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:• Skip counts in 2s to 10,forwards and backwards• Skip counts in 2s, 5s, 10sto 100• Skip counts in 2s,5s, 10s to100 and relates this tomultiplication (e.g. says“five, ten, fifteen, twenty isfour lots of 5”)• Uses the patterns in ahundreds chart to helpunderstand multiplicationtables (up to 10 x 10) andknows that because of theproperty of commutativityof multiplication (i.e. a x b= b x a) they only have tolearn half of them• Knows what factors andmultiples are for 2 and 3-digit numbers (e.g. knowsthe first six multiples of 25and the factors of 80)• Knows that ‘25% off’ thefull price means theywould save ¼ of the priceand that ‘50% off’ meansthey would save half thefull price; knows and canshow that 50% of ahundreds square meansthat 50 of the 100 squaresare shaded and they canbe any 50 of the squares• Knows and can show on ahundreds square that 12/20as a percentage is 12 out ofevery 20 squares on thehundreds square; calculateswith fractions andpercentages based onmultiples of 10% and 25%of a given unit or quantity(e.g. 60% of a 1 kg bag ofnuts; what proportion of 2 Ljuice bottle is mango juiceif 30% is mango juice)• Uses a calculator toexpress one quantity as a% of another and to findfractions and percentagesof numbers (e.g. can find38% of 4 500) estimatingfirst to gain a sense of thereasonableness of theanswer produced; Recordsstages of findingpercentages of quantitieswhich they cannot findmentally (e.g. finds 20% of384 by writing !0% of 384= 38.4 and doubles that toget 20% is 3.8.4 + 38.4 =76.8)• Critically interpretspublished percentages bydeciding what the ‘whole’is first (e.g. knows what‘increased by 200%’means and determineswhether it is correctly usedin an advertisement);knows how to increasenumbers by a percentageusing a calculator (e.g.knows that to increase avalue by 20% they need tomultiply it by 1.2)• Uses technology for singleoperations involving singledigit numbers (e.g. presses‘4’ ‘+’ ‘2’ ‘=’ on a simplecalculator)• Uses technology for singleoperations involving 2-digit numbers and explainswhat they have done• Uses technology for singleoperations involving 2 and3-digit numbers andexplains what they havedone• Uses technology for singleoperations for 2 and 3-digitnumbers and explains whatthey have done and found• Uses technology includinga calculator for singleoperations and explainsand shows what they havedone and found (e.g.knows that 3 x 15 is threelots of 15 and can prove itby adding 15 + 15 + 15);uses a calculator to divideand knows that 4)35 isentered as 35 ÷ 4• Understands the ‘rule oforder’ for +, -, x, ÷ (ie,that in a string ofoperations, multiplicationand division are done firstin the order in which theyoccur; 2+4 x 3 will bedone as 4 x 3 and 2 addedto the result); can explorewhether their calculatorfollows this rule of orderor not and explains howthey know; Can use thememory to store the resultof 4 x 3 and adds thenumber stored to 2 if theircalculator doesn’t use therule of order• Uses a calculator orspreadsheet to carry outcomplex repetitivecomputations, payingattention to rule of order(order of operations) (e.g.adds amounts for itemsfrom a mail order catalogueand includes GST andpostage); uses a calculatorto carry out and checkcalculations involvingrational numbers andjustifies the size of theanswer (e.g. 4¾ - 2 1/3 =2.41666…) based onknowledge of the operationand the numbers used; usesa calculator memory orbrackets to calculateexpressions such as (4.1 x1.2) + (3.5 x 3)• Plans and explains asequence of calculationsusing a calculator memoryfacility when there are nobrackets on the calculator(e.g. to calculate (2.358 x3.5) + 2.4 3 ) plans toexecute the calculation as2.358 x 3.5 saving theanswer in their calculatormemory, clearing, finding2.4 x 2.4 x 2.4 and thenadding their result to thenumber stored in thecalculator memory, andexplains this sequence oftheir activities)• Uses technologicalcalculation tools to carryout efficient computations(e.g. √(27.4 3 – 18.6 2 , $4800 x (1.05) 10 to calculatecompound interest) givinganswers to a reasonablelevel of accuracy; Carriesout, with technology,computations involvingdecimal approximations toirrational numbers inmeasurement contexts andto given degrees ofaccuracy (e.g. says ” thediagonal of a rectanglewith side lengths 10m and5m is √125 ≈ 11.18 or 1.2metres to one degree ofaccuracy” and “a circlewith a circumference of100 m has a diameter of100 ÷ π which is about31.8 metres”)• Identifies additionsituations from simplenumber stories (e.g. the 3bears) and draws a pictureto represent the situation• Identifies addition andsubtraction situations fromsimple number stories;writes simple stories aboutsingle operations (e.g. forthe operation 5 – 3, writes“there were 5 baby turtlesand 3 of them got eaten bythe birds”)• Represents mathematicalquestions using objects orpictures or symbols orparaphrasing (e.g. whentold there were 5 babyturtles and 3 of them goteaten by the birds, writes 5– 3)• Interprets (and creates)problems based around asingle operation anddecide which operation isrequired; +, -, x, ÷ (e.g. for“20 lollies are sharedequally between 4 boys;how many will they eachget?” can determine thatsharing is needed to solve)• Explains and comparesstrategies for solvingsimple problems (e.g. says“I gave out the 20 lolliesone at a time to eachperson until I ran out, butNatalie did it another waysheput the lollies in littlegroups on the table”)• Reads and interpretspractical problems,identifies which operation(+, -, x, ÷) to use,expresses itmathematically and thensolves it• Reads and interpretspractical problems,identifies which operation(+, -, x, ÷) to use,expresses itmathematically and thensolves it, making sure theiranswer makes sense in thecontext• Reads and interpretspractical problems,identifies which operationto use, expresses itmathematically and thensolves it, making suretheir answer makes sensein the context, andexplains their choice ofoperation• Interprets problemsituations to choose and usean appropriate sequence ofoperations and appliessuitable methods ofcomputation (e.g. choosesto calculate a 20% discountusing multiplication andsubtraction)• Uses a number line ormaterials to solve practicalproblems involving additionand subtraction of integers(e.g. uses a number line toshow that an overnighttemperature drop of 12°Cfrom 5°C results in aminimum of -7°C)• Recognises and informallyexplain negatives whichmay appear on a calculatordisplay when somesubtractions are carried outin a context (e.g. whenusing a calculator to findhow much more they needto pay if they’ve paid 156out of 234 explains whythe display shows -78 ifthey enter ‘156 – 234’ inerror); Knows how to usethe ‘+/-‘ key on acalculator when entering asubtraction anderroneously entering thesmaller number first• Understands the sequenceof operations used bysimple technologies (e.g. a4-function calculator) maydiffer and checks andinterprets these when usingthem; Is able to explain thesequence of operationsneeded to duplicate thesequence of operationsused by a calculator (e.g.says “to show using acalculator that (3 x 4) ÷(2 x 6) is equal to one Ineed to press the ÷ keytwice since I’m dividing by2 and by 6”)Bound for Success Scope and Sequence Statements V2 Page 33 Working Document Semester One 2007