Bound for Success Scope and Sequence Statements

MATHEMATICSNumberConcept In Year 1the student:In Year 2the student:In Year 3the student:In Year 4the student:In Year 5the student:In Year 6the student:In Year 7the student:In Year 8the student:In Year 9the student:Operations,calculating andproblem-solvingin Number• Understands addition as aconcept of ‘finding thetotal’ and the ‘+’ symbolas representing theoperation• Understands addition andsubtraction concepts,symbols and words thatindicate these including‘difference’, ‘total’, ‘sum’,‘altogether’, ‘adding to’,‘taking away’• Works out and extendsaddition and subtractionfacts and recognises bywords and situations wheneach is required (e.g.knows that “how much is 4and 3?” means add 4 and 3together)• Recalls or calculatesmentally addition andmultiplication facts for anypair of whole numbers upto 5 (i.e. 5 + 5 and 5 x 5)• Recalls or calculatesmentally addition andmultiplication facts for anypair of whole numbers upto 10 and uses their inverseoperations when needed(i.e. knows to use the factthat 3 x 5 = 15 to find15 ÷ 3)• Recalls most basicmultiplication facts to 10x 10 and mentally extendsto multiply one-digitnumbers by multiples of10 (e.g. says “4 x 90 is 4times 9 lots of ten so it’s36 lots of ten, 360”)• Mentally multiplies doubledigitby single-digitnumbers using partitioningstrategies (e.g. says “6thirty-eights is 6 thirties and6 eights which is 180 and48, that’s 228”)• Applies number facts andproperties to carry outmental calculations (e.g.says “the GST on $156 is$15.60 which gives a totalof $171.60”)Understanding theoperations of addition,subtraction,multiplication anddivision;Choosing the correctoperation for aparticular situationand using it to solveproblems• Partitions single-digitnumbers using additionand subtraction (e.g.partitions 5 as 4 and 1, 3and 2, 7 take away 2)• Places up to 10 objects inequal groups (e.g. 2 lots of5 pencils, 3 lots of 3 toys)• Partitions 2-digit numbersusing addition andsubtraction (e.g. partitions16 as 15 + 1, 14 + 2, 13 +3, …) and shows this withmaterials• Uses mental strategies tocompute addition andsubtraction of 1 and 2-digitnumbers• Knows all doubles facts to20 (e.g. knows that double19 is 38)• Use words, drawing andrepresentations of arrays toexpress ‘lots of’ (e.g. 2 lotsof 3: # # ## # # )• Knows single-digitaddition and relatedsubtraction facts bypartitioning (e.g. knows 9+ 7 = 9 + 1 + 6 so it mustbe 10 + 6 which is 16) anddemonstrates this usingsymbols and materials• Uses mental strategies tocompute addition andsubtraction of 1 and 2-digitnumbers and choosesbetween mental andwritten methods to do thesame• Uses words and models ofarrays to express ‘lots of’and solve multiplicationsituations (e.g. uses anarray to determine howmany apples each personwill have if they have 4each)• Knows that subtraction isthe inverse (i.e. ‘undoes’)of addition and vice-versaand that division is theinverse of multiplicationand can show theserelationships for numbersusing drawings• Knows that subtraction isnot commutative (i.e. 7 – 3≠ 3 – 7)• Uses mental strategies toestimate computationsinvolving a singleoperation (e.g. 45.3 + 190is about 50 plus 200, or250)• Multiplies whole numbersup to 3 digits by numbersup to 10 using mentalstrategies as a first choiceand other written orcalculator strategies fornumbers beyond theirmental scope• Recalls addition andsubtraction facts, andworks out multiplicationand related division,applying numberproperties and mentalcomputation strategies tolarger numbers (e.g. says“3 eights is 24 so 6 eightswill be double that so 6times 8 is 48”)• Multiplies and dividesnumbers by 10 and 100mentally and shows‘what’s changing’ whenthey do this using a placevalue chart or calculator)• Multiplies whole numbersup to 6 digits by numbersup to 10, using mentalstrategies as a first choiceand other written orcalculator strategies fornumbers beyond theirmental scope (e.g. says“4 530 times 3 is 12thousand plus onethousand 500 – which is13 500 and then addanother 90 – answer is 13590”)• Partitions double-digitnumbers in order tomentally multiply bysmall single-digitnumbers (e.g. realises that3 twenty-sixes is the sameas 3 twenties added to 3sixes which is 60 + 18which is 78; factorises 38in order to make thecomputation of 38 x 5easier; thus 38 x 5 = 19 x2 x 5 = 19 x 10 = 190)• Multiplies by tenths andhundredths and explainsthat multiplying by tenthsis the same as finding onetenth of it and multiplyingby one hundredth is thesame as finding onehundredth of it• Multiplies whole numbersup to 6 digits by numbersup to 10 using roundingand mental strategies inorder to estimate first,when written andcalculator methods areneeded (e.g. uses acalculator to multiply62 350 by 5, estimatingthat the answer obtainedwill be between 300 000and 400 000 in order tojudge whether the answerobtained on their screen isreasonable)• Partitions double-digitnumbers in order tomentally divide by smallsingle-digit numbers (e.g.realises that 97 ÷ 3 is 90divided by 3 and 7 dividedby 3 which is 30 and twowith one left over; thirtytwo and one left over)• Divides by tenths andhundredths and explainsthat dividing a number byone tenth makes it ten timeslarger (since there are tentenths in every wholenumber) and similarly forhundredths• Applies effective writtenmethods (not necessarilyalgorithms) to carry outcomputations with decimalsto at least thousandths (e.g.2.852 x 12.3) by mentallyestimating the result first inorder to judge thereasonableness of theanswer obtained• Knows to divide when thedivisor is less than one(e.g. knows that tocalculate how many piecesof string 0.3 metres longcan be cut from a roll ofstring 2 m long they needto divide 2 m by 0.3 m);Knows to multiply whenthe multiplier is a fractionor decimal less than 1 (e.g.when given the cost of onemetre of ribbon knows tomultiply it by 0.75 to findwhat 0.75 m will cost)• Multiplies and dividesdecimals by one-digitnumbers, interpretingremainders for divisionand deciding whether toround up or downdepending on the context(e.g. divides 39.5 by 6 toshare $39.50 among 6people, calculates theanswer as 6.58333… andknows to round the answerdown to $6.55 because ifthey round up to $6.60there will not be enoughmoney to share equally)• Understands the effect ofmultiplying and dividingby fractional and decimalnumbers less than 1 (e.g.when given a number suchas 220 and challenged tofind a number to multiplyit by to get 200 using acalculator, selects anumber slightly less than1); Understands thatdividing a fraction by afraction will result in anumber greater than theinitial fraction (e.g.recognises that 2/5 ÷3/4could not possibly be 1/5)Calculates problemsinvolving two integers anda single operation usingeffective written methods(e.g. when calculating 20billion divided by 350 000,or 546 x -389) byestimating first (e.g. says“546 x 389 is about 550times 400 which is about22 000 so I’m expectingabout -22 000”) ; thewritten method will notnecessarily be an algorithmbut may be based on theirunderstanding of numbersand number properties(e.g. 546 x 300 + 546 x 80+ 546 x 9)• Shares materials equally(e.g. given 10 objects for 5people gives each person2)• Shares and groupsmaterials up to 100 (e.g.given 40 objects and 6people gives them out andnotices there are some leftover)• Shares and groupsmaterials (for single digitdivisors i.e. up to 10shares) up to 1 000)• Understands that divisionis about repeatedsubtraction and usesdrawings (by hand or withtechnology) to representdivision of quantities up to100• Knows that prime numbersare numbers that divideevenly (with no left oversor remainders) by themselfand one, and knows theseup to 19• Identifies prime factors ofany whole number up to100• Identifies and uses factors,including prime factors, toassist mental computation(e.g. 27 x 3 = 9 x 3 x 3 = 9x 9 = 81)• Calculates and recallssimple powers and squareroots (e.g. 3 4 = 3 x 3 x 3 x3 and √169 = 13) mentallyand uses technology formore difficult cases (e.g.√4509)Bound for Success Scope and Sequence Statements V2 Page 32 Working Document Semester One 2007