Using Units Of Measurement: Years 5–7
Using units of measurement: Years 5–7MATHEMATICS CONCEPTUAL NARRATIVELeading Learning: Making the Australian Curriculum work for usby bringing CONTENT and PROFICIENCIES togetherwww.acleadersresource.sa.edu.au
ContentsWhat the Australian Curriculumsays about ‘using units ofmeasurement’Proficiency: Problem Solving3Content descriptions, Year level descriptions,Achievement standards and NumeracycontinuumProficiency: ReasoningWorking with units of measurement 5Important things to notice5A quick look at Year 3 to Year 4Developing an ability to estimate6Different ways to reason when estimating lengthEngaging learners7Harnessing students fascination with scale40Proficiency emphasis and what questionsto ask to activate it in your students(Examples 17–24)Connections between ‘usingunits of measurement’ andother maths contentEmbedding the Australian Curriculum:Mathematics proficiencies8A summary of connections made in thisresource and suggestion for other possibleconnectionsPedagogy supporting you to embedthe proficiencies‘Using units of measurement’from Foundation to Year 10AProficiency: Understanding36Proficiency emphasis and what questionsto ask to activate it in your students(Examples 15–16)Proficiency: FluencyBuilding on learning frompast years30Proficiency emphasis and what questionsto ask to activate it in your students(Examples 12–14)485110Resource keyProficiency emphasis and what questionsto ask to activate it in your students(Examples 1–11)This teacher willraise questions,answer students’questions andshare some of herclassroom practice.This teacher willgive you his toppedagogy tips.Bringing it to Life (BitL): keyquestions are in bold orange text.2These students will raisequestions and modelstudent thinking.Sub-questions from the BitL toolare in green medium italics – thesequestions are for teachers to usedirectly with students.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
What the Australian Curriculum saysabout ‘using units of measurement’Content descriptionsYear level descriptionsStrand Measurement and geometrySub-strand Using units ofmeasurementYear 5 Students choose appropriateunits of measurement for calculationof perimeter and area.Year 5 ACMMG108 Students chooseappropriate units of measurement forlength, area, volume, capacity and mass.Year 5 Students formulate and solveauthentic problems using wholenumbers and measurements.Year 5 ACMMG109 Studentscalculate the perimeter and area ofrectangles using familiar metric units.Year 6 Students measure usingmetric units.Year 6 ACMMG135 Students connectdecimal representations to the metricsystem.Year 6 ACMMG136 Students convertbetween common metric units of length,mass and capacity.Year 6 ACMMG137 Students solveproblems involving the comparison oflengths and areas using appropriate units.Year 6 Students formulate andsolve authentic problems usingfractions, decimals, percentagesand measurements.Year 7 Students calculate areasof shapes and volumes of prisms.Year 7 Students formulate and solveauthentic problems using numbersand measurements.Year 6 ACMMG138 Students connectvolume and capacity and their unitsof measurement.Year 7 ACMMG159 Studentsestablish the formulas for areas ofrectangles, triangles and parallelogramsand use these in problem solving.Year 7 ACMMG160 Students calculatevolumes of rectangular prisms.Source: ACARA, Australian Curriculum: Mathematics, Version 8.0Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE3
Achievement standards Numeracy continuumYear 5 Students use appropriate unitsof measurement for length, area, volume,capacity and mass, and calculateperimeter and area of rectangles.Year 6 Students connect decimalrepresentations to the metric systemand choose appropriate units ofmeasurement to perform a calculation.They make connections betweencapacity and volume. They solveproblems involving length and area.Year 7 Students use formulas forthe area and perimeter of rectanglesand calculate volumes of rectangularprisms.4End of Year 6 Estimate andmeasure with metric unitsStudents choose and use appropriatemetric units for length, area, volume,capacity and mass to solve everydayproblems.End of Year 8 Estimate andmeasure with metric unitsStudents convert between commonmetric units for volume and capacityand use perimeter, area and volumeformulas to solve authentic problems.In the Australian Curriculum: Mathematics,the concept of ‘time’ is addressed in thesub-strand ‘Using units of measurement’, butin this resource, ‘time’ has its own narrative.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
Working with units of measurementImportant things to noticeWhen we design learning aboutmeasurement, it is easy to think solelyabout ‘using measuring instruments’. Itis also important to design opportunitiesfor students to: select appropriate units identify measurable attributesI wonder if allstandard unitsare metric? develop language associatedwith measurementI want to becomegreat at estimatingmeasurements! estimate using metric units.There is lotsof measurementlanguage thatI’ll need time topractise using.I need to bechallenged tochoose appropriateunits myself.Building on learning from past yearsA quick look at Year 3 to Year 4In Year 3, students make the transitionfrom the use of informal units to familiarmetric units. During Year 3 familiarmetric units are introduced for length,mass and capacity. Working withmetric units is extended in Year 4 toinclude familiar metric units for areaand volume.Familiar metric units are metricunits that would most commonly beexperienced by a student of that age.For example, centimetres, metres,grams and kilograms would be morefamiliar (and relevant) to young learnersthan kilometres, millimetres, tonnesand milligrams.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE5
Developing an ability to estimateDifferent ways to reason when estimating lengthIs estimatingguessing?No. Estimatingis reasoning, notguessing. We canestimate in lots ofdifferent ways.Typically we estimate distance in one of the following ways:A comparison to another known distance:I know myclassroom is about5m wide and thisroom is aboutthe same as myclassroom.A comparison to another lengthand then an adjustment:I am about150 cm tall and thiscupboard is a bittaller than me,so it’s about.6Pacing or marking out:I know my pacesare about half ametre, so 10 pacesis 5 metres.Visualise/mark out the unit distanceand count:I can think about howlong a ‘one metre’ ruler isand visualise laying ‘one metre’rulers end to end across theroom. Sometimes, I visualisethe rulers to the half waypoint and double thatmeasurement.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
Engaging learnersHarnessing students’ fascination with scalePeople are often fascinated with verylarge or very small items. We areparticularly fascinated with large itemsthat should be small and small itemsthat should be large. For an exampleof this fascination, follow the linkbelow to the news story about giantmarionettes in Perth, WA. An estimated1.4 million people attended ‘The yfnhocxo3-1227220081679Perth NowFebruary 2015Picture: Stewart AllenTo use this story to engage learners wewould play one of the news stories, without the audio (at first) and ask students:What questions do you have?There are films, such as ‘The Borrowers’and ‘Gulliver’s Travels’, that play onour fascination with scale. Such filmsand images can be used to makeconnections between measurement,scale, enlargement and fractions.Images of large amounts of moneyand movie scenes that involve thetransaction of large amounts of cashin small bags, or briefcases, provideanother engaging context for workingwith units of measurement.We can support our students to developa disposition towards using maths intheir lives, ie becoming numerate, notonly through the use of ‘real world’maths problems, but through fostering adisposition towards asking mathematicalquestions about everything they see.We develop this disposition in ourstudents when we promote, valueand share their curiosity and provideopportunities for them to develop theirquestions and explore solutions totheir questions.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE7
!PAGES 8/9 ARE REALLY IMPORTANT – you will be tempted to skip them in yourenthusiasm to get to the examples. You only need to READ THIS ONCE EVER.Embedding the Australian Curriculum:Mathematics proficienciesPedagogy supporting you to embed the proficienciesAC: Mathematics proficienciesThe verbs used in the four Mathematicsproficiencies from the AustralianCurriculum (AC: Proficiencies) describethe actions in which students canengage when learning and usingmathematics content.To embed the AC: Proficiencies instudents learning experiences, we needto ask questions that activate thoseactions in students. But what questionswill achieve this? The AC: Proficienciesdescribe the actions, but not thequestions that can drive those actions.There are four proficiencystrands in the AustralianCurriculum: Mathematics: Understanding Problem Solving Reasoning Fluency.Bringing it to Life toolThe Bringing it to Life (BitL) tool wasdeveloped by the South AustralianTeaching for Effective Learning (TfEL)team, to support teachers to bringthe AC: Proficiencies to life in theclassroom. The BitL tool modelsquestions that can be used to drivethe actions described in the AC:Proficiencies.8The Bringing it to Life toolis located in the LeadingLearning: Making theAustralian Curriculum Workfor Us resource (www.acleadersresource.sa.edu.au), in the section Bringingit to Life – essence meetscontent.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
Beware of the old paradigmThere is a prevalent assumptionthat we should instruct our studentswith processes and develop theirunderstanding before we challengethem to problem solve and reason.In this paradigm students will onlygain problem solving experience atthe end of the unit of work, assumingthey get through all of the practicequestions quickly enough.The pedagogy shift of innovativeeducators across the worldacknowledges that new understandingand the ensuing fluency are not simplya resource for problem solving andreasoning, but a product of problemsolving and reasoning.Students can constructnew understanding whenwe support them, as theygrapple with questions thatchallenge them to reasonwith, and extend their currentunderstanding. Instructioncan be used at thepoint of need.Why does this resourcelook at each proficiencyseparately, when they areintertwined skills?We acknowledge that the proficienciesintertwine and that it is possible toexperience a range of proficiencies withinone particular problem. However, wehave used the BitL questions to organisethe examples into categories thatemphasise each particular proficiency.The intention in doing this is to supportteachers to understand the emphasis ofeach proficiency deeply in order to beable to intertwine them as appropriate.You will find less of an emphasis, in thisresource on fluency examples, as manytextbook and worksheet resourcesalready provide this.Examples modelling embedding theproficiencies using BitL questions: UnderstandingExamples 1–11 Problem SolvingExamples 12–14 ReasoningExamples 15–16 FluencyExamples 17–24It is intended that teachers will select/adapt and sequence examples thatare appropriate for their students.These examples have been groupedby proficiency, not learning sequence.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE9
Proficiency: UnderstandingProficiency emphasis and what questions to askto activate it in your students (Examples 1–11)The AC: Mathematics defines the proficiency of ‘Understanding’ as:What theAC saysProficiency: UnderstandingBitL toolThere are three BitL questions associated with this proficiency. Theyreflect the student actions as described in the AC: Mathematics.The three questions are:Students build a robust knowledge of adaptable and transferablemathematical concepts. They make connections between relatedconcepts and progressively apply the familiar to develop new ideas.They develop an understanding of the relationship between the‘why’ and the ‘how’ of mathematics. Students build understandingwhen they connect related ideas, when they represent conceptsin different ways, when they identify commonalities and differencesbetween aspects of content, when they describe their thinkingmathematically and when they interpret mathematical information.Q1 What patterns/connections/relationships can you see?Q2 Can you answer backwards questions?Q3 Can you represent or calculate in different ways?Q1What patterns/connections/relationships can you see?ExamplesoverviewThe intent of this question is to promote learning design thatintentionally plans for students to develop a disposition towardslooking for patterns, connections and relationships.Example 1: Area of a rectangleEstablishing formulae for calculating the area of a rectangleExample 2: Area of a triangleEstablishing formulae for calculating the area of a triangleExample 3: Area of a parallelogramEstablishing formulaeExample 4: Converting between unitsLength, mass and capacity—connecting decimals to the metric system10Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
Q1ExamplesoverviewQ2ExamplesoverviewExample 5: Connecting volume and capacityConnections between units of different attributes (volume and capacity)Example 6: Relationships between attributesArea and perimeterCan you answer backwards questions?The intent of this question is to promote learning design thatintentionally plans for students to develop flexibility in the way thatthey can work with a concept.Example 7: Rectangles —connecting area and perimeterApplying formulae for calculating the area of a rectangleExample 8: Volume of a rectangular prismApplying formulae for calculating the volume of a rectangular prismExample 9: Area of triangles and parallelogramsApplying formulae for calculating the area of triangles and parallelogramsExample 10: Calculations using the four operations in thecontext of measurementQ3ExamplesoverviewCan you represent or calculate in different ways?The intent of this question is to promote learning design throughwhich students experience multiple representations and createmultiple approaches. We encourage teachers to look foropportunities to: present information/problems in a range of ways ask the questions:Is there another possibility?Is there another way?Example 1, Example 6, Example 7 and Example 8 all requirestudents to think about multiple ways to create, represent orcalculate in relation to area.Example 11: Ordering in different waysUsing different attributesUsing units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE11
Understanding Q1 What patterns/connections/relationships can you see?Example 1: Area of a rectangleEstablishing formulae for calculating the area of a rectangleEncourage students to record length, width and area of the rectangles in a tablelike the one in Figure 1, and ask:What connections do you notice?Figure 1Providing (or asking students to create)a group of rectangles that all havethe same area can help to avoid thedistraction of all values being different.We can challenge students to generalisetheir observation and create a rule forcalculating the area of a rectangle.Students who can already generalisethe rule for calculating the area of arectangle can begin to explore rules forother 2D shapes. The same process canbe used with older students for calculatingthe volume of a rectangular prism.Often, it can be easier tonotice a pattern or connectionwhen data is arranged in a table.Arranging the data in a logical/progressive order is also beneficialon many occasions and at least notdetrimental on any occasion, sothe use of tables and logical/progressive arrangements aregood strategies to modelwith students.12Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
LEARNING IN CONTEXTWhen we provide the conditions forstudents to spot connections for themselves,often we remove the need to ‘tell’ studentsfacts and instruct processes. This mode oflearning is empowering for learners. Knowingthey have the capacity to construct theirown knowledge and understanding, ratherthan simply receive and use knowledge,underpins being a powerful learner.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE13
Understanding Q1 What patterns/connections/relationships can you see?Example 2: Area of a triangleEstablishing formulae for calculating the area of a triangleFirst ask students about Figure 2:What’s the same about the way that each of the triangles has been formed here?Figure 2Figure 3There are many ways to describe this,but essentially, one edge of the triangleis always the same length as one edgeof the rectangle and the highest pointof the triangle is as tall as the otheredge of the rectangle.Another way to think about this is thata rectangle has been drawn around thetriangle. The specifics of the languagedon’t really matter at this stage. Whatdoes matter is that the students see aconnection between the rectangle andthe triangle.We can continue to develop studentthinking by asking:Could you generate some morepossible triangles that fit inside thisrectangle? Show me.What fraction of the rectangle is coveredby the triangle in the first image?What about the next image and thenext etc ? Convince me/yourself!14It doesn’t matter if the student’s firstidea is right or wrong. If it’s wrong, theywill find that out and they can try, or bedirected towards, a different idea, untilthey reach the point of understandingthat the triangle is half of the area of therectangle that fits around it. You cansee, in Figure 3, that triangles A and Bcould be cut off, rotated and positionedto cover triangle C.Support further development ofunderstanding by asking:What’s the area of the rectangle?So what’s the area of the triangle?What’s the connection between thearea of the rectangle and the areaof the triangle?Encourage students to generalise,by asking:Is there a rule that you could useto describe a way to work out thearea of a triangle?Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
Figure 4What if you change the size of therectangle/triangle? Does your rulework for any size of triangle?What if the triangle is still as tall asthe rectangle and it still shares thesame base, but it falls outside therectangle, as in Figure 4. Does yourrule still work now? Is the trianglestill half the area of the rectangle withthe same base and height? Convinceyourself. Convince me.LEARNING IN CONTEXTUsing variables to establishformulae for the area/volume of shapesis a good context to experiment withvariables because it is related to aconcrete representation. It is beneficialfor students to experiment with differentrepresentations of their formula, comparingtheir formula to their peers and thento conventional representationsthat they can find on theinternet or in textbooks.Figure 5It is very likely that this question willnow become a problem solving questionfor many students. Rearranging thisform of triangle to create half of therectangle is problematic. Most studentswill try to cut off the section of thetriangle that overhangs the rectangleand place it inside the rectangle in thehope of making clear that half of therectangle is now covered. This tendsnot to work. We can allow studentsto discover this for themselves, thenchallenge them to think about otherways they could show the triangle tobe half of the rectangle.We could use the following enablingprompts:If the triangle was half the area of therectangle, how many triangles would ittake to cover all of the rectangle? (Two)Could you try using two triangles tomake one rectangle? (Refer to Figure 5for an example of how this can work)Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE15
Understanding Q1 What patterns/connections/relationships can you see?Example 2 continuedLanguage associated with trianglesWhen working with triangles it is usefulto introduce the language ‘base’ and‘height’. These words are used inthe same kind of way as ‘length’ and‘width’ for rectangles and squares. Itis important to note that the base andheight are at right angles to each other.This will sometimes mean that the heightgoes through the middle of the triangle,rather than being along one edge.Rather than telling students what baseand height are, in relation to triangles,first find out what they think. We can say:‘Base’ and ‘height’ are words thatwe (as mathematicians) will use todescribe lengths on triangles. Wheredo you think the base and height wouldbe on this triangle? (Draw a triangle)Show students images such as thosein Figure 6, revealing the images oneby one and allowing students to adjusttheir understanding of the terms baseand height.Notice: The base is always one of the sidesof the triangle. The height is always at right anglesto the base.16Figure 6Challenge students thinking by saying:In these images the height is not oneof the sides of the triangle. For whattype of triangle could the height be oneof the sides of the triangle? (A rightangle triangle)The key point to establish is that baseand height are relative to each other.In maths worksheets the base is oftenpresented as a horizontal side on atriangle. This causes confusion forstudents when they are presented witha triangle that doesn’t have any horizontalsides. We can support students tounderstand that it doesn’t matterwhich side of the triangle you choosefor the base, but it does matter thatyou position the height at rightangles, relative to that base.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
Example 3: Area of a parallelogramEstablishing formulae for calculating the area of a parallelogramAsk students about Figure 7:Which is bigger, the area of theparallelogram or the area of therectangle?If students recognise the areas of therectangle/parallelogram pairs to beequal, then say:Encourage students to find the simplestway to rearrange the parallelogram toform its partner rectangle. Figure 8shows that it’s possible to make avertical cut and move that piece ofthe parallelogram to the opposite endof the shape to form a rectangle.Prove it to me/convince me!We can create opportunities for studentsto generalise, by asking:If students don’t recognise the areasof the rectangle/parallelogram pairsto be equal, then say:Is there a rule that you could use todescribe a way to work out the areaof a parallelogram?I think they are the same as each other.What if you change the angles withinthe parallelogram? Does your rulework for parallelograms with differentinternal angles?Students can prove you right or proveyou wrong. Either way, they are provingtheir thinking.Move the triangle to the other end of theparallelogram to produce a rectangleFigure 7Figure 8Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE17
Understanding Q1 What patterns/connections/relationships can you see?Example 4: Converting between unitsLength, mass and capacity—connecting decimals to the metric systemStudents will have been using metricunits of measure since Year 3 (andpossibly earlier), so when we begin tofocus on converting between differentunits, we can use their prior learning.We can ask students to completetables, such as those in Figure 9.These tables can be completedfrom recall or students can work outsolutions by looking at containers,scales and tape measures.We can then ask questions such as:What connections can you seebetween litres and millilitres?What operation ( ) could beused to change from the number oflitres to the number of millilitres? Theoperation that you choose must workon every row of your table.Is there a rule that you could use tochange from the number of litres tothe number of millilitres? How couldyou write that rule down (in words andperhaps in symbols for Year 7)?Figure 9We can make connections to decimalrepresentations:What if you use numbers other thanwhole numbers and halves, doesyour rule still work?Try changing ¼ (0.25) of a litre intomillilitres.Try changing 200 ml into litres etc.What if you didn’t have a wholenumber of litres, say 1½ litres, doesyour rule still work? How do youknow? Convince me!What if you wanted to change frommillilitres to litres, does your rule stillwork?18Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
It is important to point out tostudents that if they rememberthe basic connection:1 L 1000 ml, they will always beable to work out what to do (arule) to change between litres andmillilitres.To do this, just think:What do I need to or by, to getfrom 1 to 1000? I need to multiply by1000 to get from 1 to 1000, so, to getfrom Litres to millilitres I must multiplyby 1000.What do I need to or by, to getfrom 1000 to 1? I need to divide by1000 to get from 1000 to 1, so, to getfrom millilitres to Litres I must divideby 1000.Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE19
Understanding Q1 What patterns/connections/relationships can you see?Example 5: Connecting volume and capacityConnections between units of different attributes (volume and capacity)The metric system is beautifullyconstructed, such that there is arelationship between the different units.For example, 1 cm3 is the same as 1 mland for water this quantity has a massof 1 g! At this stage of developmentit is only necessary for students tounderstand the connection betweenvolume and capacity. For example:1 ml 1 cm3.Submerging MAB blocks in a measuringcylinder (like those shown in Figure10) containing water and observingthe effect on the water level, is a veryeasy way to establish this connection,without instructing students. We canask students to submerge differentquantities of MAB blocks in a measuringcylinder and ask:What connection do you noticebetween the number of centimetrecubes that you place in the measuringcylinder and the number of millilitresthe water level rises by?Figure 10Take care to use MABcubes/lengths that have beencut to metric measurements.Cubes should be 1 cm x 1 cm x1 cm and the 10 lengths shouldbe 1 cm x 1 cm x 10 cm.It’s worth checking yourMAB blocks before usingthem in this way.20Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE
For larger volumesUsing a bucket of water, filled to thepoint of overflow, ask students tosubmerge a 1000 cm3 (10 cm x 10cm x 10 cm) MAB block in the water.Capture (in a tray) the water that flowsover the edge of the bucket andmeasure this in a measuring jug.Before doing this ask students:How many millilitres do you think willbe displaced? Why?Encourage students to makeconnections to familiar items such ascans and bottles of soft drink. Have arange of items for students to handleas they make their predications.We are aiming for students to befamiliar with the connection betweenvolume and capacity:1 cm3 1 ml, therefore 1000 cm3 1000 ml 1 LOnce students have established thisconnection, displacement becomesan accessible way to approximate thevolume of any solid object. Given thatat this stage of development studentsare only familiar with the formula forthe volume of a rectangular prism,displacement facilitates students orderinga collection of objects by volume, evenif they cannot calculate the volume.WORKING IN AUTHENTICCONTEXTS—CREATINGCONNECTED LEARNING EXPERIENCESWhen students carry out practical exercisessuch as this, they are unlikely to gatherperfectly accurate data. There will be a rangeof solutions for the same displacementcarried out by different students or by thesame students on different occasions.This is a perfect opportunity to workwith averages in a meaningfulcontext. (Year 7)Using units of measurement: Years 5–7 MATHEMATICS CONCEPTUAL NARRATIVE21
Understanding Q1 What patterns/connections/relationships can you see?Example 6: Relationships between attributesArea and perimeterWhen students enlarge shapes (AC:Mathematics Year 5), say by a scalefactor of 2, they double the length ofthe sides of the image and therefore: the perimeter doubles (x2) the area quadruples (x4) if you work with 3D objects thevolume of the enlarged object is8 times the volume of the originalobject (x8).An understanding of the relationshipsdescribed here, can be developed,rather than instructed.The websiteNRICH enrichingmathematicsprovides a detailedintroduction toinquiry about theserelationships and as always, it alsoprovides a sample of correct possiblesolutions that have been submittedby students from across the world.‘Growing rectangles’ link: http://nrich.maths.org/6923However, an introduction to thislearning, could be as simple asshowing students images such asthose in Figure 11 and asking:What relationships can you seebetween the small shape and thelarger shape?22Figure 11This question provides an opportunityfor students to use language related toshape, angle, symmetry and fractions aswell as area, perimeter and enlargement.We can allow time for discussion andvalue the connections that studentsidentify across a range of topics.Ask students to focus on the fact thatin each of these pairs, the length of thesides has doubled. If students have notnoticed or commented on the lengthof the sides, the perimeter or the areathen ask:If the lengths of the sides are twiceas long, what does that mean for theperimeter?If students don’t know the word perimeterthen trace the perimeter of the shapeswith your finger and say that you aretracing the perimeter, then ask thestudent what they think the wordperimeter means.Using units of mea
metric units. During Year 3 familiar metric units are introduced for length, mass and capacity. Working with metric units is extended in Year 4 to include familiar metric units for area and volume. Familiar metric units are metric units that would most commonly be experienced by
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2.1 Units of Measurement The standard of measurement used in science are those of the metric system. All the units are based on 10 or multiples of 10. SI Units: The International System of Units is a revised version of the metric system. There are seven base SI units.
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Fundamentals Chapter 1 1 1.1 Units Wherever measurements are performed there is a need for a coherent and practical system of units. In science and engineering the International System of units (SI units) form the basis of all units used. There are seven ‘ base ’ units from which all the other units are derived, called derived units.
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