and order the duration of events using the language of time (F) Be Fluent in sequencing and comparing the duration of events (F) Reason by explaining comparisons of time (R) Name and order the days of the week (F) Connect days of the week to familiar events and actions (U) Understand connections between days of the week and familiar events (U) Sort and describe squares, circles, triangles, rectangles, spheres and cubes (U) Show Understanding by connecting names with objects (U) Problem Solve through sorting, describe and classify objects (PS) Reason by comparing and naming the shapes and attributes of objects (R) Describe position and movement Know the everyday language of location and direction (F) Understand and use the language of location and direction (U) Follow and give simple directions using the language of location and direction (PS) 0.5 Foundation may, for example: Compare lengths and masses of familiar objects. Identify measurement attributes of length and mass in practical situations. Order events in a day. Name the days of the week, in order. Identify simple shapes in their environment. Use simple location words. Standard F.0 Compare lengths, masses and capacities of familiar objects. Identify measurement attributes in practical situations. Order events and explain their duration. Match days of the week to familiar events. Identify simple shapes in their environment. Sort shapes by their common and distinctive features. Use simple statements and gestures to describe location. Content Descriptions Foundation Statistics and Probability Essential Learnings with Proficiencies DATA REPRESENTATION AND INTERPRETATION (F-10) Answer yes/no questions to collect information Organise answers to yes/no questions into simple data displays using objects and drawings Interpret simple data displays about yes/no questions pose questions about themselves and familiar objects and events (U) represent responses to questions using simple displays (PS) use data displays to answer simple questions (R) Problem Solve through modelling authentic problems, using familiar counting sequences to solve unfamiliar problems (PS) Discussing the reasonableness of the answers (R) Reason by explaining comparisons of quantities (R) Represent responses to questions using simple displays, including grouping students according to their answers Use data displays to answer simple questions such as how many students answered yes to having pets? 0.5 Foundation may, for example: Answer simple yes/no questions about given categorical data that are sorted. Standard F.0 Sort familiar categorical data into sets and use these to answer yes/no questions and make simple true/false statements about the data.

3 Content Descriptions NUMBER AND PLACE VALUE (F-8) Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line. Count collections to 100 by partitioning numbers using place value Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts Level 1 Number and Algebra F.5 Level 1 may, for example: Count forwards and backwards to and from 100 from any number (F) Count beyond 100 by 1s from 0 (F) From a number beyond 100 count forwards and backwards from any given number (F) Count orally by 2 s, 5 s, 10 s to and beyond 100 starting at 0 (F) Understand and connect names, numerals and quantities Order Number sequences (U) Use number lines and number grids to count forwards, backwards and by patterns (F) Model counting using number lines (F) Fluent in counting numbers in sequences readily, continuing patterns, and comparing objects directly Reason by explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparisons Bundle ones to create ten and tens to create 100 (F) Create, name and order teen numbers as 10 and some more (F) Understanding partitioning of numbers and the importance of grouping in tens Understanding two digit numbers as comprised of tens and ones/units calculation of the next number when asked to add 1 or 2 to any natural number from 0 to 10 drawing of diagrams to show subtraction activities addition and subtraction of two-digit multiples of ten by counting on and counting back *counting on from the larger of two collections to find their total *use of the number properties (commutative and associative) of addition in mental computation, and recognition of complements to ten; for example, = = = 20 Model with materials, number lines and number grids addition and subtraction within and including 10 (F) Model with materials, number lines and number grids addition and subtractions within and including 20 (F) Discuss and compare strategies for addition and subtraction (R) develop a range of mental strategies for addition and subtraction problems (F) Real world (authentic) problems modelling addition and subtraction (U) Represent a given problem using pictures, numbers or words (F) Convert between pictures, numbers and words (story problems)(show understanding and interpretation) (PS) Problem Solve using materials to model authentic problems, sort objects, use familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS) Represent practical situations that drawing of diagrams to show sharing of up to 20 items model sharing sharing a set of objects, such as a packet of sweets, equally between a small group of people using one-to-one correspondence recognising whether there is a remainder or not after sharing equally FRACTIONS AND DECIMALS (1-6) Recognise and describe one-half Model the partitioning of one whole into two equal parts (U) as one of two equal parts of a Model the partitioning of a group into two equal parts (U) whole Name equal parts as halves, one equal part as one half (R) sharing a collection of readily available materials into two equal portions (F) Show reasoning by splitting an object into two equal pieces and describing how the pieces are equal MONEY AND FINANCIAL MATHEMATICS (1-10) Recognise, describe and order Recognise Australian coins according to their value (F) Australian coins according to Order Australian coins according to their value (F) their value Describe and order Australian coins according to their value (R) showing that coins are different in other countries by comparing Asian coins to Australian coins (U) Understanding that the value of Australian coins is not related to size Show reasoning by describing the features of coins that make it possible to identify them PATTERNS AND ALGEBRA (F-10) Investigate and describe number patterns formed by skip counting Identify and say patterns counting by 1 s forwards and backwards from any point to 100 (F) Identify and say patterns counting by 2 s to 50, 5 s to 100 and 10 s to and beyond and patterns with objects 100 (F) Identify and say patterns with explanation of the repeating elements (R) Investigate and model patterns on a number grid and a number line as skip counting (PS) Create patterns with explanation of the repeating elements (R) Be Fluent when counting numbers in sequences readily, continuing patterns, and comparing objects directly Recognise the importance of repetition of a process in solving problems Reason when explaining comparisons of quantities, creating patterns, and explain processes for indirect comparisons using one-to-one correspondence to determine which of two sets is larger, or if they are of equal size dividing a set of blocks in a simple ratio such as 2 for me, 1 for you Connect number names and numerals with sets of more than 20 elements, and order the first 20 elements of a set. Subitise small collections of objects. Represent and solve simple addition and subtraction problems, using materials. Investigate simple patterns of objects and their images. Standard 1.0 Describe number sequences resulting from skip counting by 2s, 5s and 10s. Count to and from 100 and locate these numbers on a number line. Partition numbers using place value. Carry out simple additions and subtractions, using counting strategies. Identify representations of one half. Recognise Australian coins according to their value. Continue simple patterns involving numbers and objects with and without the use of digital technology.

4 Level 1 Measurement and Geometry Content Descriptions F.5 Level 1 may, for example: USING UNITS OF MEASUREMENT (F-10) Measure and compare the lengths, masses and capacities Use uniform informal units to compare longer, shorter, same and explain reasoning (R) of pairs of objects using uniform Use uniform informal units to compare heavier, lighter, same and explain informal units reasoning (R) Use uniform informal units to compare which holds more, less or same and explain reasoning (R) Understand that in order to compare objects, the unit of measurement must be the same size (U) Be Fluent in comparing objects directly (F) Reason by explaining comparisons of quantities and explaining processes for indirect comparison of measurement (R) Tell time to the half-hour To know and use the language of time (F) Compare and order the duration of events using the language of time (PS) Knowledge of the relationship between analogue and digital clocks read time on analogue and digital clocks and observing the characteristics of half hour times (F) Be Fluent in sequencing and comparing the duration of events (F) Reason by explaining comparisons of time (R) Describe duration using months, Connect months, weeks and days to familiar events and actions (U) weeks, days and hours Describe durations using months, weeks, days and hours (U) Understand connections between days, weeks and months Understand and order relative size of months, weeks, days and hours SHAPE (F-7) Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features LOCATION AND TRANSFORMATION (F-7) Give and follow directions to familiar locations Sort and describe squares, circles, triangles, rectangles, spheres and cubes (F) Connect shape names to everyday objects (F) Explore geometric features and describe shapes and objects using everyday words such as 'corners', 'edges' and 'faces' (R) Use of labelling on diagrams of shapes Show Understanding by connecting names with objects Problem Solve through sorting, describing and classify objects by corners, edges and faces Recognise the congruence of two shapes Reason by comparing and naming the shapes and attributes of objects Know the everyday language of location and direction (U) follow and give simple directions using the language of location and direction (PS) Understand the language of location and direction (U) Understand that people need to give and follow directions to and from a place, and that this involves turns, direction and distance (U) Understand the meaning and importance of words such as clockwise, anticlockwise, forward and under when giving and following directions interpreting and following directions around familiar locations (U) Use direct and indirect comparisons to decide which of two objects is longer, heavier or holds more, and explain reasoning. Place familiar events in time order. Identify, sort and name familiar three-dimensional objects in their environment. Describe movement, and follow and give simple directions. Standard 1.0 Use informal units of measurement to order objects based on length, mass and capacity. Tell time to the half-hour. Explain time durations. Describe two-dimensional shapes and threedimensional objects. Use the language of distance and direction to move from place to place. Level 1 Statistics and Probability CHANCE (1-10) Identify outcomes of familiar Pose questions about themselves and familiar objects and events (U) events involving chance and Identify outcomes of familiar events involving chance, describing them using everyday language (R) describe them using everyday Represent responses to questions using simple displays such as a probability line language such as will happen, (F) won t happen or might happen Problem Solve through modelling authentic problems, using familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS) Reason by explaining comparisons of quantities (R) DATA REPRESENTATION AND INTERPRETATION (F-10) Choose simple questions and gather Use data displays to answer simple questions, developing the language of least, responses most, same amount (U) Use tally marks to record (F) determine which questions will gather appropriate responses for a simple investigation (R) Problem Solve through modelling authentic problems, using familiar counting sequences to solve unfamiliar problems. (PS) Discuss the reasonableness of the answers (PS) Reason by explaining comparisons of quantities (R) Represent data with objects and Understand that one object or drawing represents on data value (U) drawings where one object or drawing Explain the display and what it tells us about the data (U) represents one data value. Describe Compares categories using language such as greatest or least (R) the displays Describe outcomes of simple familiar events using 'will happen', 'won't happen' or 'might happen'. Sort objects into designated categories on diagrams and create their own visual records by sorting objects or their images. Classify outcomes of simple familiar events. Ask questions to collect data and draw simple data displays. Describe data displays.

5 Level 2 Number and Algebra Content Descriptions NUMBER AND PLACE VALUE (F-8) Investigate number sequences, Count orally forwards and backwards by 1 s from any number beyond 100 to initially those increasing and 1000 (F) decreasing by twos, threes, fives Counting orally by 2 s, 5 s and 10 s to 100 and beyond (F) and ten from any starting point, Count backwards by 10 s from 3 digit multiple of 10 (F) then moving to other sequences Count by 100 s to 1000 and beyond (F) Investigate and describe patterns in number sequences, such as adding 10 always results in the same final digit (R) Understand and describe final digit patterns of familiar patterns (U) Developing fluency and confidence with numbers and calculations by saying number sequences (F) Fluent in counting numbers in sequences readily, continuing patterns, and comparing objects directly (F) Reason by explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparisons (R) Recognise, model, represent and Modelling numbers with materials and diagrams (U) order numbers to at least 1000 recognising there are different ways of representing numbers (U) Order numbers in ascending and descending order (F) Compare numbers on a number line (U) Identifying patterns going beyond 100 (R) Developing fluency with writing numbers in meaningful contexts (F) Use materials to model and represent numbers understanding three digit numbers as comprised of hundreds, tens and ones/units (U) Demonstrate and use models to compare value of numbers in base 10 places (U) Group, partition and rearrange Use Place Value chart bundling sticks, sticks of Unifix or Base Ten Blocks to collections up to 1000 in model partitioning of 3 digit numbers (F) hundreds, tens and ones to Investigate and discover strategies for efficient counting such as counting up by facilitate more efficient counting multiples of 10 then some more on a number line (PS) Show Understanding of expanding numbers in 2 and 3 digit numbers through modeling, drawing visuals and describing what is happening with the hundreds, tens and ones (U) Explore the connection between addition and subtraction Solve simple addition and subtraction problems using a range of efficient mental and written strategies Recognise and represent multiplication as repeated addition, groups and arrays Recognise and represent division as grouping into equal sets and solve simple problems using these representations development and use of a fact family linking = 30 to = 30, 30 5 = 25 and = 5 Real world (authentic) problems modeling addition and sharing with 2 digit numbers (U) Represent problems using pictures, numbers and words (F) Convert between pictures, numbers and words (story problems) (PS) Create addition and subtraction story problems (PS) Create, model and record efficient methods for addition and subtraction (R) Use number lines and parts and totals models to show the connections between addition and subtraction (U) Use counting-on to identify the missing element in an additive problem (F) Becoming fluent with partitioning numbers to understand the connection between addition and subtraction (F) Automatic recall of tens and twentys facts Use commutative and associative properties of + n and x n in mental computation (for example, = and can be done as or 3 + 9). Becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10 (F) Problem Solve using materials to model authentic problems, sort objects, use familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS) Show reasoning by explaining strategies and understanding of connections between addition and subtraction (R) Model and represent simple additive situations using materials such as 10 frames, 20 frames and empty number lines (F) Use skip counting on a number line to find four twos as an additive concept (F) Describe and calculate simple multiplication as repeated addition, such as 3 5 = ; and division as sharing, such as 8 shared between 4. Represent array problems with available materials and develop the language of rows and columns (F) Use skip counting to count groups of and rows or columns in arrays (F) Represent array problems with available materials and explain reasoning (R) Show understanding by visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups (U) Dividing the class or a collection of objects into equal sized groups (U) Identify the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three (R & U) Develop the language of equal sharing and how many? (U) Show Understanding by modelling and creating word problems to represent division concepts (U) Progression Score 1.5 Count to and from, and order numbers up to hundreds. Recognise different ways of writing the same number. Group collections of objects in units, tens and hundreds. Write and solve number sentences involving addition or subtraction. Standard 2.0 Recognise increasing and decreasing number sequences involving 2s, 3s, 5s and 10s. Count to and from, and order numbers up to Perform simple addition and subtraction calculations, using a range of strategies. Use digital technology to produce sequences by constant addition.

6 FRACTIONS AND DECIMALS (1-6) Recognise and interpret common Making models of common fractions such as ½ ¼ 1/3 (F) uses of halves, quarters and Recognise that sets of objects can be partitioned in different ways to eighths of shapes and collections demonstrate fractions (U) Show understanding by relating the number of parts to the size of a fraction Name the fractions, identify in a counting sequence and make connection to the written words (U,F) MONEY AND FINANCIAL MATHEMATICS (1-10) Count and order small collections Identify equivalent values in collections of coins or notes, such as two of Australian coins and notes five cent coins having the same value as one 10cent coin (F) according to their value Counting collections of coins or notes to make up a particular value, such as that shown on a price tag (U) Grouping of coins of the same denomination in sets of $1 Solving real life money problems using 5 cent and 10 cent combination Solving real life money problems using coin and note combinations Showing Reasoning through justifying solutions and finding alternate representations PATTERNS AND ALGEBRA (F-10) Describe patterns with numbers Describe a pattern created by skip counting and representing the pattern and identify missing elements on a number line (R) Investigating features of number patterns resulting from adding twos, fives or 10s, 3 s and 4 s (PS) Use reasoning to make connections between and describe number patterns Solve problems by using number Representing a word problem as a number sentence (PS) sentences for addition or Writing a word problem to represent a number sentence (PS) subtraction Interpret between Pictures, Numbers and Words to show understanding of addition and subtraction (U) Solve authentic addition and subtraction problems, explaining strategies and reasoning (R) Apply repetition in arithmetic using technology to construct a sequence of numbers based on constant operations, including addition or subtraction from a given starting value multiplication as repeated sharing a set of objects equally between a small number of groups addition and division as repeated subtraction Recognise and interpret common uses of halves and quarters. Describe patterns with numbers and recognise simple digit patterns in number sequences. Represent multiplication and division by grouping into sets. into halves, quarters and eighths Find the total value of simple collections of Australian notes and coins. Identify the missing element in a number sequence. Write and solve number sentences involving addition or subtraction.

7 (what to teach/learn) USING UNITS OF MEASUREMENT (F-10) Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units Compare masses of objects using balance scales Tell time to the quarter-hour, using the language of 'past' and 'to' Level 2 Measurement and Geometry Compare shapes and determine attributes of length, area, volume and capacity (R) Order shapes by one attribute, discuss using the language of larger, smaller, longer, shorter, least, most, same, equal value (F) Comparing lengths using finger length, hand span or a piece of string (U) Estimate and use base ten block minis and longs to measure length in centimetres (PS) Compare areas using the palm of the hand or a stone (R) Use uniform grid paper to find the area in squares of given shapes (U) Estimate and compare capacities using a range of containers and pouring materials (U) Estimate and stack containers with uniform cubes (unifix or base ten block (minis) to find volume in cubes (U) Compare capacity of a range of containers using the same uniform cubes (R & U) Name and order months and seasons Use a calendar to identify the date and determine the number of days in each month SHAPE (F-7) Describe and draw two-dimensional shapes, with and without digital technologies Show Understanding by using length, area, volume and capacity in problem solving contexts (U) Show understanding by making and drawing models and recording measurements of length, area, volume and capacity of objects (U) Estimate mass by hefting, using the language of heavier, lighter and similar when comparing objects (R) Using balance scales to determine whether the mass of different objects is more, less or about the same, or to find out how many single items are need to balance a different item (PS) Use a uniform object to compare items to on the balance scale (U) Estimate and compare objects using uniform metric weights to compare items on the balance scale (U) Show fluency through using units iteratively (repeatedly) to compare measurements (F) Identify and mark quarters on the analogue clock (U) Identifying the quarter after an hour as quarter past an hour and the quarter before an hour as quarter to an hour (U) Link the quarter past as 15 minutes and the quarter to as 45 minutes (U) Describe the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three (R) Describe the characteristics of quarter to times on an analogue clock, and identifying that the small hand is pointing almost to the next number and the big hand is pointing to the nine (R) Show fluency through describing and comparing time durations (F) Problem Solving using time and formulating problems from authentic situations to represent quarter past and quarter to (PS) Identify and describe features of a calendar (U) Create a calendar to represent a specific time period (PS) Understand the current use of Seasons representing a specific time period Use a calendar as an ongoing tool to record time and specific events each month (U) Use a calendar to predict time frames by month, week and days (PS) Use a calendar to identify the date and to determine the number of days in each month (PS & R) Use calendars to locate specific information, such as finding a given date on a calendar and saying what day it is, and identifying personally or culturally specific days (F) Investigate the seasons used by Aboriginal people and compare them to those used in Western society, recognising the connection to weather patterns (U) Show understanding by connecting knowledge of time from smallest time frame to largest time frame (days, weeks, fortnight, month etc) (U) Identify and name 2 dimensional shapes (F) Compare and describe 2D shapes to develop the vocabulary of straight and curved lines, edges, points and corners, number of sides (U) Identifying key features of squares, rectangles, triangles, kites, rhombuses and circles, such as straight lines or curved lines, and counting the edges and corners (R) Show reasoning by sorting shapes by key features and describing the categories Describe the features of threedimensional Identify and name known 3 dimensional shapes such as cube, cone, sphere, pyramid (F) objects Identifying geometric features of known shapes such as the number of faces, corners or edges (U) Investigate and identifying geometric features of prisms and other 3D shapes through the use of models, such as the number of faces, corners or edges (R) Use Pictures, Numbers, Words to show what is known about 3D shapes (PS) Show reasoning by describing connections between 2D and 3D representations LOCATION AND TRANSFORMATION (F-7) Interpret simple maps of familiar locations and identify the relative Understand and use directional language left and right, up (top) and down (bottom) on a page and transfer this to reading a map positions of key features Use directional language of beside, between, next to, to tell directions on a map (PS) Construct arrangements of objects from a set of directions (PS) Use problem solving strategies to plan problems for others by planning routes on maps and recording the directions (PS) Through problem solving match transformations with their original shape (PS) Understand that we use representations of objects and their positions, such as on maps, to allow us to receive and give directions and to describe place (U) Investigate the effect of one-step Investigate one step slides using models (PS) slides and flips with and without Investigate one step flips using models (PS) digital technologies Show understanding by using Pictures, Numbers, Words to show, describe and compare slides and flips (U) Identify and describe half and quarter Students model half and quarter turns related to analogue clock (F) turns predict and reproduce a pattern based around half and quarter turns of a shape and sketching the next element in the pattern (PS) Investigate the real world application of flips, slides and turns (PS) understand that objects can be moved but changing position does not alter an object s size or features (U) 1.5 Standard 2.0 Compare and order familiar objects by their length and relative mass. Describe the duration of familiar events in terms of hours, days and weeks. Recognise and classify familiar shapes and objects, using their features. Give and follow directions to and from a place using everyday language for orientation, relative position, direction and distance. Order shapes and objects, using informal units for a range of measures. Tell time to the quarter hour. Use a calendar to identify the date, days, weeks and months included in seasons and other events. Draw two-dimensional shapes, and specify their features. Recognise the features of three-dimensional objects. Interpret simple maps of familiar locations. Explain the effects of onestep transformations.

8 CHANCE (1-10) Identify practical activities and everyday events that involve chance. Describe outcomes as likely or unlikely and identify some events as certain or impossible Level 2 Statistics and Probability Create a probability meter to place everyday events to match the language of chance (R) Identify practical activities and everyday events that involve chance. (U) Describe outcomes as likely or unlikely and identify some events as certain or impossible (U) Classify a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning Make conjectures about chance events and test these (PS) Show fluency through listing possible outcomes of chance events (F) Formulate problems from authentic situations, (PS) DATA REPRESENTATION AND INTERPRETATION (F-10) Identify a question of interest based on one categorical variable. Gather data relevant to the question Collect, check and classify data Create displays of data using lists, table and picture graphs and interpret them Determine questions for gathering data (R) Determine methods for gathering and recording data including a table (F) Gather data relevant to the question (F) Recognise the usefulness of tally marks (F) Identifying categories of data and using them to sort data (R) Check and classify data (F) Create picture graphs to represent data using one to one correspondence (PS) Create displays of data using lists, table and picture graphs (PS) Compare the usefulness of different data displays (R) Show reasoning by creating and interpreting simple representations of data (R) 1.5 Level 2 may, for example: Explain why they think an event is 'certain' or 'impossible'. Use tallies and tables to record answers to questions and summarise the answers by counting. Standard 2.0 Use everyday language to describe outcomes of familiar events. Collect data from relevant questions to create lists, tables and picture graphs with and without the use of digital technology. Interpret data in context.

9 NUMBER AND PLACE VALUE (F-8) Investigate the conditions required for a number to be odd or even and identify odd and even numbers Recognise, model, represent and order numbers to at least Apply place value to partition, rearrange and regroup numbers to at least to assist calculations and solve problems Recognise and explain the connection between addition and subtraction Recall addition facts for singledigit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation Recall multiplication facts of two, three, five and ten and related division facts Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies FRACTIONS AND DECIMALS (1-6) Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole Level 3 Number and Algebra Explain if and why a number is odd or even. (U) Read, write and order numbers to (F) Model numbers to (U,F) MONEY AND FINANCIAL MATHEMATICS (1-10) Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents PATTERNS AND ALGEBRA (F-10) Describe, continue, and create number patterns resulting from performing addition or subtraction Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes Rename larger numbers using place value and using other non-place value partitions. (F) Partition larger numbers into place value parts to use to assist calculations (Partial sums, Partial products). (R,F) Apply knowledge of partitioning to problem solving situations Understand subtraction is the inverse of addition (U) Be able to write addition and subtraction fact family number sentences for a set of numbers. (F) Know addition facts and strategies such as compliments to ten, doubles and near doubles and counting by tens and ones forwards and backwards. (F) Apply a range of mental and written strategies to solve the result of addition and subtraction calculations such as partial sums and compensation. (U,F) Know multiplication facts for 2 s, 3 s, 5 s and 10 s. (F) Relate skip counting to multiplication to division. (U) Relate multiplication facts to division facts (U) Use a range of strategies for multiplication such as the area model and the partitioning of numbers.(u,f) Understand and model unit fractions. Find and relate unit fractions of a group through sharing (such as shared between ( ) 3 is 1/3) Count by ½ s, 1/3 s and 1`/4 s to 1. (F) use of fractions with numerators other than one; for example, 3 of a 4 block of chocolate use of money as a model for grouping and unpacking lots of 10s rounding of amounts of money up and down to the nearest dollar Partition money amounts using place value denominations ($100 s, $10 s, $1 s) and also with other denomination partitions.(f) Calculate change using strategies such as counting up. (F) Solve addition and subtraction problems using money as a context using strategies such as counting on for addition and counting up for subtraction. (F) Understand and apply skip counting number patterns in solving problems involving repeated addition and repeated subtraction (U,F) finding and describing simple rules in words to solve problems using simple function machines to represent and apply a process or the inverse process, such as increase or decrease the value of a number by a specified amount 2.5 Level 3 may, for example: Count and order numbers to and from thousands. Apply place value to partition, rearrange and regroup numbers to help with calculations and solve problems. Recall multiplication facts for 2, 5 and 10. Model and represent the unit fractions of halves, thirds, quarters, fifths and eighths. Explore language differences associated with fractions. Describe, continue and create number patterns formed by repeated addition or subtraction. Standard 3.0 Classify numbers as either odd or even. Count and order numbers to and from Recognise the connection between addition and subtraction. Recall addition and multiplication facts for single-digit numbers. Explore simple number sequences based on multiples. Solve problems using efficient strategies for multiplication with and without the use of digital technology. Model and represent unit fractions for halves, thirds, quarters, fifths and eighths, and multiples of these up to one. Represent money values in various ways and correctly count out change from financial transactions. Continue number patterns involving addition or subtraction.

10 USING UNITS OF MEASUREMENT (F-10) Measure, order and compare objects using familiar metric units of length, area, mass and capacity Tell time to the minute and investigate the relationship between units of time SHAPE (F-7) Make models of threedimensional objects and describe key features LOCATION AND TRANSFORMATION (F-7) Create and interpret simple grid maps to show position and pathways Level 3 Measurement and Geometry Recognise the importance of using common units of measurement. (R) Recognise and use centimetres and metres, grams and kilograms, and millilitres and litres. (F) Tell and write time to the minute. (F) Understand, use and order units of time. (U,F) Recognise there are 60 minutes in an hour and 60 seconds in a minute (U) Use nets to make three-dimensional objects and identify faces, edges and vertices. (P) Create simple maps. (P) Use simple maps such as theme park or zoo maps. (U) 2.5 Level 3 may, for example: Compare the masses of objects, using balance scales. Interpret digital and analogue representations of minutes, hours, days, weeks and years. Explore the properties of prisms. Interpret grid maps of their local environment. Standard 3.0 Use metric units for length, area, mass and capacity. Tell time to the nearest minute. Make models of threedimensional objects. Create simple maps. Match positions on maps with given information. Identify symmetry in the environment Identify symmetrical patterns, pictures and shapes. (P) Identify symmetry in natural and constructed environments. Identify and describe slides and turns found in the natural and built environment recognising and representing slides and turn used in brickwork around the school recognising and representing slides and turn used in sporting activities GEOMETRIC REASONING (3-10) Identify angles as measures of turn and compare angle sizes in everyday situations Identify comparative sizes of angles in everyday situations including the hands on a clock. (R) Recognise angles in terms of turns in everyday situations. Use angle size as a measure of turn in real situations. CHANCE (1-10) Conduct chance experiments, identify and describe possible outcomes and recognise variation in results Level 3 Statistics and Probability Conduct repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials. (F,R) DATA REPRESENTATION AND INTERPRETATION (F-10) Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies Interpret and compare data displays Collect and record categorical data to answer an identified question. (R) Identify efficient ways to record data, and representing and reporting the results of investigations including using digital technologies. (P) Compare and contrast between displays of data and make appropriate conclusions. (U) 2.5 Level 3 may, for example: Place events from familiar contexts in order of how likely they are to happen. Recognise variation in measurements and other data. Make tallies and convert them into one-to-one picture graphs (pictographs) and bar charts. Standard 3.0 Conduct chance experiments, list possible outcomes and recognise variations in results. Carry out simple data investigations for categorical variables. Interpret and compare data displays.

11 (what to teach/learn) Level 4 Number and Algebra NUMBER AND PLACE VALUE (F-8) Investigate and use the properties Explain why a number is odd or even. (U) of odd and even numbers Relate the properties of odd or even to authentic contexts. (R) Recognise, represent and order Read, write and order numbers up to and back from s. (F) numbers to at least tens of thousands Apply place value to partition, Rename larger numbers using place value and using other non-place value rearrange and regroup numbers to partitions. (F) at least tens of thousands to assist Partition larger numbers into place value parts to use to assist calculations calculations and solve problems (Partial sums, Partial products). (R,F) Apply a range of mental strategies to solve and/or estimate the result of calculations. (F) Investigate number sequences Understand the number patterns for the multiples of 3-9 and use in assisting involving multiples of 3, 4, 6, 7, 8, with determining multiplication facts. (U) and 9 Recall multiplication facts up to 10 Know multiplication facts to 10x10. (F) 10 and related division facts Be able to relate all four fact family number facts for multiplication and division to any multiplication or division number sentence. (U) Develop efficient mental and use of written number sentences such as 20 4 = 5 to summarise sharing written strategies and use (partition) and how many? (quotition) processes appropriate digital technologies for representation of multiplication as a rectangular array and as the area of a multiplication and for division rectangle where there is no remainder use of fact families (5 7 = 35, 35 7 = 5) to solve division problems estimate the results of computations and recognise whether these are likely to be over-estimates or under-estimates. Use a range of techniques for multiplication such as the area model, repeated addition and the partitioning of numbers.(f) Use a range of techniques for division such as the area model, repeated subtraction and the partitioning of numbers.(f) Recognise the multiplication and division are inverse operations (U) FRACTIONS AND DECIMALS (1-6) Investigate equivalent fractions Understand the relationship between ½, 2/4 and 4/8 in authentic contexts and used in contexts other equivalent fractions. (U) development and use of fraction notation and recognition of equivalent fractions 4 such as 1 = 8, including the ordering of fractions using physical models 2 Count by quarters halves and Count by ½ s, 1/3 s and 1`/4 s with and without a number line. (F) thirds, including with mixed develop fraction notation and compare simple common fractions such as numerals. Locate and represent 3 these fractions on a number line > 2 using physical models. 4 3 Recognise that the place value Understand the place value system into the hundredths using real life contexts system can be extended to tenths such as money. (U,R) and hundredths. Make connections use of place value (as the idea that ten of these is one of those ) to determine between fractions and decimal the size and order of decimals to hundredths notation Relate fractions as another way of representing division. Relate fractions to decimals through fractions of 100 (1 metre, $1.00, 100 piece block of chocolate). (R) MONEY AND FINANCIAL MATHEMATICS (1-10) Solve problems involving Solve addition and subtraction problems using money as a context using purchases and the calculation of strategies such as counting on for addition and counting up for subtraction. (F) change to the nearest five cents addition and subtraction of amounts of money including calculation of change with and without digital from $10 technologies PATTERNS AND ALGEBRA (F-10) Explore and describe number patterns resulting from performing multiplication Solve word problems by using number sentences involving multiplication or division where there is no remainder Use equivalent number sentences involving addition and subtraction to find unknown quantities Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions Understand and apply the multiplication (skip counting) number patterns in solving multiplication and resulting products. (U,F) Apply a variety of strategies for multiplication and division including mental strategies for problem solving. (F) Rearrange subtraction number sentences into addition and vice versa to solve for unknown quantities. (F) Use partitioning to find missing numbers/digits in a number sentence eg.56+?=136 or 53+8?=136 (U,F) constructing and applying an algorithm for multiplication of two-digit numbers partitioning and ordering a set of Australian coins by denomination 3.5 Level 4 may, for example: Count and order numbers to and from tens of thousands. Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9. Use addition and subtraction facts to develop efficient mental strategies for computation. Count by quarters, halves and thirds, including with mixed numbers. Make connections between fractions and decimal notation. Calculate change and round to the nearest five cents. Solve word problems by using number sentences involving multiplication or division. Use equivalent number sentences involving addition and subtraction to find unknown quantities. Standard 4.0 Use the properties of odd and even numbers. Continue number sequences involving multiples of singledigit numbers and unit fractions, and locate them on a number line. Recall multiplication facts to 10 x 10 and related division facts. Choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology. Estimate answers accurately enough for the context. Recognise common equivalent fractions in familiar contexts. Locate familiar fractions on a number line. Make connections between fractions and decimal notations up to two decimal places. Solve simple purchasing problems with and without the use of digital technology. Describe number patterns resulting from multiplication. Identify unknown quantities in number sentences.