Key+Declarative+and+Procedural+Knowledge+-+Graphic+Organiser


 * ** Content Descriptons: Number & Algebra ** || ** Declarative Knowledge ** || ** Procedural Knowledge ** ||
 * ** Formation ** ||
 * 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) || Learner can count to 20, is able to start at any number and count on from there, understand there are different ways of representing a number (word and digit) can recognise phonics and read numbers. || Read cultural stories featuring counting in sequence, identify number words in sequences, develop fluency with forwards and backwards counting in meaningful context (rhymes, song and stories) and understand that numbers are said in a particular order and pattern. ||
 * Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) || Students can count using objects and answer mathematical questions posed to them, can use their knowledge of counting and apply it to understanding various cultures and why counting is important. || Understanding to only count each object once, the arrangement does not affect how many there are, the last number counted answers the question how many are there? using scenarios from various cultures enabling students to understand there are many ways and reasons for counting. ||
 * Subitise small collections of objects (ACMNA003) || Place numbers into order - sequence numbers into a number line, comparing digits. || Using subitising as the basis for ordering and comparing a collection of numbers. ||
 * Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289) || Count to 20, understand the meaning and use in correct context of more, less, same as and not the same, be able to justify your answers when working with numbers, know ordinal numbers up to 10. || comparing and ordering items of similar and diverse characteristics using the words more, less, same/not the same as and justifying. indicating ordinal position and numbers, using objects which are personally and culturally relevant ||
 * Represent practical situations to model addition and sharing (ACMNA004) || Be able to add small groups of numbers (counting on). || Using a range of practical strategies for adding small groups of numbers, using Aboriginal and TSI methods of adding (spatial patterns and reasoning). ||
 * **// Identified Issues and Challenges for Students in Formation //** |||| Missing numbers when counting in sequence, when counting objects missing one or counting twice, comparing and collecting a group of similar objects - not being able to justify why. ||
 * ** Year 1 ** ||
 * 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) || Count backward and forward, follow rules and instructions. || Skip counting - using practical games, developing fluency with forwards and backward counting in context. ||
 * Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line(ACMNA013) || Count in sequence, order numbers in correct place, read written form of numbers, understand number line. || Modelling numbers, number line work identifying and placing sequentially. ||
 * Count collections to 100 by partitioning numbers using place value(ACMNA014) || Have knowledge of number grouping and equal groups, place value up to the tens and ones. || Grouping numbers, understanding place value (two digit numbers are comprised of 10s and 1s). ||
 * Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015) || Know what addition and subtraction is, count on and backwards – understand there are ways to do these problems in your head (doubles and near doubles for example). || Developing a range of mental strategies for addition and subtraction problems. ||
 * **// Identified Issues and Challenges for Students in Year 1 //** |||| Counting to and from 100 - missing numbers, not knowing the tens column numbers (what comes next), counting in 2's, 5's, 10's - a pattern has to be understood before students will understand how to do this, writing numbers correctly (no backward numbers, understanding place value with digits which column do the numbers belong to? ||
 * ** Year 2 ** ||
 * Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026) || Understand number sequences and number patterns – be able to justify why there is a number pattern in a sentence, speak in mathematical terms. || Develop fluency and confidence with numbers and calculations through number sequences, recognising patterns in number sequences. ||
 * Recognise, model, represent and order numbers to at least 1000 (ACMNA027) || Can count to 1000 and recognise numbers and their place value, know how to write numbers with correct spelling. || Recognising there are various ways of representing and identifying patterns beyond 100, develop fluency with writing numbers in context. ||
 * Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) || Understand how to use an abacus model and how to count numbers to represent place value, know place value up to the hundredths, speak mathematically to justify decisions and explain numbers in their positions. || Use an abacus to model and represent numbers, understand place value of three digit numbers, demonstrate using models and explain reasoning. ||
 * Explore the connection between addition and subtraction (ACMNA029) || Can add and subtract without assistance with numbers up to two and three digits long, can identify missing elements of a sum using addition and subtraction with numbers. || Become fluent with partitioning numbers to understand the connection with addition and subtraction, counting on and identifying the missing element in an additive problem. ||
 * Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) || Can add and subtract easily without using their fingers students must be able to do sums in their heads that are simple using mental strategies and concrete materials. || Become fluent with a range of mental strategies for addition and subtraction, modelling and representing simple additive situations using materials. ||
 * Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) || Use examples such as vehicles to add a group of numbers together (the amount of tyres on a car is 4, add the amount of tyres on a truck 8, equals how many tyres) and can speak in mathematical sentences to express maths as a language. || Represent an array of proplems with materials and justify, visualise a group of objects as a unit and use 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) || Can group numbers equally from a whole and separate them, understand the structure of a sentence and differences in mathematical problems. || Dividing into equal groups (use concrete materials for example the class), identify the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three. ||
 * **// Identified Issues and Challenges for Students in Year 2 //** |||| Recognising and understanding number patterns, justifying why there is a pattern with numbers may be a challenge for students if the concept is not fully understood, addition and subtraction common challenges - counting on and counting back needs to be known effectively, grouping - are the groups split equally? getting to know the innovative mathematics language. ||
 * ** Year 3 ** ||
 * Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051) || Count in 2's, know and recognise what makes an odd and even number. || Identifying even numbers by skip counting, counting in 2's or by grouping in 2's, explaining odd and even numbers. ||
 * Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) || Count up to the thousands, understand sequential numbers and scales, writing numbers with correct spelling and in the right place (being able to say a number out loud as a digit and write down the word for it. || Placing 4 digit numbers on a number line and using the appropriate scale, reproducing numbers in words using their numerical representation. ||
 * Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) || Be able to group numbers, speak and justify answers to problems with mathematical terminology. || Justify choices about partitioning and regrouping numbers in terms for their usefullness for particular calculations. ||
 * Recognise and explain the connection between addition and subtraction (ACMNA054) || Able to write a number sentence, understand the difference and connection between addition and subtraction. || Demonstrate the connection of addition and subtraction through partitioning or by writing equivalent number sentences. ||
 * Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055) || Can count efficiently to 1000, can add and subtract numbers and recognise similar rules for numbers that have 4 digits and apply these rules to common problems. || Recognise single digit number combinations result in the same answer for subtraction and addition, transfer this knowledge for larger numbers, combine knowledge of addition and subtraction facts and partitioning to aid computation. ||
 * Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056) || Know how to multiply and divide, understand the rules that apply with such problems. || Establishing multiplication facts using number sequences. ||
 * Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) || Create mathematical word problems can form a number from a written word form to a digit, knows how to use a calculator to check and mark own work. || Writing simple word problems in numerical form, using a calculator to check the situation and reasonableness of the answer. ||
 * **// Identified Issues and Challenges for Students in Year 3 //** |||| Writing and spelling numbers correclty - children should be able to use their knowledge of phinics although will need to learn to write numbers, learning maths as a language. ||
 * ** Year 4 ** ||
 * Investigate and use the properties of odd and even numbers (ACMNA071) || Recall the properties of even numbers (odd numbers can not be divided evenly by 2; even numbers can be divided evenly by 2). || Demonstrate strategies to check reasonableness of answers to mathematical operations which identify the properties of odd and even numbers. ||
 * Recognise, represent and order numbers to at least tens of thousands (ACMNA072) || Identify place value of numbers up to tens of thousands. || Convert numbers (of up to five digits) into words, and worded representations into numerical. ||
 * Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) || be able to group numbers, speak and justify answers to problems with mathematical terminology || Demonstrate that the operations of multiplication or division of tens is the basis of place-value patterns. ||
 * Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) || Know times tables for numbers 3, 4, 5, 6, 7, 8 and 9. || Identify patterns in number sequence and establish that sequences can continue without any ending point. ||
 * Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075) || Understand that performing multiplication facts will enable working out division facts. E.g. 5 times 10 = 50 will help the student solve 50 divided by 5 = 10. || Implement multiplication facts to assist in determining division facts relating to the same number. ||
 * **// Identified Issues and Challenges for Students in Year 4 //** |||| Getting place values confused - ones, tens, hundreds, thousands and millions. Confusion with how to read large numbers. ||
 * ** Year 5 ** ||
 * Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) || Understand that a written problem can be written in a number sentence. E.g. Sue has 5 baskets and 50 apples so how many apples should she put in each basket? = 50 divided by 5 = 10 in a number sentence. || Utilise number sequences, factors and multiples, and divisiblity tests to solve problems based on whole numbers. ||
 * Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) || Identify which numbers are rounded up, and which numbers are rounded down. || Demonstrate an understanding of the benefits of estimating calculations, and implement ways to mentally demonstrate this understanding. ||
 * Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) || Know the correct procedures for multiplying numbers and how to present this information. || Produce arrays to illustrate strategies used to calculate multiplication problems. ||
 * Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101) || Know the correct procedure to perform a division problem and how to present this information. || Demonstrate abiltiy to solve oned digit number division problems which should not exclude problems which have a remainder in the solution. ||
 * Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) || Understand which buttons on the calculator to perform specific functions. || Compare mental and written answers to problems with the answers found by using a calculator. ||
 * **// Identified Issues and Challenges for Students in Year 5 //** |||| Poor rounding and estimating skills might lead to major errors in problem solving. ||
 * ** Year 6 ** ||
 * Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122) || Know that a prime number is only divisible by 1 and itself; that a composite number is any number greater than 1 that is not a prime number; that a square number is the number you get when you multiply an integer by itself; and a triangular number is a number that can make a triangular dot pattern. || Examine prime, composite, square and triangular numbers and construct an understanding of the attributes of each type of number. ||
 * Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (AMNCA123) || Identify which operation is required to solve problems. || Develop problem solving skills that incorporate all four operations which involve whole numbers, small numbers and large numbers and relate these skills to real-life scenarios. ||
 * Investigate everyday situations that use integers. Locate and represent these numbers on a number line(ACMNA124) || Understand how to construct a number line and identify which information is to be placed on it. || Extend knowledge of integers and time lines by identifying real-life scenarios which utilise this knowledge. ||
 * **// Identified Issues and Challenges for Students in Year 6 //** |||| Misunderstanding of problem solving; using incorrect order of operations in problem solving. ||
 * ** Year 7 ** ||
 * Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149) || Recall what a prime number is; and know that index notation and powers of numbers is how many times to use a number in a multiplication. || Convert factor knowledge into factor trees to assist problem solving. ||
 * Investigate and use square roots of perfect square numbers (ACMNA150) || Understand that a perfect square is a number that has a rational number as its square root; know that a square root is a number that can be multiplied by itself to give the original number. || Constuct factor trees to assist in understanding square roots. ||
 * Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151) || Know that the associative law means that which way numbers are grouped does not matter when adding or multiplying; the commutative law says that you can swap numbers around when adding and multiplying; and the distributive law says that you get the same number when you multiply a number by a group of numbers added together as when you do each multiplication separately. || Identify which law will be suitable to use in different mathematical situations. ||
 * Compare, order, add and subtract integers (ACMNA280) || Know when it is appropriate to use a number line; and how to correctly create a numberline || Construct a number line to assist with adding and subtracting integers. ||
 * **// Identified Issues and Challenges for Students in Year 7 //** |||| Confusion with square roots and perfect squares; confusion differentiating which law applies to different sorts of mathematical sums. ||
 * ** Year 8 ** ||
 * Use index notation with numbers to establish the index laws with positive integral indices and the zero index(ACMNA182) || Know that the zero index generally means that any number (except 0) raised to the power of 0 has a numerical value of 1; and that when multiplying powers with the same base, add the indices. || Apply index laws when identifying numbers with powers of positive integers. ||
 * Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183) || Know how to perform each of the four operations and when to use them. || Construct number lines to establish possible patterns when adding and subtracting rational numbers. ||
 * **// Identified Issues and Challenges for Students in Year 8 //** |||| Not understanding index notation and index laws. ||