lpfprocessed.json

{"97":{"Background":"The students compare quantities using informal language. They know some number names and parts of the number-word sequence, and they may subitise (instantly recognise) small quantities.","exemplars":{"1":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010101.pdf","Title":"Dice"},"2":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010102.pdf","Title":"How many spots?"},"3":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010103.pdf","Title":"Card matching"},"4":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010104.pdf","Title":"Teddies and cards"}}},"98":{"Background":"The students use one-to-one correspondence, their knowledge of the number-word sequence, cardinality, and ordinality as they count sets of objects.","exemplars":{"5":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010201.pdf","Title":"Tens frames"},"6":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010202.pdf","Title":"Matching game"},"7":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010203.pdf","Title":"JAM Task 5A"},"8":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010204.pdf","Title":"How many?"}}},"99":{"Background":"The students count all of the objects to solve simple addition or subtraction problems. They do this with real objects or by imaging the objects.","exemplars":{"9":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010301.pdf","Title":"Bears in the cave"},"10":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010302.pdf","Title":"Popping balloons"},"11":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010303.pdf","Title":"Visiting the library"},"12":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010304.pdf","Title":"Ladybirds"},"13":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010305.pdf","Title":"Handy Counters"}}},"100":{"Background":"The students solve problems involving the addition or subtraction of single-digit numbers by counting on or back from the larger number. The language of the problem guides the student to the operation of addition or subtraction.","exemplars":{"14":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010401.pdf","Title":"Trusting the Count"},"15":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010402.pdf","Title":"Counting back"},"16":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010403.pdf","Title":"More dinosaurs"},"17":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010404.pdf","Title":"Cars in the carpark"},"18":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010405.pdf","Title":"People on the bus"}}},"101":{"Background":"The students have begun to recognise that numbers are abstract units that can be either treated as wholes or partitioned and recombined. This is called part-whole thinking. Students partition single-digit numbers to form \u201ctidy numbers\u201d or use known addition facts to ten to solve problems. The language of the problem guides the student to the operation of addition or subtraction.","exemplars":{"19":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010501.pdf","Title":"Rotten plums"},"20":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010502.pdf","Title":"Adding dinosaurs"},"21":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010503.pdf","Title":"Parking cars"},"22":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010504.pdf","Title":"Scoring points"},"23":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010505.pdf","Title":"Money in the bank"}}},"102":{"Background":"The students solve problems involving two- and three-digit numbers, in which the mathematical operation is transparent in the wording, by applying a strategy from a limited rehearsed repertoire. The strategies are most likely to involve place-value partitioning, or compensation when the number is close to a tidy number.","exemplars":{"24":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010601.pdf","Title":"Getting off the bus"},"25":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010602.pdf","Title":"Buying a cell phone"},"26":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010603.pdf","Title":"Final score"},"27":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010604.pdf","Title":"The marathon"},"28":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010605.pdf","Title":"My bank account"}}},"103":{"Background":"The students respond flexibly to addition and subtraction problems involving whole numbers and simple decimals by applying and explaining a range of strategies, including the use of inverse operations, as they seek the most efficient method.","exemplars":{"29":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010701.pdf","Title":"The meeting"},"30":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010702.pdf","Title":"Over the line"},"31":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010703.pdf","Title":"DVD collections"},"32":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010704.pdf","Title":"Comparing scores"},"33":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010705.pdf","Title":"The ball dress"}}},"104":{"Background":"The students demonstrate flexibility, a strong number sense, and an ability to carry out multiple steps as they estimate and solve complex problems that involve adding and subtracting whole numbers, decimals, fractions, and integers.","exemplars":{"34":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010801.pdf","Title":"Bags of wheat"},"35":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010802.pdf","Title":"Estimates"},"36":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010803.pdf","Title":"Pipe pieces"},"37":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010804.pdf","Title":"Sugar for jam"},"38":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010805.pdf","Title":"Still chilly"},"39":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M010806.pdf","Title":"The leaky tank"}}},"105":{"Background":"The students demonstrate early multiplicative thinking as they understand the concept of \u201csame\u201d and recognise equal groups. However, they are unable to quantify the objects to solve multiplication problems.","exemplars":{"40":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020001.pdf","Title":"Three by three"},"41":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020002.pdf","Title":"Parking up"},"42":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020003.pdf","Title":"Legs"}}},"106":{"Background":"The students solve multiplication problems by considering each object one at a time and by counting from one to find the total number of objects in equal sets. The student solves simple division problems by equally distributing objects one at a time into sets, and by counting from one to check that the sets are of the same size.","exemplars":{"43":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020101.pdf","Title":"Matching wings"},"44":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020102.pdf","Title":"Lambs' legs"},"45":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020103.pdf","Title":"Fair shares "},"46":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020104.pdf","Title":"Long legs"}}},"107":{"Background":"The students solve single-digit multiplication and division problems by using additive thinking strategies, including skip counting, repeated addition, and repeated subtraction.","exemplars":{"47":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020201.pdf","Title":"Balloons, balloons"},"48":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020202.pdf","Title":"The chicken and the egg"},"49":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020203.pdf","Title":"Total days"},"50":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020205.pdf","Title":"Five dollar notes"},"51":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020206.pdf","Title":"Sheep legs"},"52":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020207.pdf","Title":"Buddy reading"}}},"108":{"Background":"The students solve single-digit, single-step multiplication problems by applying known multiplication facts or by using known facts to derive unknown ones. The students solve simple division problems by using known multiplication facts or by trial and error with different-sized groups.","exemplars":{"53":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020301.pdf","Title":"Trees in the forest"},"54":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020302.pdf","Title":"Happy faces"},"55":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020303.pdf","Title":"Buying books"},"56":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020304.pdf","Title":"Divisibility by 10"},"57":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020305.pdf","Title":"Sharing licorice logs"}}},"109":{"Background":"The students use their known multiplication basic facts and place-value knowledge to solve multiplication and division problems involving single-digit multipliers or divisors.","exemplars":{"58":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020401.pdf","Title":"Dragon teeth"},"59":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020402.pdf","Title":"Tennis balls"},"60":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020403.pdf","Title":"Sharing time"},"61":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020404.pdf","Title":"Sports teams"},"62":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020405.pdf","Title":"Croft's cows"}}},"110":{"Background":"The students solve multi-digit problems in which the mathematical operation is transparent in the wording. They do this by applying a multiplicative strategy from a limited rehearsed repertoire that is likely to include place value, or compensation when the number is close to a tidy number.","exemplars":{"63":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020501.pdf","Title":"Blueberries"},"64":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020502.pdf","Title":"Pointing to the stars"},"65":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020503.pdf","Title":"Garden metres"},"66":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020504.pdf","Title":"Money for school camp"},"67":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020505.pdf","Title":"The car ferry"},"68":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020506.pdf","Title":"Saving for an Ipod "}}},"111":{"Background":"The students respond flexibly to multiplication and division problems involving whole numbers, common fractions, decimals, and percentages by selecting from a range of strategies based on the type of problem and numbers involved.","exemplars":{"69":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020601.pdf","Title":"Is it Wednesday?"},"70":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020602.pdf","Title":"Seedlings galore"},"71":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020603.pdf","Title":"Punnets of strawberries"},"72":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020604.pdf","Title":"Paper run pay"}}},"112":{"Background":"The students demonstrate flexibility and a strong number sense as they estimate and solve complex problems that involve whole numbers, decimals, fractions, and integers.","exemplars":{"73":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020701.pdf","Title":"Computer discount"},"74":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020702.pdf","Title":"How deep?"},"75":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020703.pdf","Title":"Paying full price"},"76":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020704.pdf","Title":"Wooden spears"},"77":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020705.pdf","Title":"Mince patties"}}},"113":{"Background":"The students apply proportional thinking to solve real problems involving percentages, rates, and ratios, and form one- and two-step algebraic equations to solve for an unknown.","exemplars":{"78":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020801.pdf","Title":"How Much?"},"79":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020802.pdf","Title":"An Abundance of Isotopes "},"80":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M020803.pdf","Title":"How much faster? "}}},"114":{"Background":"The students copy or create simple patterns with a unit repeat of two, but they are unable to discuss or explain their thinking.","exemplars":{"181":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070001.pdf","Title":"Sound patterns"},"182":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070002.pdf","Title":"Cube patterns"}}},"115":{"Background":"The students create, continue, and describe repeating patterns to solve problems.","exemplars":{"183":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070101.pdf","Title":"Garden creatures"},"184":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070102.pdf","Title":"Pattern hunt"},"185":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070103.pdf","Title":"Flower power"},"186":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070104.pdf","Title":"Beating to the rhythm"}}},"116":{"Background":"The students continue and describe growing sequential spatial and number patterns to solve problems.","exemplars":{"187":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070201.pdf","Title":"Coloured cubes"},"188":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070202.pdf","Title":"Shaping up colours"},"189":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070203.pdf","Title":"Matchstick moves"},"190":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070204.pdf","Title":"Numbering up"}}},"117":{"Background":"The students connect the elements of sequential patterns with their ordinal position to solve problems.","exemplars":{"191":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070301.pdf","Title":"Growing numbers "},"192":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070304.pdf","Title":"Folding fractions"},"193":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070305.pdf","Title":"Christmas cards"}}},"118":{"Background":"The students use tables, graphs, and rules to solve problems that involve sequential patterns.","exemplars":{"194":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070401.pdf","Title":"Fencing it in"},"195":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070403.pdf","Title":"Little boxes"},"196":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070404.pdf","Title":"Mathematics hunt"}}},"119":{"Background":"The students use diagrams, tables, graphs, and equations to solve problems that involve linear relationships.","exemplars":{"197":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070501.pdf","Title":"Matching up"},"198":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070502.pdf","Title":"Equation stories"},"199":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070503.pdf","Title":"Going up in twos"},"200":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070504.pdf","Title":"Fibonacci"}}},"120":{"Background":"The students graph linear relationships, demonstrate understanding of a standard parabola, and form equations to describe relational representations, and they can apply these to solve real problems.","exemplars":{"201":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070601.pdf","Title":"Find the Rule "},"202":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070602.pdf","Title":"Find the Rule "},"203":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M070603.pdf","Title":"Find the Rule "}}},"121":{"Background":"The students recognise some numeral and operation symbols and know what these stand for.","exemplars":{"204":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080101.pdf","Title":"Pictures and numbers "},"205":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080102.pdf","Title":"Bingo! "},"206":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080103.pdf","Title":"Number words "},"207":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080104.pdf","Title":"Nimble Numbers "}}},"122":{"Background":"The students record equations for simple addition and subtraction problems and explain their thinking. They are able to read simple additive equations and suggest appropriate problem contexts.","exemplars":{"208":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080201.pdf","Title":"The teddy bears' picnic"},"209":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080202.pdf","Title":"Hone's chocolates "},"210":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080203.pdf","Title":"The team's points "},"211":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080204.pdf","Title":"Runaway ponies "}}},"123":{"Background":"The students record equality and simple inequality statements for additive and multiplicative problems and can explain their thinking. They are able to read equality and simple inequality statements and can suggest appropriate problem contexts.","exemplars":{"212":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080301.pdf","Title":"Classroom desks"},"213":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080302.pdf","Title":"Sharing lollies"},"214":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080303.pdf","Title":"Team time "},"215":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080304.pdf","Title":"Book worms"},"216":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080305.pdf","Title":"Blues and Reds"}}},"124":{"Background":"The students read and record additive and multiplicative equality and inequality equations for problems involving unknowns. They are able to suggest appropriate problem contexts for equations involving unknowns, and they recognise the need to use an inverse operation to find an unknown.","exemplars":{"217":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080401.pdf","Title":"Text times"},"218":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080402.pdf","Title":"Minibuses"},"219":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080403.pdf","Title":"Spending money"}}},"125":{"Background":"The students use the algebraic convention of letter symbols and the concept of equivalence to solve simple proportional problems.","exemplars":{"220":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080501.pdf","Title":"The value of n"},"221":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080502.pdf","Title":"The value of x"},"222":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080503.pdf","Title":"Triple x"},"223":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080504.pdf","Title":"What number am I?"},"224":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080505.pdf","Title":"Mona's lemonade"},"225":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080506.pdf","Title":"T-shirt sales"}}},"126":{"Background":"The students write equality statements of problem situations involving four or more terms or factors, including one unknown. They use formal operations to solve equations involving real numbers by operating equally on both sides.","exemplars":{"226":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080601.pdf","Title":"Booked in"},"227":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080602.pdf","Title":"Kapa haka"},"228":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080603.pdf","Title":"Late for class"},"229":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080604.pdf","Title":"Sale time"},"230":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080605.pdf","Title":"Fuelling up"},"231":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080606.pdf","Title":"Plant problems"}}},"127":{"Background":"The students use a systematic approach and algebraic notation, including quadratic equations, to model real world situations and to solve problems.","exemplars":{"232":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080701.pdf","Title":"Which Student is Correct? "},"233":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080702.pdf","Title":"How big is the pen? "},"234":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080703.pdf","Title":"Are these expressions equivalent? "},"235":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M080704.pdf","Title":"Are these expressions equivalent? "}}},"128":{"Background":"The students are becoming aware of space and shape as they interact with and navigate their immediate environment.","exemplars":{"81":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030101.pdf","Title":"Shape Puzzle"},"82":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030103.pdf","Title":"Jigsaw Puzzles"},"83":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030104.pdf","Title":"Find and Place Game"},"84":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030105.pdf","Title":"In, out, over and under"}}},"129":{"Background":"The students notice shapes and use their appearance to solve problems. They flip, turn, and slide shapes, and describe their location in relation to other things in their immediate environment.","exemplars":{"85":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030201.pdf","Title":"The Same and Different Game"},"86":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030202.pdf","Title":"Fold and Cut"},"87":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030203.pdf","Title":"Barrier Game"},"88":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030204.pdf","Title":"Treasure hunt"}}},"130":{"Background":"The students notice and use features of shapes and transformations to solve single-step problems. They describe features and explain in their own words why shapes and transformations are the same or different. They are able to see things from a perspective other than their own and are learning to use geometric terms appropriately.","exemplars":{"89":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030301.pdf","Title":"North South East West Maze"},"90":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030302.pdf","Title":"Shapes in the real world"},"91":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030303.pdf","Title":"Pacific Island Tapa Cloth Designs"},"92":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030304.pdf","Title":"Building Boldly"}}},"131":{"Background":"The students understand and use the features of shapes and transformations to solve multi-step problems. They are able to view and draw shapes from multiple perspectives. The students use the language of geometry accurately as they measure and quantify space and shape, and they demonstrate precision in their solutions.","exemplars":{"93":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030401.pdf","Title":"Triangle Teaser"},"94":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030402.pdf","Title":"Nets"},"95":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030404.pdf","Title":"Blocked Plans"},"96":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030405.pdf","Title":"Patchwork quilts"}}},"132":{"Background":"The students understand, use, and generalise the properties and classes of shapes and transformations to solve problems. They are able to reason and justify their solutions and use formal geometric language in a clear and precise way.","exemplars":{"97":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030501.pdf","Title":"Faces, Vertices and Edges"},"98":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030502.pdf","Title":"Cross Sections"},"99":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030503.pdf","Title":"Finding Treasure"},"100":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030504.pdf","Title":"Draw the Model "},"101":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030505.pdf","Title":"Which shapes tessellate?"}}},"133":{"Background":"The students understand and can use a scale factor of enlargement, the angle properties of polygons, and trigonometric approaches to solve real-world problems. They are able to describe a locus defined by a set of points, and they can explain their mathematical reasoning within a practical situation.","exemplars":{"102":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030601.pdf","Title":"The Glass Wedge "},"103":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030602.pdf","Title":"Designing a Shape "},"104":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030603.pdf","Title":"Investigating Right Angled Triangle Ratios "},"105":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M030604.pdf","Title":"Finding Angles "}}},"134":{"Background":"The students physically manipulate objects to directly compare them.","exemplars":{"106":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040101.pdf","Title":"Comparing two objects by weight"},"107":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040102.pdf","Title":"Direct comparison "},"108":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040103.pdf","Title":"Shorter, longer or the same?"}}},"135":{"Background":"The students make multiple comparisons between objects and order the objects according to the attribute being measured. They use an indirect or intermediary measure to compare the length of two objects that cannot be directly compared.","exemplars":{"109":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040201.pdf","Title":"Comparing coloured strips"},"110":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040202.pdf","Title":"Greedy Cat takes the shorter path"},"111":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040203.pdf","Title":"Weighing and comparing three objects"},"112":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040204.pdf","Title":"What's the measure?"}}},"136":{"Background":"The students use numbers and a non-standard unit to quantify the attribute that is being measured, for example, five rods for length or nine scoops for capacity. They understand that, when comparing objects, the unit being used to measure must not change. They also understand that, when measuring length or area, they cannot leave gaps or create overlaps as they repeatedly place the measuring unit to mark out the total length or area.","exemplars":{"113":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040301.pdf","Title":"Coloured strips"},"114":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040302.pdf","Title":"Sausage factory"},"115":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040303.pdf","Title":"Water bottles"},"116":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040304.pdf","Title":"Oranges and teddy bears"}}},"137":{"Background":"The students estimate and measure using the commonly used standard metric units of measure: centimetre, metre, litre, and kilogram. They are developing an understanding of the concept of a scale; for example by constructing a measuring device and accurately marking the device with numbers for all units in that measure, including the positioning of zero. They are able to partition a unit of measure and measure a half unit.","exemplars":{"117":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040401.pdf","Title":"Matchstick rulers "},"118":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040402.pdf","Title":"Measuring strips"},"119":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040403.pdf","Title":"The bench seat"},"120":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040404.pdf","Title":"Onions"},"121":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040405.pdf","Title":"Measuring milk"}}},"138":{"Background":"The students measure length, capacity, and weight by selecting an appropriate measuring device. They demonstrate greater precision in their measurements by reading scales to marked and unmarked intervals. The students have knowledge of the standard metric units and are able to name and record these units in abbreviated forms (mm, cm, m, km, g, kg, ml, l). They use benchmarks to help them estimate measurements. The students\u2019 understanding of how an array is structured supports their calculation of area and volume.","exemplars":{"122":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040501.pdf","Title":"Make a shake"},"123":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040502.pdf","Title":"Birthday cake decorations"},"124":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040503.pdf","Title":"The new key"},"125":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040504.pdf","Title":"Kitchen tiles "},"126":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040505.pdf","Title":"Estimation and benchmarks for length "},"127":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040506.pdf","Title":"Cuboids"}}},"139":{"Background":"The students derive measurements of area and of the volume of cuboids from measurements of length. For example, they find the area of shapes by separating or reconstructing the shapes into rectangles. They understand the relationship between related units in the metric system, and they multiply and divide by powers of 10 to convert into those related units. They understand that the attributes of area and perimeter are not dependent on each other.","exemplars":{"128":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040601.pdf","Title":"New carpet for the library"},"129":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040602.pdf","Title":"Sail for the yacht"},"130":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040604.pdf","Title":"The volume of boxes"},"131":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040605.pdf","Title":"Plastic buckets"}}},"140":{"Background":"The students deduce and use formulae to measure perimeter, area, and volume. They are able to separate a two-dimensional shape into familiar shapes to calculate area. They understand that the volume of a prism is calculated by measuring the area of the base and by multiplying that area by the prism\u2019s height. They calculate circumference from the measurement of diameter or radius, and they understand that the relationship between circumference and diameter (or radius) is a constant ratio. They understand the metric relationship of: 1 g = 1 ml= 1 cm\u00b3.","exemplars":{"132":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040701.pdf","Title":"Complex area"},"133":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040702.pdf","Title":"Triangular prisms"},"134":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040703.pdf","Title":"Calculating circumference"},"135":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040704.pdf","Title":"The fish aquarium"}}},"141":{"Background":"The students can recognise the complexity of the attribute being measured and use correct units with precision. They can solve measurement problems by splitting shapes into component parts, applying formulae, and using measurement ratios and trigonometric approaches appropriately.","exemplars":{"136":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040801.pdf","Title":"How Much Concrete? "},"137":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040802.pdf","Title":"Investigating Round Objects "},"138":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M040803.pdf","Title":"Are these expressions equivalent? "}}},"142":{"Background":"The students participate in a teacher-led investigation that involves the collection and display of category data in order to answer an investigative question. However, the students are unable to explain their reasoning.","exemplars":{"163":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060001.pdf","Title":"What to buy?"},"164":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060002.pdf","Title":"Tipurangi (unintentional gift)"}}},"143":{"Background":"The students participate in a teacher-led investigation that involves the collection and display of category data in order to answer an investigative question, and they can explain and make sense of the findings.","exemplars":{"165":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060101.pdf","Title":"Getting to school"},"166":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060102.pdf","Title":"Class pets"},"167":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060103.pdf","Title":"Soft toys"}}},"144":{"Background":"The students conduct a statistical investigation that involves the collection, display, and discussion of category and whole-number data in order to answer an investigative question posed by their teacher. They draw an appropriate conclusion and communicate their findings in context.","exemplars":{"168":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060201.pdf","Title":"How far can we throw?"},"169":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060202.pdf","Title":"Sizing up families"},"170":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060203.pdf","Title":"Seashell squares"}}},"145":{"Background":"The students pose summary-type investigative questions. They collect and display whole-number data in different ways and communicate their findings in context.","exemplars":{"171":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060301.pdf","Title":"Sleepy heads"},"172":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060302.pdf","Title":"Spinning tops"},"173":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060303.pdf","Title":"Fundraising"}}},"146":{"Background":"The students pose questions to compare or investigate relationships between variables of interest. They collect multivariate category, measurement, or time series data, and they can choose the appropriate displays to analyse and communicate their findings in context.","exemplars":{"174":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060401.pdf","Title":"Long showers"},"175":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060402.pdf","Title":"Litter problems"},"176":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060404.pdf","Title":"Investigating hamstrings"},"177":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060405.pdf","Title":"The Easter holiday road toll"}}},"147":{"Background":"The students pose investigative questions about a wider population. They collect samples of multivariate data and analyse these using displays to find patterns within, between, and beyond the data, and to notice unusual values. They recognise whether data need to be cleaned and can discuss appropriate reasons for variations in the data. The students communicate their findings with appropriate displays and generalise in context.","exemplars":{"178":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060501.pdf","Title":"The weight of school bags"},"179":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060502.pdf","Title":"Changes in technology usage"},"180":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M060504.pdf","Title":"Which Shoe? "}}},"148":{"Background":"The students participate in class statistical investigations and recognise certainty and uncertainty in simple chance situations. They can acknowledge an incorrect statement, but they are unable to explain their reasoning.","exemplars":{"139":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050001.pdf","Title":"Will it happen?"},"140":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050002.pdf","Title":"Am I right?"},"141":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050003.pdf","Title":"Goldilocks"}}},"149":{"Background":"The students can explain whether statements about data displays are correct with reference to the data. They can identify different outcomes in simple chance situations, and they are able to explain their thinking.","exemplars":{"142":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050101.pdf","Title":"Beetle"},"143":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050102.pdf","Title":"Favourite soft toys"},"144":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050103.pdf","Title":"End-of-year trip"},"145":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050104.pdf","Title":"Animal memories"},"146":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050105.pdf","Title":"More Goldilocks"}}},"150":{"Background":"The students identify and explain errors in statements and\/or data displays of others\u2019 statistical investigations. They identify whether an outcome is more likely by systematically recording the results of chance experiments.","exemplars":{"147":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050201.pdf","Title":"Where do you come from? "},"148":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050202.pdf","Title":"Sporting ways"},"149":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050203.pdf","Title":"Duck Race"},"150":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050204.pdf","Title":"Naming graphs"},"151":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050205.pdf","Title":"Spinning games"}}},"151":{"Background":"The students examine and question the steps in the process and results of others\u2019 statistical investigations in order to evaluate the appropriateness of the methods and conclusions. They investigate chance situations using experiments and simple models.","exemplars":{"152":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050301.pdf","Title":"Favourite sports"},"153":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050302.pdf","Title":"House points"},"154":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050303.pdf","Title":"Heads or tails?"},"155":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050304.pdf","Title":"Dicey games"},"156":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050305.pdf","Title":"Standing for the trees"}}},"152":{"Background":"The students examine the process and results of others\u2019 statistical investigations in order to evaluate whether or not their claims are believable and reasonable. They understand and explain why statistical investigations might be presented in particular ways. The students investigate chance situations by making connections between experimental results and theoretical models.","exemplars":{"157":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050401.pdf","Title":"Maths after school"},"158":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050402.pdf","Title":"Energy consumption"},"159":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050403.pdf","Title":"The money in milk"},"160":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050404.pdf","Title":"TV habits"},"161":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050405.pdf","Title":"Murphy's Law"},"162":{"PDFFileUrl":"\/assets\/IllustrationPDFs\/M050406.pdf","Title":"The Sausage Sizzle "}}}}