Number+and+Place+Value+Continuum

=__Number and Place Value Curriculum__=

This page details the number and place value substrand within the Number and Algebra strand in the Australian curriculum. It is simply copied directly from the curriculum and is our reference point for study of this sub strand. Foundation Year Literacy Intercultural understanding Numeracy Aboriginal and Torres Strait Islander histories and cultures Asia and Australia´s engagement with Asia || * Reading stories from other cultures featuring counting in sequence to assist students to recognise ways of counting in local languages and across cultures Literacy Intercultural understanding Numeracy Aboriginal and Torres Strait Islander histories and cultures Asia and Australia´s engagement with Asia || * understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the ‘how many’ question Literacy Intercultural understanding Personal and social capability Critical and creative thinking Aboriginal and Torres Strait Islander histories and cultures Asia and Australia´s engagement with Asia || * comparing and ordering items of like and unlike characteristics using the words ‘more’, ‘less’, ‘same as’ and ‘not the same as’ and giving reasons for these answers Critical and creative thinking Numeracy Aboriginal and Torres Strait Islander histories and cultures || * using a range of practical strategies for adding small Year 1 Literacy Intercultural understanding Numeracy Asia and Australia´s engagement with Asia || * using the popular Korean counting game (samyukgu) for skip counting Literacy Critical and creative thinking || * modelling numbers with a range of material and images Literacy Critical and creative thinking || * understanding partitioning of numbers and the importance of grouping in tens Literacy Critical and creative thinking Numeracy || * developing a range of mental strategies for addition and subtraction problems ||
 * Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)
 * Identifying the number words in sequence, backwards and forwards, and reasoning with the number sequences, establishing the language on which subsequent counting experiences can be built
 * developing fluency with forwards and backwards counting in meaningful contexts, including stories and Rhymes
 * understanding that numbers are said in a particular order and there are patterns in the way we say them ||
 * Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
 * using scenarios to help students recognise that other cultures count in a variety of ways, such as by placing one pebble in a bag to represent one object (for example to count the number of cattle). ||
 * Subitise small collections of objects (ACMNA003) Numeracy || * using subitising as the basis for ordering and comparing collections of numbers ||
 * Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
 * understanding and using terms such as ‘first’ and ‘second’ to indicate ordinal position in a sequence.
 * using objects which are personally and culturally relevant to students ||
 * Represent practical situations to model addition and sharing (ACMNA004)
 * groups of numbers, such as visual displays or concrete materials
 * using Aboriginal and Torres Strait Islander methods of adding, including spatial patterns and reasoning ||
 * 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 (ACMNA012)
 * developing fluency with forwards and backwards counting in meaningful contexts such as circle games ||
 * Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)
 * identifying numbers that are represented on a number line and placing numbers on a prepared number line ||
 * Count collections to 100 by partitioning numbers using place value (ACMNA014)
 * understanding two digit numbers as comprised of tens and ones/units ||
 * Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)

Year 2 Literacy Critical and creative thinking || * developing fluency and confidence with numbers and calculations by saying number sequences Literacy Critical and creative thinking Numeracy || * recognising there are different ways of representing numbers and identifying patterns going beyond 100 Literacy Intercultural understanding Critical and creative thinking Numeracy Aboriginal and Torres Strait Islander histories and cultures Asia and Australia´s engagement with Asia || * using an abacus to model and represent numbers Critical and creative thinking || * becoming fluent with partitioning numbers to understand the connection between addition and subtraction Literacy Critical and creative thinking Numeracy || * 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 Literacy Critical and creative thinking Numeracy || * representing array problems with available materials and explaining reasoning Critical and creative thinking Numeracy || * dividing the class or a collection of objects into equalsized groups
 * Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026)
 * recognising patterns in number sequences, such as adding 10 always results in the same final digit ||
 * Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
 * developing fluency with writing numbers in meaningful contexts ||
 * Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
 * understanding three digit numbers as comprised of hundreds, tens and ones/units
 * demonstrating and using models such as linking blocks, sticks in bundles, place value blocks and Aboriginal bead strings and explaining reasoning ||
 * Explore the connection between addition and subtraction (ACMNA029)
 * using counting on to identify the missing element in an additive problem ||
 * Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)
 * modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines ||
 * Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
 * visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups ||
 * Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)
 * identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three ||

Year 3 number to be odd or even and identify odd and even numbers (ACMNA051) Literacy Critical and creative thinking || * identifying even numbers using skip counting by twos or by grouping even collections of objects in twos Literacy Critical and creative thinking Numeracy || * recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones Literacy Critical and creative thinking || * demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences || Critical and creative thinking || * recognising that certain singledigit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers Literacy Information and communication technology capability Critical and creative thinking Numeracy || * writing simple word problems in numerical form and vice versa
 * Investigate the conditions required for a
 * explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd ||
 * Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) Literacy || * placing four digit numbers on a number line using an appropriate scale
 * reproducing numbers in words using their numerical representations and vice versa ||
 * Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)
 * justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations ||
 * Recognise and explain the connection between addition and subtraction (ACMNA054)
 * Recall addition facts for single digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
 * combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1) ||
 * Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056) || * establishing multiplication facts using number sequences ||
 * Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)
 * using a calculator to check the solution and reasonableness of the answer ||

Year 4 Critical and creative thinking Numeracy || * using the four operations with pairs of odd or even numbers or one odd and one even number, then using the relationships established to check the accuracy of calculations || Literacy || * reproducing five digit numbers in words using their numerical representations, and vice versa || Literacy Critical and creative thinking Numeracy || * recognising and demonstrating that the place-value pattern is built on the operations of multiplication or division of tens || Literacy Critical and creative thinking || * recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences || Information and communication technology capability Critical and creative thinking Numeracy || * using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder ||
 * Investigate and use the properties of odd and even numbers (ACMNA071)
 * Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
 * Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)
 * Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)
 * Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075) || * using known multiplication facts to calculate related division facts ||
 * Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

Year 5 Literacy Critical and creative thinking Numeracy || * exploring factors and multiples using number sequences Literacy Information and communication technology capability Critical and creative thinking Numeracy || * recognising the usefulness of estimation to check calculations numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Literacy Information and communication technology capability Critical and creative thinking Numeracy || * exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers Literacy Information and communication technology capability Critical and creative thinking Numeracy || * using the fact that equivalent division calculations result if both numbers are divided by the same factor Literacy Information and communication technology capability Critical and creative thinking Numeracy || * using calculators to check the reasonableness of answers ||
 * Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)
 * using simple divisibility tests ||
 * Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)
 * applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load ||
 * Solve problems involving multiplication of large numbers by one or two digit
 * applying the distributive law and using arrays to model multiplication and explain calculation strategies ||
 * Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)
 * interpreting and representing the remainder in division calculations sensibly for the context ||
 * Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Year 6 Literacy Information and communication technology capability Critical and creative thinking || * understanding that some numbers have special properties and that these properties can be used to solve problems (ACMNA123) Literacy Information and communication technology capability Critical and creative thinking Numeracy || * applying strategies already developed for solving problems involving small numbers to those involving large numbers Literacy Critical and creative thinking Numeracy || * understanding that integers are ...3, 2, 1, 0, 1, 2, 3,..... l solving everyday additive problems using a number line
 * Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)
 * representing composite numbers as a product of their prime factors and using this form to simplify calculations by cancelling common primes
 * understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number (for example 216 is divisible by 8 because the number represented by the last three digits is divisible by 8, and hence 216 is also divisible by 2 and 4) ||
 * Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
 * applying a range of strategies to solve realistic problems and commenting on the efficiency of different strategies ||
 * Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)
 * investigating everyday situations that use integers, such as temperatures
 * using number lines to position and order integers around zero
 * solving everyday additive problems involving positive and negative integers without developing formal rules for the operations (for example using a number line and counting to find the resulting outside temperature if it is 5°C at 7pm and drops by 8°C overnight) ||

Year 7 Literacy Critical and creative thinking || * defining and comparing prime and composite numbers and explaining the difference between them square numbers (ACMNA150) Critical and creative thinking || * investigating square numbers such as 25 and 36 and developing square-root notation Critical and creative thinking || * understanding that arithmetic laws are powerful ways of describing and simplifying calculations || (ACMNA280) Critical and creative thinking Numeracy ||  ||
 * Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)
 * applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees
 * solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation ||
 * Investigate and use square roots of perfect
 * investigating between which two whole numbers a square root lies ||
 * Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
 * Compare, order, add and subtract integers

Year 8 (ACMNA182) Critical and creative thinking || * evaluating numbers expressed as powers of positive integers || Information and communication technology capability Critical and creative thinking || * using patterns to assist in finding rules for the multiplication and division of integers The information on this page is taken directly from the Australian Curriculum (see reference list)
 * Use index notation with numbers to establish the index laws with positive integral indices and the zero index
 * Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)
 * using the number line to develop strategies for adding and subtracting rational numbers ||