math curriculum sept 2011

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JUNIOR SCHOOLMATH CURRICULUM 2011 1

St Dominic’s International School, Portugal

Junior School

Mathematics Curriculum

2011 – 2012




Contents

1. Beliefs and values in Mathematics2. Good mathematics practise

Constructing meaning about mathematicsTransferring meaning into symbolsApplying with understanding

3. Mathematic Strands4. Key concepts in the PYP : What do we want students to understand about mathematics?5. Examples of questions that illustrate the key concepts6. Learning objectives

Data HandlingMeasurementShape and spacePattern and functionNumber

7. Strategies for pencil and paper procedures

8. Basic layout for pen and paper procedures




Beliefs and values in mathematics

All students deserve an opportunity to understand the power and beauty of mathematics.

Principles and standards for school mathematicsNational Council of Teachers of Mathematics (NCTM 2000)

In the PYP, mathematics is viewed primarily as a vehicle to support inquiry, providing a global language through which wemake sense of the world around us. It is intended that students become competent users of the language ofmathematics, and can begin to use it as a way of thinking, as opposed to seeing it as a series of facts and equations tobe memorized. The power of mathematics for describing and analysing the world around us is such that it has become ahighly effective tool for solving problems. It is also recognized that students can appreciate the intrinsic fascination ofmathematics and explore the world through its unique perceptions. In the same way that students describe themselves as―authors or ―artists , a school‘s programme should also provide students with the opportunity to see themselves as―mathematicians , where they enjoy and are enthusiastic when exploring and learning about mathematics. The IB learner profile is integral to teaching and learning mathematics in the PYP because it represents the qualities of effective learners

and internationally minded students. The learner profile, together with the five essential elements of the programme — knowledge, concepts, skills, attitudes and action — informs planning, teaching and assessing in mathematics.




Good mathematics practice

It is important that learners acquire mathematical understanding by constructing their own meaning throughever-increasing levels of abstraction, starting with exploring their own personal experiences, understandings andknowledge. Additionally, it is fundamental to the philosophy of the PYP that, since it is to be used in real-lifesituations, mathematics needs to be taught in relevant, realistic contexts, rather than by attempting to impart afixed body of knowledge directly to students. How children learn mathematics can be described using thefollowing stages

How children learn mathematics

Applying with understandingTransferring meaningConstructing meaning

It is useful to consider these stages when planning developmentally appropriate learning experiences at allages. Schools that have local and/or national curriculum requirements in mathematics should articulate howbest these can be incorporated into their planning, teaching and assessing of mathematics.




Constructing meaning about mathematics

Learners construct meaning based on their previous experiences and understanding, and by reflecting upon their interactions with objects and ideas. Therefore, involving learners in an active learning process, where they are providedwith possibilities to interact with manipulatives and to engage in conversations with others, is paramount to this stage of

learning mathematics. When making sense of new ideas all learners either interpret these ideas to conform to their present understanding or they generate a new understanding that accounts for what they perceive to be occurring.This construct will continue to evolve as learners experience new situations and ideas, have an opportunityto reflect on their understandings and make connections about their learning.

Transferring meaning into symbols

Only when learners have constructed their ideas about a mathematical concept should they attempt to transfer thisunderstanding into symbols. Symbolic notation can take the form of pictures, diagrams, modeling with concrete objectsand mathematical notation. Learners should be given the opportunity to describe their understanding using their ownmethod of symbolic notation, then learning to transfer them into conventional mathematical notation.

Applying with understandingApplying with understanding can be viewed as the learners demonstrating and acting on their understanding. Throughauthentic activities, learners should independently select and use appropriate symbolic notation to process and recordtheir thinking. These authentic activities should include a range of practical hands-on problem-solving activities andrealistic situations that provide the opportunity to demonstrate mathematical thinking through presented or recordedformats. In this way, learners are able to apply their understanding of mathematical concepts as well as utilizemathematical skills and knowledge. As they work through these stages of learning, students and teachers use certainprocesses of mathematical reasoning.




Mathematics strandsWhat do we want students to know?

Data handling

Data handling allows us to make a summary of what we know about the world and to make inferences about what we do notknow.Data can be collected, organized, represented and summarized in a variety of ways to highlight similarities, differences andtrends; the chosen format should illustrate the information without bias or distortion.Probability can be expressed qualitatively by using terms such as ―unlikely , ―certain or ―impossible . It can be expressedquantitatively on a numerical scale.

MeasurementTo measure is to a ttach a number to a quantity using a chosen unit. Since the attributes being measured are continuous, waysmust be found to deal with quantities that fall between numbers. It is important to know how accurate a measurement needs tobe or can ever be.

Shape and spaceThe regions, paths and boundaries of natural space can be described by shape.An understanding of the interrelationships of shape allows us to interpret, understand and appreciate our two-dimensional (2D)and three dimensional (3D) world.

Pattern and functionTo identify pattern is to begin to understand how mathematics applies to the world in which we live.The repetitive features of patterns can be identified and described as generalized rules called ―functions . This builds a foundationfor the later study of algebra.

NumberOur number system is a language for describing quantities and the relationships between quantities. For example, the value

attributed to a digit depends on its place within a base system.Numbers are used to interpret information, make decisions and solve problems. For example, the operations of addition,subtraction, multiplication and division are related to one another and are used to process information in order to solveproblems.The degree of precision needed in calculating depends on how the result will be used.

Related concepts: There are many related concepts that could provide further links to the transdisciplinary programme of inquiry or further understanding of the subject area. Related concepts, such as pattern, boundaries and base systems, have been embedded intothe descriptions for each of the strands above. Schools may choose to develop further related concept s.




Key concepts in the PYP:

What do we want students to understand aboutmathematics?

Central to the philosophy of the PYP is the principle that purposeful, structured inquiry is a powerful vehicle for learning thatpromotes meaning and understanding, and challenges students to engage with significant ideas. Hence in the PYP there is also acommitment to a concept-driven curriculum as a means of supporting that inquiry. There are clusters of ideas that can usefully begrouped under a set of overarching concepts, each of which has major significance within and across disciplines, regardless oftime or place.

These key concepts are one of the essential elements of the PYP framework. It is accepted that these are not, in any sense, the onlyconcepts worth exploring. Taken together they form a powerful curriculum component that drives the teacher- and/or student-constructed inquiries that lie at the heart of the PYP curriculum.




Examples of questions that illustrate the key conceptsThe following table provides sample teacher/student questions that illustrate the key concepts, and that may help to structure or frame an inquiry. These examples demonstrate broad, open-ended questioning — requiring investigation, discussion, and a full andconsidered response — that is essential in an inquiry-led programme.

Concept Sample teacher/student questionsFormWhat is it like?

What is a pattern?How can we describe these shapes?What is a fraction?How can we describe time?

FunctionHow does it work?

How does the scale on a graph work?What happens if we keep adding?What is each shape being used for?How can we record time?

CausationWhy is it like it is?

Why is a block the best shape for building a tower?Why do these calculations produce patterns?What prompted people to develop a place value system?Why was the data displayed in this form?

ChangeHow is it changing?

How can we convert from the 12- • hour clock to the 24 -hour clock?How can you change one quadrilateral into another?What do all patterns have in common?What would happen to the area of something if … ?




ConnectionHow is it connected to other things?

How can you use fractions to explain musical notation?How are 4 + 3 and 3 + 4 connected?What do you already know that helps you to read and interpret this display of data?How is area connected to perimeter?

PerspectiveWhat are the points of view?

Are there some different ways of explaining this?Who might be interested in, or be able to use, the results of our survey?How do people calculate in different cultures?What would make this game fair to all players?

ResponsibilityWhat is our responsibility?

What makes your answer reasonable?Why does the measurement need to be accurate?

How have you collected all the relevant data?

ReflectionHow do we know?

How do you know that you are correct?Which way works the best? Why?What could you do differently if you repeated the survey?Why are our estimates realistic?




Data Handling

Data handling allows usto make a summary of

what we know about theworld and to makeinferences about whatwe do not know.• Data can be collected,organized, representedand summarized ina variety of ways tohighlight similarities,differences and trends;the chosen format shouldillustrate the information

without bias or distortion.• Probability can beexpressed qualitativelyby using terms such as“unlikely”, “certain” or“impossible”. It can beexpressed quantitativelyon a numerical scale.

Phase 1 Phase 2 Phase 3 Phase 4

Nursery & Kindergarten Reception & Grade 1 Grade 2 & Grade 3 Grade 4 &Grade 5

Learners will develop anunderstanding of how thecollection and organizationof information helps to makesense of the world. They willsort, describe and labelobjects by attributes andrepresent information ingraphs including pictographsand tally marks. The learnerswill discuss chance in dailyevents.

Learners will understandhow information can beexpressed as organizedand structured data andthat this can occur in arange of ways. They willcollect and representdata in different types ofgraphs, interpreting theresulting information for the purpose of answeringquestions. The learners will

develop an understandingthat some events in dailylife are more likely tohappen than others andthey will identify anddescribe likelihood usingappropriate vocabulary.

Learners will continue tocollect, organize, displayand analyse data,developing anunderstanding of howdifferent graphs highlightdifferent aspects of datamore efficiently. They willunderstand that scalecan represent differentquantities in graphs andthat mode can be used

to summarize a set ofdata. The learners willmake the connectionthat probability is basedon experimental eventsand can be expressednumerically.

Learners will collect,organize and display datafor the purposes of validinterpretation andcommunication.They will be able to use themode, median, mean andrange to summarize a setof data. They will createand manipulate anelectronic database for their own purposes,

including setting upspreadsheets and usingsimple formulas to creategraphs. Learners willunderstand thatprobability can beexpressed on a scale (0 – 1or 0% – 100%) and that theprobability of an eventcan be predictedtheoretically.




Data handling Data handling allows us to make a summary of what we know about the world and to make inferences about what wedo not know.

Data can be collected, organized, represented and summarized in a variety of ways to highlight similarities, differencesand trends; the chosen format should illustrate the information without bias or distortion.

Probability can be expressed qualitatively by using terms such as “unlikely”, “certain” or “impossible”. It can beexpressed quantitatively on a numerical scale.

Learning Objective Notes for teachers

Nursery Sort real-life objects into sets by attribute(size, shape, colour)Graph real-life objects

What things belong together?Who is/is not here today?Why do they belong together?

Who has a red jumper /blue jumper?Can we sort them in another way?

Kindergarten Sort real-life objects into sets by attributeGraph real-life objects and comparequantities

What things belong together?Why do they belong together?Can we sort them in another way?What different ways are there to show what we have done?Which has more?Which has the most?Which has the least?

Can we see any patterns in the graph?How can we describe the information in these graphs?How can we use number words to describe what we see onthe graph?




chancePlace outcomes in order of likelihoodCommunicate predictions and findingsusing vocabulary of probability

Is the game fair?What makes a fair game?What can you think of that would never happen, that itwould be impossible for it to happen?Is it impossible / unlikely / likely / certain that this will happen.

Grade 3 Decide how best to organise and present

findingsDetermine and identify the mode as away of analysing and interpreting dataInterpret tables, lists and charts used ineveryday lifeSolve problems involving dataUse squared paper to represent larger quantities to scaleDetermine the probability of events anddefend their answer

What are the most important things we want to show?

Is this the best way to show them?What other ways could we display the information?What is this chart/table/list showing us?What information can you find in this diagram/chart/table?Would you add anything else to i t?How can we fit data on this piece of squared paper whenthe range of numbers is so large?On what should we base our decision?Do you think this will happen /won‘t happen? Is it possible /impossible?Is it probable that it will rain today?Why do you think so?

Grade 4 Gain information on a topic by designinga survey, processing the data andinterpreting the resultsDetermine and identify the mean, medianand mode as a way of analysing andinterpreting dataChoose whether to display data as a bar graph or pie chartUse a probability scale from 0 to 1 or 0% to100%to express probabilityCreate a database to organise

information

What are the most important pieces o f information that weneed?How best would we display this information?Which type of diagram / graph would be the mostappropriate for the information we want to convey? (Venndiagram, pictogram, Carroll diagram, tables, bar graphs, piecharts)What is/are the mean / median / mode o f the informationshown?What is the difference between a bar graph and a piechart?

When would we use a bar graph / pie chart?If 0 means impossible and 1 means certain, where would youplace unlikely/ likely/ equal chance on the line?If 0% means impossible and 100% means certain whatpercentages would you use to reflect unlikely / equalchance / likely?Why would you create a database?




When would you create a database?Grade 5 Determine and identify the mean, median

and mode as a way of analysing andinterpreting dataKnow that mean, median and mode aremeasures of average and that range is a

measure of spreadRecognise the difference betweendiscrete and continuous dataDraw conclusions from statistics andgraphs and recognise when information ispresented in a misleading wayUnderstand that different outcomes mayresult from repeating an experimentUse a spreadsheet to process and displaynumerical informationUse a probability scale from 0 to 1 or 0% to100% to express probability

Use IT to generate appropriate graphs toreflect data collected.

What is the mean, median and mode of the data reflectedin your graph?What do the mean, median and mode measure? (average)What does the range measure? (spread)Which graph would best display this information?

Does this graph portray anything that could be misleading?Why would you set up a database?What would be a useful database to create?If we repeat an experiment will the results change?What happens the more we repeat an experiment?How many times do you think we should repeat theexperiment to get the most truthful results?If 0 means impossible and 1 means certain, where would youplace unlikely/ likely/ equal chance on the line?If 0% means impossible and 100% means certain whatpercentages would you use to reflect unlikely / equalchance / likely?




Measurement

To measure is to attach anumber to a quantityusing a chosen unit.Since theattributes beingmeasured arecontinuous, ways mustbe found to deal withquantities that fallbetween numbers. It isimportant to know how

accurate ameasurement needs tobe or can ever be .

Phase 1 Phase 2 Phase 3 Phase 4Nursery & Kindergarten Reception & Grade 1 Grade 2 & Grade 3 Grade 4 &

Grade 5Learners will develop anunderstanding of howmeasurement involves thecomparison of objects andthe ordering and sequencingof events. They will be able toidentify, compare anddescribe attributes of realobjects as well as describeand sequence familiar events in their daily routine.

Learners will understandthat standard units allowus to have a commonlanguage to measure anddescribe objects andevents, and that whileestimation is a strategythat can be applied for approximatemeasurements, particular tools allow us to measureand describe attributes ofobjects and events withmore accuracy. Learnerswill develop theseunderstandings in relationto measurement involvinglength, mass, capacity,money, temperature andtime.

Learners will continue touse standard units tomeasure objects, inparticular developingtheir understandingof measuring perimeter,area and volume. Theywill select and useappropriate tools andunits of measurement,and will be able todescribe measures thatfall between twonumbers on a scale. Thelearners will be given theopportunity to constructmeaning about theconcept of an angle as ameasure of rotation.

Learners will understandthat a range ofprocedures exists tomeasure differentattributes of objects andevents, for example, theuse of formulas for findingarea, perimeter andvolume. They will be ableto decideon the level of accuracyrequired for measuringand using decimal andfraction notation whenprecise measurements arenecessary. To demonstratetheir understanding ofangles as a measure ofrotation, thelearners will be able tomeasure and construct

angles.




Measurement To measure is to attach a number to a quantity using a chosen unit.

Since the attributes being measured are continuous, ways must be found to deal with quantities that fall betweennumbers.

It is important to know how accurate a measurement needs to be or can ever be.


Nursery Directly compare attributes of objects andevents

Which one is longer, taller, heavier, hotter?Can you show me which one is longer, taller?Which holds more?How do we know it is heavier?How will we know when it is time to go home?

What will happen before....?What happens after ...?Why do we put our socks on before our shoes?What is your favourite part o f the day and why?

Kindergarten Directly compare attributes of objectsIdentify and sequence events in their daily lives(put in chronological order)Introduce children to using a calendar on adaily basis

Which one is bigger, smaller?Which one is heavier, lighter?How will we know when it is time to go home?What will happen before....?What happens after ...?What day is it today?What happens today?

When will we have snack, lunch?What month is it?What happens this month?Whose birthday is it today?

Reception Compare attributes of objects using non- When would we want to measure something?




standard unitsIdentify, compare and sequence events in their daily livesBegin to think about the need for standard unitsof measurementUse a calendar to determine the day, date andmonth of the year (daily)Identify and compare lengths of time eg. hour,day, week, year Explore telling the time to the hour (analogue)Make up amounts to 10c using 1c, 2c, 5c and10c coins (explore to 20c)

How can we find out how long/heavy something is?How can we know if one thing is longer/heavier thanother things we have measured?Why would we want to estimate the measurement ofsomething?What tools can we use to measure?Does the measurement of the same object changewhen we use different measuring tools?How can we compare and describe themeasurement of two objects so that other people canunderstand?Why do we use calendars?How can we use a calendar to find out the date?What patterns are there on the calendar?Why is it important to be able to put the days of theweek and months of the year in the correct order?What language do we use to describe time?Why would we want to measure time?How do we measure time?What can you do in an hour?How do we know what a day/a week/a month beginsand ends?Why is time referred to in hours?How do we record the time of day?What time is it? (on the hour)

Grade 1 Begin to understand why standard units ofmeasurement are used to measure andcompareMeasure using the standard units of length,capacity, mass, time and temperatureMake reasonable estimates of length, capacity,mass, time and temperatureIdentify and compare lengths of time eg.minute, hour, day, week, month, year Tell the time to the hour and explore half hour (analogue)

When would we want to measure something?How can we find out how long/heavy something is?How can we know if one thing is longer/heavier thanother things we have measured?Why would we want to estimate the measurement ofsomething?What tools can we use to measure?Does the measurement of the same object changewhen we use different measuring tools?Why did John and Jane get different results when theymeasured the classroom using their feet?




Understand angles as a ‗measure of turns‘, usingwhole turns and half turnsHandle and explore money and look at coins to€1 (How many ways can we make €1?)

How can we compare and describe themeasurement of two objects so that o ther people canunderstand?How could Sam and Jenny get the same result whenmeasuring how heavy something is?What can you do in an hour/a minute/a second?What could you do in a day/a week/ a month?What time is it now? (on the hour, on the half hour)The time is now 11 o‘clock. How far has the handturned since 10 o‘clock? (full turn) How far has the hand turned now it is half past? (half aturn)How many ways can we mak e €1?

Grade 2 Describe measures that fall between wholenumbers on a scale (between, more than, etc)Begin to think about and compare theconcepts of area and volumeBegin to use standard units of measurementDistinguish between length, volume, capacity,etc and units used to measure eachDistinguish between calibrations in length – mm,cm and m.Identify which calibration is appropriate to thetask Read and write time to the hour and half hour (analogue)Model addition using money, exploresubtr action (coins up to €2) Children should be able to recognize differentnotes

Is this more than 100g?Is this less than 200g?Is this more than 100g but less than 200gWhere does this measurement lie? (between 100g and200g)What is the perimeter?What is the area?What is the volume?How is area connected to perimeter?How is volume connected to 3 -D shapes?How much can this container hold? What do we callthis? (capacity)How can we describe a measure that falls betweentwo numbers on a scale?What unit of measurement is best used to measure thisobject? (cm, mm, m)How can we make up €2? I would like to buy this item, do I have enough money?Will I get change? How much will it be?What notes of money can we use to buy things?

Grade 3 Describe measures that fall between whole How are we going to represent measurements that fall




numbers by using smaller unitsMeasure using the standard units for area andperimeter, using the formulaeMake reasonable estimates for area andperimeter Measure, label and compare perimeter andareaModel addition and subtraction using moneyIncorporate change as being the differencebetween how much you have and what is leftafter the purchaseSolve simple addition and subtraction problemsinvolving moneyRead and write time to the hour, half hour, andquarter hour (analogue)

between numbers on the scale?How do we find the perimeter?How do we measure area?Do I have enough money to buy this? How much morewill I need? What change will I get? What is thedifference between how much I have and how muchthe item is?I have 50c here. What fraction is that of €1? It is quarter past 10. What part of a full turn has thehand moved?

Grade 4 Select and use appropriate standard units ofmeasurement when estimating, describing,comparing and measuringUse measuring tools with simple scalesaccurately (rulers, scales, temperature gauges)Develop procedures for finding area, perimeter and volumeEstimate, measure, label and compare usingformal methods and standard units ofmeasurement and the dimensions of area,perimeter and volumeUse decimal notation in measurement: 3.5 cmIntroduce the right angle. Identify that it is 90º.Identify acute, obtuse and straight anglesRead and write the time to the minute andsecond on an analogue clock Apply to the 24 hour clock Use and construct timetables using 12 and 24hour clock Use and construct timelines

How can we accurately measure a given object?What unit should we use?How do we choose an appropriate measuring tool?Which instrument is best for this measurement?How do we read simple scales?How do we find the perimeter? Are there shortcuts tofinding perimeter? Can you find a formula that willwork every time?How do we measure area? Are there shortcuts tofinding area? Can you find a formula that will work every time?What will the unit of measurement be for perimeter/area?What is volume? How is volume linked to area?When we talk about volume are we looking at 2-D or 3-D shapes?How do we measure volume? Are there shortcuts tofinding volume? Can you find a formula that will work every time?When do we need to estimate?How can we make a reasonable estimate ofmeasurement?




How can we test our estimate?What are all the possible dimensions?How can we deal with the part of the measurementthat is left over?How can we apply our understanding of decimalnotation to measurement scales?What language to we use to describe angles?How can we identify angles?What are the relationships between the differentangles?Where are angles found in the immediateenvironment?Why are angles a useful form of measurement?What is the 24 hour clock?Why do we use the 24 hour clock? Give an example ofwhen the 24 hour clock is useful.When do we use timetables / timelines?How do we read timetables / timelines?How do we create our own timetables / timelines?

Grade 5 Select and use appropriate standard units ofmeasurement when estimating, describing,comparing and measuringUse measuring tools accuratelyEstimate and compare, using formal methodsand standard units of measurement thedimensions of area, perimeter and volumeRecord measurements accurately withappropriate and correct standard unitDiscover the formulae for finding area,perimeter and volumeAccurately calculate area, perimeter andvolume using correct standard unitUse decimal notation in measurement : 3.2cm,1.47kg (Link to fractions as part of a whole)Introduce the reflex angle and rotationAccurately construct, measure and label angles

How can we accurately measure a given object?What unit should we use?How do we choose an appropriate measuring tool?Which instrument is best for this measurement?How do we read simple scales?Does everything have an area?How can we know the area of this rectangle withoutcounting the squares?How can we calculate the area of an irregular shape?Are there short cuts to fining the perimeter ofpolygons?How can we find the volume of something withoutfilling it with cubes?How do mathematicians use formulas to calculatearea / perimeter / volume?Do all shapes with the same perimeter have the samearea? (and vice versa)




Shape and space

The regions, pathsand boundaries ofnatural space can bedescribed by shape.An understanding ofthe interrelationshipsof shape allows us tointerpret, understandand appreciate ourtwo-dimensional (2D)and threedimensional (3D)world .

Phase 1 Phase 2 Phase 3 Phase 4

Nursery & Kindergarten Reception & Grade 1 Grade 2 &

Grade 3

Grade 4 &

Grade 5Learners will understandthat shapes havecharacteristics that canbe described andcompared. They willunderstand and usecommon language todescribe paths, regionsand boundaries of their immediate environment.

Learners will continue towork with 2D and 3Dshapes, developing theunderstanding that shapesare classified and namedaccording to their properties. They willunderstand that examplesof symmetry andtransformations can befound in their immediate

environment. Learners willinterpret, create and usesimpledirections and specificvocabulary to describepaths, regions, positionsand boundaries of their immediate environment.

Learners will sort, describeand model regular andirregular polygons,developing anunderstanding of their properties. They will be ableto describe and modelcongruency and similarity in2D shapes. Learners willcontinue to develop their understanding of symmetry,

in particular reflective androtational symmetry. Theywill understand howgeometric shapes andassociated vocabulary areuseful for representing anddescribing objects andevents in real-worldsituations.

Learners will understandthe properties of regular and irregular polyhedra.They will understand theproperties of 2D shapesand understand that 2Drepresentations of 3Dobjects can be used tovisualize and solveproblems in the real world,for example, through the

use of drawing andmodeling. Learners willdevelop their understanding of the useof scale (ratio) to enlargeand reduce shapes. Theywill apply the languageand notation of bearing todescribe direction andposition.




Shape and SpaceThe regions, paths and boundaries of natural space can be described by shape.

An understanding of the interrelationships of shape allows us to interpret, understand and appreciate our two-dimensional (2D) and three dimensional (3D) world .


Nursery Be able to sort, describe and compare 2-D/3-Dshapes according to attributes such as size or form.Begin to use Maths language for shapesUse everyday words to describe position.(Example: inside, outside, on, off)

Can we make this shape from another shape?Is this cube (block) the best shape to use to buildthis tower?

Kindergarten Be able to sort, describe and compare 2-D/3D

shapes according to attributes such as size or form.Begin to use Maths language for shapesIncrease the use of everyday words to describeposition. (Example: in front, behind, next to, up,down)Be introduced to simple directions using ―left and―right .

Can we make this shape from another shape?

Is this cube (block) the best shape to use to buildthis tower?Does a shape change if its size changes?Does its size change if the shape changes?Does it always look the same from any side?Does it look the same if I turn it around?Have you seen a shape like this at home?Use music and movement to enhanceunderstanding of the language – (example: TheHokey Kokey)

Reception Be able to sort, describe and compare 2-D/3Dshapes according to attributes such as size or form.Begin to use Maths language for shapesIncrease the use of everyday words to describeposition. (Example: in front, behind, next to, up,down)Use simple directions ―left and ―right .

Can we make this shape from another shape?Is this cube (block) the best shape to use to buildthis tower?Does a shape change if its size changes?Does its size change if the shape changes?Does it always look the same from any side?Does it look the same if I turn it around?




Be able to name common 2-D and 3-D shapes,Be able to name attributes of common 2-D and 3-D shapesBe able to create 2-D shapesBe introduced to symmetry.

Have you seen a shape like this at home?Use music and movement to enhanceunderstanding of the language – (example: TheHokey Kokey)Why is this a 2-D shape?Why is this a 3-D shape?Can we fold this 2-D shape exactly in half?

Grade 1 Be able to sort, describe and compare 2-D/3Dshapes according to attributes such as size or form.Use Maths language for shapesIncrease the use of everyday words to describeposition. (Example: in front, behind, next to, up,down)Use si mple directions ―left and ―right .Be able to name common 2-D and 3-D shapes,Be able to name attributes of common 2-D and 3-D shapesBe able to create 2-D shapesUnderstand symmetry.be able to find lines o f symmetry in the worldaround them.Be able to create and explain simple symmetricaldesigns.Be able to give and follow simple directionsdescribing paths, regions and boundaries in their immediate environment.

Can we make this shape from another shape?Is this cube (block) the best shape to use to buildthis tower?Does a shape change if its size changes?Does its size change if the shape changes?Does it always look the same from any side?Does it look the same if I turn it around?Have you seen a shape like this at home?Why is this a 2-D shape?Why is this a 3-D shape?What mathematical names do we give to theseshapes?What words to mathematicians use to describeparts of shapes?What is symmetry?How do we know i f something is symmetrical?How do we find a line of symmetry?Why do we need directions?When would be need to receive directions?How precise do directions need to be?

Grade 2 Sort, describe and model regular and irregular polygons e.g. triangles, hexagons, trapeziums;Identify, describe and model congruency in 2-Dshapes;Combine and transform 2-D shapes to makeanother shape;Create symmetrical patterns, including tessellation;Identify lines and axes of reflective and ro tational

What polygons can you see around the classroom?What are the properties of polygons?How are these shapes similar/different?What do these shapes have in common?How could we sort these?What rule have we used to sort these shapes?Can you find two identical shapes?What makes them identical?




symmetry;Understand an angle as a measure of rotation bycomparing and describing rotations: whole turns,half turn, quarter turn, north, south, east and weston a compass;Locate features on a grid using coordinates.

When will our knowledge of shapes be useful?What happens if we flip the shape? Is it stillcongruent?What happens when we combine 2D shapes?What happens when we stretch the sides of ashape?What happens when we change the angles on a 2-D shape?What names do mathematicians give to these newshapes?Where in the design do we see a flip (reflection),turn (rotation) slide (translation)?Do all quadrilaterals tessellate? Why?What is an axis of symmetry?How does it help us define if things aresymmetrical?What happens if you place the edge of a shapeagainst the edge of a mirror?What happens if we move the mirror further away?Which of these shapes do you think you could foldso that the two sections match up?How can we measure the size of a turn that wemake?If we turn from north to south, how much of a turndo we make?How do mathematicians describe this?How can we describe the position of something?

Grade 3 sort, describe and model regular and irregular polygons e.g. triangles, hexagons, trapeziums;identify, describe and model congruency in 2-Dshapes;combine and transform 2-D shapes to makeanother shape;create symmetrical patterns, including tessellation;identify lines and axes of reflective and ro tationalsymmetry;understand an angle as a measure of rotation by

What polygons can you see around the classroom?What are the properties of polygons?How are these shapes similar/different?What do these shapes have in common?How could we sort these?What rule have we used to sort these shapes?Can you find two identical shapes?What makes them identical?When will our knowledge of shapes be useful?What happens if we flip the shape? Is it still congruent?




comparing and describing rotations: whole turns,half turn, quarter turn to north, south, east andwest on a compass;Discuss half way between N and E, N and W, S andW, and S and E. (NE, NW, SW, SE)locate features on a grid using coordinates.Model 3-D shapes.Discuss 3-D vocabulary (edge, parallel, vertex,faceIntroduce features of circles (centre, radius,circumference, diameter)

-

What happens when we combine 2D shapes?What happens when we stretch the sides of a shape?What happens when we change the angles on a 2-Dshape?What names do mathematicians give to these newshapes?Where in the design do we see a flip (reflection), turn(rotation) slide (translation)?Do all quadrilaterals tessellate? Why?What is an axis of symmetry?How does it help us define if things are symmetrical?What happens if you place the edge of a shape againstthe edge of a mirror?What happens if we move the mirror further away?Which of these shapes do you think you could fold so thatthe two sections match up?How can we measure the size o f a turn that we make?If we turn from north to south, how much of a turn do wemake?How do mathematicians describe this?How can we describe the position of something?

Grade 4 Use the geometric vocabulary of 2-D and 3-Dshapes: parallel, edge, vertex, congruent.Understand and use the vocabulary of lines, raysand segments: parallel, perpendicular;Understand and use the vocabulary of types o fangles: obtuse, acute, straight, reflex, right;Understand and use geometric vocabulary for circles: diameter, radius, circumference, chord,arc;Classify, sort and label all types of triangles andquadrilaterals: scalene, isosceles, equilateral, rightangled, rhombus, trapezium, parallelogram, kite,square, rectangle;Describe, classify and model 3-D shapes;Turn a 2-D net into a 3-D shape and vice versa;Find and use scale (ratios) to enlarge and reduce

What happens when we change the angles on a 2-Dshape?What names do mathematicians give to these newshapes?Where in the design do we see a flip (reflection), turn(rotation) slide (translation)?Do all quadrilaterals tessellate? Why?What is an axis of symmetry?How does it help us define if things are symmetrical?What happens if you place the edge of a shape againstthe edge of a mirror?What happens if we move the mirror further away?Which of these shapes do you think you could fold so thatthe two sections match up?How can we measure the size o f a turn that we make?If we turn from north to south, how much of a turn do we




shapes;Use the language and compass points to describeposition;Read and plot coordinates in one quadrant.

make?How do mathematicians describe this?How can we describe the position of something?What features to 2-D shapes have in common?What features to 3-D shapes have in common?What is an edge?What is a vertex?What are lines, rays and segments?When are two lines parallel?Where do you find parallel lines?What words to mathematicians use to describe thedifferent types of angles?How are these angles connect to one another?Where can we find examples of circles in our environment?How does the name relate to the shape?What does 3-D mean?Why are 3-D shapes named as they are?Where does the name polyhedral originate?What is a net?How is a net created?What is a scale? What is a ratio?Why would we reduce or enlarge a shape?How is scale used in real life?How is a ratio interpreted?Why do plans and maps use scale?What is the notation used to describe position?What is a quadrant?In what circumstances can we use coordinates to describeposition or location?

Grade 5 Understand and use geometric vocabulary for circles: diameter, radius, circumference, chord,arc;Classify, sort and label all types of triangles andquadrilaterals: scalene, isosceles, equilateral, right

What features to 2-D shapes have in common?What features to 3-D shapes have in common?What is an edge?What is a vertex?What are lines, rays and segments?




angled, rhombus, trapezium, parallelogram, kite,square, rectangle;Know the features of different triangles andquadrilateralsDescribe, classify and model 3-D shapes;Turn a 2-D net into a 3-D shape and vice versa;Find and use scale (ratios) to enlarge and reduceshapes;Use the language and compass points to describeposition;Read and plot coordinates in four quadrants.Identify, sketch and measure acute, right, obtuseand reflex angels;Use a pair of compasses;Use the language and notation of compass pointsto describe position;

When are two lines parallel?Where do you find parallel lines?What words to mathematicians use to describe thedifferent types of angles?How are these angles connected to one another?Where can we find examples of circles in our environment?How does the name relate to the shape?When is a triangle called a scalene triangle?Why is this shape a rhombus?What does 3-D mean?Why are 3-D shapes named as they are?Where does the name polyhedral originate?What is a net?How is a net created?What is a scale? What is a ratio?Why would we reduce or enlarge a shape?How is scale used in real life?How is a ratio interpreted?Why do plans and maps use scale?What is the notation used to describe position?What is a quadrant?In what circumstances can we use coordinates to describeposition or location?What skills are needed to accurately draw angles?How do you move a protractor to measure an angle?What would happen if you intersected two lines?When, why and how do you use a pair of compasses?How are angles used to describe a compass point?What is the notation used to described position?




Pattern and FunctionTo identify pattern is to begin to understand how mathematics applies to the world in which we live.

The repetitive features of patterns can be identified and described as generalized rules called “functions”.

This builds a foundation for the later study of algebra.

Learning Objectives Teacher notes

Nursery Find and describe simple patterns.Create simple patterns using real objects.

What is a pattern?Can we describe these patterns?Is there another way to describe this pattern?What patterns can we see?What patterns can we make with these?Identify patterns in music. What is the pattern in thispiece of music?

Kindergarten Predict the next step in a pattern.Identify similarities and differences in apattern.Create a rhythm pattern using clappingand stamping feet.

What is a pattern?Can we describe these patterns?Is there another way to describe this pattern?What patterns can we see?What patterns can we make with these?Identify patterns in music. What is the pattern in thispiece of music?Can we make a rhythm using our hands and feet.

Reception Extend different number patterns.Complete patterns filling in missing spaces.Find different patterns on the 100 square.Recognise, describe and extend patternsin numbers: odd, even, skip counting. 2s,5s, 10s.Indentify patterns and rules for addition 4+ 3 = 7, 3 + 4 = 7 (commutative property);Identify patterns and rules for subtraction:

Where do we find patterns?What do you know about patterns?How can patterns help us?In what ways are these patterns similar and/or different?What can go in the missing space?How many different ways can you describe this patter?What patterns do you notice in the numbers youknow?




7 – 3 = 4, 7 – 4 = 3Model, with manipulatives, the relationshipbetween addition and subtraction. 3 + 4 =7,7 – 3 = 4

How are 4 + 3 and 3 + 4 connected?In what ways are 3 + 4 and 4 + 3 the same/different?Why does the sum remain the same even if theaddends appear in a different order?How are 7 - 3 and 7 - 4 connected?In what ways are 7 - 3 and 7 - 4 the same/different?Why is the order o f numbers in subtraction soimportant?What effect does the order of numbers have on thedifference?How are addition and subtraction connected?What do you know about addition that can help youwith subtraction?

Grade 1 Extend different number patternsComplete patterns filling in missing spacesFind different patterns on the 100 squareAnalyse patterns in number systems to 100Model and explain number patternsRecognise, describe and extend patternsin numbers: odd, even, skip counting. 2s,5s, 10sIndentify patterns and rules for addition 4+ 3 = 7, 3 + 4 = 7 (commutative property)Identify patterns and rules for subtraction:7 – 3 = 4, 7 – 4 = 3Model, with manipulatives, the relationshipbetween addition and subtraction. 3 + 4 =7, 7 – 3 = 4

Where do we find patterns?What do you know about patterns?How can patterns help us?In what ways are these patterns similar and/or different?What patterns can you find on the 100 square?What can go in the missing space?How many different ways can you describe thispattern?What patterns do you notice in the numbers youknow?How are 4 + 3 and 3 + 4 connected?In what ways are 3 + 4 and 4 + 3 the same/different?Why does the sum remain the same even if theaddends appear in a different order?How are 7 - 3 and 7 - 4 connected?In what ways are 7 - 3 and 7 - 4 the same/different?Why is the order o f numbers in subtraction soimportant?What effect does the order of numbers have on thedifference?How are addition and subtraction connected?What do you know about addition that can help you




with subtraction?

Grade 2 Analyse patterns in the 1, 2, 5 and 10 timestablesModel and explain number patterns;Identify patterns and rules for multiplicationModel, with manipulatives the relationshipbetween multiplication and addition(repeated addition)Model multiplication as an array;Understand and use number patterns tosolve problems (missing numbers).

What patterns can you in these times tables?What are the features of the pattern?What will be the next items in the pattern?What do you think a growing pattern would look like?How can patterns help use remember our multiplication tables?How are multiplication and division connected?How does the way in which numbers are groupedaffect the product?How are division and subtraction related?Who can we model a multiplication equation?Which products can be represented as squares andwhich as rectangles?What symbols do mathematicians use to representunknown numbers?

Grade 3 Revise patterns for times tablesRevise patterns and rules for multiplicationRevise the relationship betweenmultiplication and addition (repeatedaddition)Identify patterns and rules for divisionModel, with manipulatives, the relationshipbetween division and subtraction(repeated subtraction)Model, with manipulatives the relationshipbetween multiplication and division;Model, with manipulatives, the relationshipbetween division and subtraction(repeated subtraction)Model multiplication as an arrayUnderstand and use number patterns tosolve problems (missing numbers)including use of multiplication and divisionwithin tables.

What will be the next items in the pattern?What do you think a growing pattern would look like?What patterns are in a row of a multiplication table?How can patterns help use remember our multiplication tables?How are multiplication and division connected?How does the way in which numbers are groupedaffect the product?How are division and subtraction related?Who can we model a multiplication equation?Which products can be represented as squares andwhich as rectangles?What symbols do mathematicians use to representunknown numbers?




Grade 4 Identify, extend and create patterns thatidentify changes in terms of two variablese.g. 1,2,4,5,7 (i.e. +1, +2)Investigate where number patterns canbe found in real-life situations e.g.Fibonnacci sequencesUse real-life problems to creat a number pattern following a rule;Introduce the relationship betweenmultiplication and division. (inversefunction/operation)Model exponents as repeatedmultiplication.

What is the relationship between the numbers?How can you explain what the next number in thispattern will be?How can an array relate to a function?How can functions help us to describe real-lifeproblems?What patterns and relationships are there?How are multiplication and division related?What is an exponent?How does an exponent relate to a given digit?How does an exponent relate to repeatedmultiplication?

Grade 5 Model and explain number andgeometric patterns;Use real-life problems to create a number pattern following a rule;Model simple algebraic formulas in morecomplex equations: x + 1 = y where y isany even whole number;Understand and use the order ofoperations (BODMAS)Model squared and cubed numbers usingconcrete materials.

How can functions help us to describe real-lifeproblems?What patterns and relationships are there?How is multiplication repeated addition?How do we determine a missing quantity?What relationships can we see between algebraicformulas and the four processes?BODMAS = Brackets, Of/exponents (Of= multiplication),Division, Multiplication, Addition and Subtraction.




Number

Our number system isa language fordescribing quantitiesand the relationshipsbetween quantities.For example, thevalue attributed to adigit depends on itsplace within a basesystem.Numbers are used to

interpret information,make decisions andsolve problems.For example, theoperations ofaddition, subtraction,multiplication anddivisionare related to oneanother and are usedto processinformation in orderto solveproblems. Thedegree of precisionneeded incalculating dependson how the result willbe used.

Phase 1 Phase 2 Phase 3 Phase 4Nursery &Kindergarten

Reception & Grade 1 Grade 2 &Grade 3

Grade 4 &Grade 5

Learners willunderstand thatnumbers are usedfor many differentpurposes in the realworld. They willdevelop anunderstanding ofone-to-onecorrespondence

and conservation ofnumber, and beable to count anduse number wordsand numerals torepresent quantities.

Learners will develop their understanding of the base10 place value system andwill model, read, write,estimate, compare andorder numbers tohundreds or beyond. Theywill have automatic recallof addition andsubtraction facts and be

able to model additionand subtraction of wholenumbers using theappropriate mathematicallanguage to describe their mental and writtenstrategies. Learners willhave an understanding offractions asrepresentations of whole-part relationships and willbe able to model fractions

and use fraction names inreal-life situations.

Learners will develop theunderstanding that fractionsand decimals are ways ofrepresenting whole-partrelationships and willdemonstrate thisunderstanding by modelingequivalent fractions anddecimal fractions tohundredths or beyond. They

will be able to model, read,write, compare and order fractions, and use them inreal-life situations. Learnerswill have automatic recall ofaddition, subtraction,multiplication and divisionfacts. They will select, useand describe a range ofstrategies to solve problemsinvolving addition,subtraction, multiplication

and division, using estimationstrategies to check thereasonableness of their answers.

Learners will understand that thebase 10 place value systemextends infinitely in two directionsand will be able to model,compare, read, write and order numbers to millions or beyond, aswell as model integers.They will develop anunderstanding of ratios. They willunderstand that fractions,

decimals and percentages areways of representing whole-partrelationships and will work towards modeling, comparing,reading, writing, ordering andconverting fractions, decimalsand percentages. They will usemental and written strategies tosolve problems involving wholenumbers, fractions and decimalsin real-life situations, using arange of strategies to evaluate

reasonableness of answers.




Number Our number system is a language for describing quantities and the relationships between quantities. For example, thevalue attributed to a digit depends on its place within a base system.

Numbers are used to interpret information, make decisions and solve problems.

For example, the operations of addition, subtraction, multiplication and division are related to one another and are usedto process information in order to solve problems. The degree of precision needed in calculating depends on how theresult will be used.


Nursery Know the language and meaning of numbers 0to 5Count reliably from 0 to 10Order and recognise numbers from 0 to 5Use 1:1 correspondence for numbers 1 to 5 intheir daily activities and routinesDevelop a sense of size and amount byobserving, exploring and discussingExplore counting and ordering numbers to 10

What number names do we know?Where do we find numbers?How can we find out how many things are here?What number comes next?What was the number before that?Do we have enough plates/crayons/ balls?How can we be sure we have enoughplates/crayons/balls?

Kindergarten Order and write numbers 0 to 10Count reliably from 0 to 20Use 1:1 correspondence for numbers 1 to 10 intheir daily activities and routinesUnderstand that numbers represent quantitiesand use them to count, create sequences anddescribe order (0 to 10)Count forwards to 10 and backwards from 10Explore number relationships to 10 (preparing for addition)Begin to use ordinal numbers for 1 st, 2 nd and last

How can we find out home many things are here?What number comes next?What was the number before this one?What number is 1 less than 5?What number is 1 more than 6?How do we know if we have enough cups andplates?How many people are there?How many shoes are there?Who is the first in line?Who wants to be second in line?Where shall I go….. last?




Reception Count reliably from 0 to 100Order and write numbers 0 to 20Use 1:1 correspondence for numbers 1 to 20 intheir daily activities and routinesUnderstand that numbers represent quantitiesand use them to count, create sequences anddescribe order (0 to 10)Count reliably forwards and backwards to 20Read, write and model addition to 10 using avariety of manipulativesWrite addition number sentences to 10Memorise number bonds to 10Read, write and model subtraction of numbersfrom 10 using a variety of manipulatives (explorewriting subtraction number sentences) Count in multiples of 10 and 5 to 100

What number comes after 81?What number comes before100?Do you think we have enough blocks? How do youknow?I have 3 apples and Sam gives me 4 applies howmany do I have altogether?Lets use the blocks to illustrate the story?I have 4 blocks. I need 10 blocks. How many must Iadd to my collection?I had 10 sweets. I ate 3. How many do I have left?How would we write this story in a number sentence?Show me what this number sentence means?

Grade 1 Recognise numbers (numerals) to 100Compare and order numbers to 100 (using <,> tocompare) Write numbers in words to 10 (explore to 20) Count forwards in 1s, 5s and 10s to 100Count forwards to 20 and backwards from 20 insteps of 2.Count forwards in steps of 1 and 10 from randomnumbers to 100 Count using ordinal numbers from 1 st to 31 st (calendar)Identify even and odd numbersWrite addition number sentences to 20Memorise number bonds to 20Write subtraction number sentences, takingaway amounts from 20Model and explore different strategies for solvingan addition or subtraction problem with amounts

Is 87 greater than or smaller than 76?Why do you say it is greater?If I count 20, 18, 16, 14 …. What number comes next?You continue.Starting at 73… count to 100. What day of the month were you born?Who is third in line? Who is seventh?When is a number even?When is a number odd?What patterns do you notice between even and oddnumbers on the 100 chart?I had 20 balls. I lost 5 in the woods. How many do Ihave left? Write a number sentence to show this story.Write a number sentence to show twenty take away7. What is the answer? What is left.What do you think would be the best way to solve

this problem?Do we need to add or subtract?




up to 20 (explore to 30) Use mathematical vocabulary and symbols for addition, subtraction and equalsRecognise that the position of a digit gives itsvalue and state place value of any digit in a 2digit number Estimate quantities to 100Introduce fraction names for a half

(explore )

What does the sentence equal?In the number 14 what does the 1 represent or mean?And the 4?Why is it important to know the different placevalues?What does estimate mean?Why is it important to estimate?Here is a pizza. Share it with your friends. You musthave the same amount of pizza each. How are yougoing to divide the whole pizza?

Grade 2 Count, compare and order numbers to 999Read and write numbers (numerals) up to 999Write numbers in words from 0 to 20, multiples of10 to 100 and multiples of 100 to 900Round numbers to the nearest multiple of 10 and100Count forwards and backwards in intervals of 1,2, 5, 10 and 100 (explore counting in other

intervals) Know number bonds to 10, 20 and 100 mentally(quick recall)Use arrays to explore multiplication factsUse and understand x symbol and appropriatevocabulary for multiplication(multiplication, multiply, groups of, lots of, times,product)Know 0, 1, 2, 5 and 10 times tables until 12 xExplore 3 digit numbers using manipulativesRecognise that the position of a digit gives itsvalue and state place value of any digit in a 3

digit number Use empty number lines to add TU + TU and HTU+ TU, by counting onUse an empty number line for subtractionTU – TU and HTU – TU, by finding the differenceEstimate quantities to 1000

How many units do we have in this number?How many tens do we have in this number?How many units to we have in this number?Where is the nearest multiple of ten to this number?Where is the nearest hundred to this number?If we add 3 + 3, how many groups of 3 do we have?Make two groups of three. How many blocks do wehave?

We have two groups of three, have we doubled thenumber 3?Look at the multiples of 2, what pattern do you see?What do you estimate the answer of 2 x 4 will be?How did you decide on that estimate?If I start at 63 and add on 15, where will I end up?On this number lines what is the difference between57 and 65?Use the 100 square grid to answer questions? Start at15 and add 10… where do you end up? Where is thisin relation to where you started? (1 row up)Use the 100 square grid to answer questions? Start at

35 and subtract 10… where do you end up ? Where isthis in relation to where you started? (1 row down)

Two people want to share a pizza equally. Whatfraction of the pizza will each person get?Will anyone get the whole pizza? What will they get of




Revisit a half and as a portion of a whole

Introduce thirds ( and )Compare halves, thirds and quarters usingmanipulativesIntroduce equivalent fractions visually(include = and 1 whole = = = )

Introduce mathematical vocabulary of fraction,numerator, denominator, equivalent and wholenumber Model addition of fractions with the samedenominator using manipulatives (pizza slices,Cuisenaire rods) and on board

+ =

the pizza? (part of the whole)How many halves make a whole?How many quarters make a whole?How many quarters make a half?What if three people wanted to share the pizza andeach have the same amount?What would we call each piece?How many thirds make a whole?If we divide the pizza into quarters and you eat onequarter and I eat two quarters how much of the pizzahave we eaten? Have we eaten the whole pizza?Is there any left?

Grade 3 Count, compare and order numbers to 9999Read and write numbers (numerals) up to 9999Write numbers in words from 0 to 100, multiples of100 to 1000

Round numbers to the nearest multiple of 10, 100and 1000Count forwards and backwards in intervals of 2,3, 4, 5, 6, 7, 8, 9, 10 and multiples of 10 (revisefrom 0 and introduce counting in intervals of 2, 3,4, 5 and 6 from random numbers) Revise number bonds to 20, 50 and 100 mentally(quick recall)Use arrays to explore multiplication factsKnow all times tables until 12 x 12Multiply and divide by single digit numbersExplore 4 digit numbers using manipulatives

Recognise that the position of a digit gives itsvalue and state place value of any digit in a 4digit number (explore to 5 digit) Use empty number lines to add TU + TU, HTU + TUand HTU + HTU, by counting onUse an empty number line for subtraction

Put these numbers into order from smallest to biggest.Put these numbers into order from biggest to smallest.What is the nearest 10 / 100 / 1000 to this number?Why is 875 rounded to 900 and not 800?

Why is 875 rounded to 880 and not 870?What patterns do you notice in the times tables?Are any tables repeated? Which ones? ( e.g. 7 x 8and 8 x 7)In the number 769 what is the tens digit / hundredsdigit / units digit?Look at the fractions one fifth, one tenth, one sixth,one twelfth and one eighth. What do you noticeabout the size of each fraction in relation to thedenominators? (The larger the denominator thesmaller the size of the fraction.)What is + ?

Is this fraction equivalent to any other fraction?




TU – TU, HTU – TU, HTU - HTU by finding thedifferenceEstimate quantities to 1000Revise , , and as a portions of a whole

Revise equivalent fractions ( = and 1 whole =

= = )

Introduce , , , and

Model addition and subtraction of fractions withthe same denominator

Grade 4 Continuous practice of times tables to 12 x 12Know number facts (doubles, halves, number bonds) to 1000Introduce decimals to hundredthsLink decimals with fractions (part of a whole)Understand place value from thousands tothousandthsUnderstand inverse operations

Add and subtract four digit numbers (extend to 5digits)Multiply and divide by two digit numbersMultiply and divide by 10s and 100sRead, write and model fractions and mixednumbersRead, write and model addition and subtractionof fractions with related denominatorsCompare and order fractions and decimalsSimplify common fractions ( = ) for half, quarter and three quartersDiscuss language of fractions

Round decimals to nearest whole number / tenthInvestigate where decimals are usedAdd and subtract decimals to hundredths usingmental and written strategiesMultiply and divide a decimal by a wholenumber

We can write fractions as a decimal. E.g. 1.65 m is myheight? Have you seen this type of number before?Where have you see it? Why do we use decimals?(Illicit everyday examples e.g. height, measuringthings, money, mass)After the decimal point we have tenths andhundredths. How many tenths do you think make onewhole? How many hundredths do you think make

one whole?What is the inverse operation of addition /subtraction?What is the inverse operation o f multiplication /division?Arrange these fractions / decimals in ascending /descending order.What is a mixed number?How many quarters are there in 5 ?

Multiply this decimal by 10. What happens to thedecimal point?When adding, subtracting and dividing decimals the

decimal point remains in the same position.When multiplying decimals, remove the point, multiplyas usual and replace the point so that there are thecombined number of places after the point e.g. 1.5 x5 = 7.5 or 2.45 x 1.5 =3.675What happens to the numerator and the




Introduce percent and percentagesRead, write and model multiples of 2, 5 and 10 aspercentages e.g. 25%, 40% 60%Interchange fractions, percentages anddecimals for whole, half, quarter, fifth, threequarters and tenthsSolve world problems using knowledge learnt.

denominator when you simplify fractionsWhen do we use percentages?Why is it useful to use percentages?

Grade 5 Automatic recall of times tables to 12 x 12Practise recall of number facts to 1000State place value of any digit in a seven digitnumber State place value of any digit up to 3 decimalplacesMentally divide two digit numbers by one digitdivisorsKnow mathematical vocabulary for four basicoperations: sum, add, subtract, difference,multiply, product, divide, quotient, divisor Add and subtract 3 digit numbers using standardalgorithmsMultiply and three digit number by two digitnumber using standard algorithmsDivide four digit number by two digit divisor usingstandard long division algorithmUnderstand factors and multiples and how tofind themExplore sevenths, eighths and ninthsIntroduce Lowest Common Multiple, HighestCommon Factor,Introduce Lowest Common Denominator andlink to LCM.Simplify fractions and improper fractionsAdd and subtract fractions with differentdenominatorsAdd and subtract simple mixed numbersRound decimals to a given place or wholenumber

What are the place values for a seven digit number?What are the place values for three decimal places?Look at the number 7 465 357. What does the 6represent? How many thousands are there?Look at 7.243. Which digit represents hundredths /thousandths / tenths?Divide 75 by 5 in your head. What strategy did youuse?How is your strategy different to others?Does their strategy seem easier? Why?Which would you rather use?What is the difference between a multiple and afactor of a number?How any factors does a number have?What is the Lowest Common Multiple (LCM) of 6, 12and 24?Is the number a factor of itself?How do we know this?What multiplied by the number equals the number itself?What is the Highest Common Factor (HCF) of 8, 24and 36?What is a mixed number?What is the relationship between mixed numbers andimproper fractions?What must we remember when we add / subtractdecimals?The Maths test was out of 50. I got 75%. How manymarks out of 50 did I get?What does mean?




Accurately read, write and apply addition andsubtraction of decimals to the thousandthsInterchange between fractions, decimals andpercentagesFind common percentages of whole numbers(10%, 20%, 25%, 50%, 75%)Introduce exponents (squared, cubed, to thepower of)Introduce integers. Use number line with 0 incentreUse temperature gauge to illustrate integersIntroduce order of operations: BEDMASIntroduce equations. Finding unknown number ( x, n) Solve simple equations n + 15 = 25Identify that 4n = 4 x nSolve word problems using knowledge.

What do we call the 3 / what do we call the 2.?How do we read ?What happens to the left o f 0 on a number line?Where in real life can we find negative numbers?What do they measure?What do you do first to solve this equation? 3 + (4 -1)What is x?How do we find x?




STRATEGIES FOR PENCIL AND PAPER PROCEDURES

Notes:Begin in Grade 1 when appropriate.Children are introduced to next strategy only when they are fully confident with the strategy they are using.Introduce strategies in this order.

ADDITION

56 + 34STRATEGY 1

Counting Up +4 +30 = 90

56 60 90

STRATEGY 2

Partitioning 56 + 34 Add the units first.

56 50 + 6+34 30 + 4

80 + 10 = 90




STRATEGY 3

CompactMethod 56 + 34

Add the unitsfirst

T U15 6

+ 3 49 0




SUBTRACTION

97 - 34STRATEGY 1

Counting Up +6 +50 +7 = 63

34 40 90 97

STRATEGY 2Example (a)

Partitioning 97 - 34 (Units first)

97 90 (+) 7

-34 - 30 (+) 4

60 (+) 3 = 63Example (b)

392 - 173

392 300 + 90 + 2-173 100 + 70 + 3

300 + 80 + 12100 + 70 + 3200 + 10 + 9 = 219




STRATEGY 3 Example (a)

CompactMethod 97 - 34 (Units first)

T U

9 7

- 3 46 3

Example (b)

392 - 173

H T U8 12

3 9 2

- 1 7 32 1 9




Example (b)35 x 15

H T U

3 5 x 1 51 2 5 ( 5 x 5 )1 5 0 (30 x 5)

5 0 (5 x 10)+ 3 0 0 (30 x 10)

5 2 5




STRATEGY 3 Example (a)

CompactMethod 35 x 15 (Units first)

H T U+2

3 5

x 1 51 7 5

+ 3 5 0

5 2 5




DIVISION

Example (a)STRATEGY 1

75 ÷ 5

Partitioning T U1 5

5 7 5- 5 0 5 X 10

2 5- 2 5 5 X 5

- - 15

STRATEGY 2Example (a) 256 ÷ 7

Compact H T U

Method - 3 6 r 4Expanded 7 2 5 6

- 2 1

4 6- 4 2

- 4




STRATEGY 3 Example (a)256 ÷ 7

CompactMethod H T U

3 6 r 4

7 2 5 6




1 Margin on left of page. (One large block, 2 smaller blocks) All calculations to have place value heading written.

11

T UH T U

(Number of problem to be written in the margin.) Leave at least two block next to the margin before

writing T, U or H, T, U to allow space for operation sign and

2 Date and Heading to be written and underlined. possibility of next place value column.

3 Margin on the right for working out. (3 blocks) Leave a line under T,U and H, T, U before writing first

number

1...

T UH T U

... 3 7 1

5 4

LAYOUT OF MATHEMATICS FOR PEN AND PAPER PROCEDURES




7 One digit per block (as above)

8 Operation sign must be written just to left of T, U or H, T, H

column in line with last number.

T UH T U

13 7 1

+ 4 5 3

5 48 2 4

+ 5

5 9

9 All lines to be ruled with a ruler. Note two lines to be ruled for the answer.

math curriculum sept 2011

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