mathematics - mathematics subject group overview · 2019-12-17 · mathematics (myp 1) unit title...

Mathematics (MYP 1)Unit Title Key concept Related

concept(s) Global context Statement ofinquiry MYP subject group objective(s) ATL skills Content (topics,

knowledge, skills)MYP1 MathsUNIT2: NumberSystems andRules inMathematics

Relationships EquivalenceQuantityRepresentation

Other:Operation

Personal andcultural expression

Rules build alanguage used toestablishrelationshipsamong quantitiesthat arecalculated,obtained orrepresented inequivalent ways.

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsii. apply the selected mathematicssuccessfully when solvingproblemsiii. solve problems correctly in avariety of contexts

B: Investigating patternsi. apply mathematical problem-solving techniques to recognizepatternsii. describe patterns asrelationships or general rulesconsistent with correct findingsiii. verify whether the patternworks for other examples

C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten statementsii. use different forms ofmathematical representation topresent informationiii. communicate coherentmathematical lines of reasoningiv. organize information using alogical structure

CommunicationI. Communication skills

ThinkingVIII. Critical thinking skills

Content:The set of natural numbers

Significance and propertiesof the sum, subtraction,multiplication and division(with remainder).

Example of applications ofproperties in order toperform mind calculations.

Formulae and identities: howdo we write rules inmathematics? How do wedescribe them?

Difference between aninstance of a general rule (anexample), its symbolicformula, and its generaldescription in words.

The order of operations andits importance.

The definition of power withnon-negative integer baseand exponent.

Properties (laws) or powers(indices).

Example of properties thatdo NOT hold for someoperations and how to provethey don’t apply.

Skills:Arithmetic operations

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Mathematics - MathematicsSubject Group Overview

Deledda International SchoolChiara Colucci on Monday, Dec 16, 2019 at 2:29 PM 1 of 31

AlgorithmsPropertiesPatterns in arithmetics

MYP1 Maths UNITA: Set Theory

Logic Representation Identities andrelationships

The word aroundus can berepresented withthe use of asymbolicLanguage throughthe concept of set.Observations anddeductions on theexternal word canbe obtainedlogically startingfrom some basicprinciples. This willsharpen theperception aboutourselves andOthers and ouridentity.


C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten statementsiii. communicate coherentmathematical lines of reasoningiv. organize information using alogical structure


Skills:Sets and Their Elements;

Subsets;

The Intesection of Sets;

The Union of Sets;

Venn Diagrams

MYP1 MathsUNIT3: Tutti d'unpezzo! (or maybenot)

Form PatternRepresentation

Scientific andtechnicalinnovation

Certaincharacteristics ofNumbers do notdepend on theForm in which werepresent them.

A: Knowing and understandingiii. solve problems correctly in avariety of contexts


C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten statementsiii. communicate coherentmathematical lines of reasoningiv. organize information using alogical structure


Content:Divisibility Tests

Factors, Prime Factors

Prime and CompositeNumbers

Multiples of natural numbers

Highest common factor(HCF)

Lowest common multiple(lcm)

Skills:Use of different Divisibilitytests on Natural Numbers

Find HCF using divisibility

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test and prime factors

Find lcm using divisibilitytest and prime factors

Represent number indifferent forms

MYP1 Maths UNITB: Orienteering

Relationships Space

Individuals andsocieties:Geography:Scale

Orientation inspace and time

Scalerepresentation andunits ofmeasurementgave mankind alanguage todescribe time andspace.



C: Communicatingi. communicate information andideas with clarityii. organize information and ideaseffectively for the taskiii. list sources of information in away that follows the taskinstructions.

Self-managementIV. Affective skills

Skills:(Maths & Geo) ReadingScales;

(Maths & Geo) ScaleDiagrams;

(Maths) Time Lines;

(Maths) Units of Time;

(Maths) Time Calculations;

(Maths) Timetables;

(Maths & Geo) MapReferences;

(Maths & Geo) FindingPoints;

(Maths & Geo) Coordinates;

(Maths & Geo) Direction.

MYP1 MathsUNIT4: BeRational!

Relationships EquivalenceQuantity


Fractions are asimple way torepresent non-integer Quantities.


Self-managementIII. Organization skills



Skills:Fractions;

Fractions as Divisions;

Fractions of Quantities;

Fractions on a Number Line;

Equal Fractions;

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Comparing Fractions;

Adding and SubtractingFractions;

Multiplying and DividingFractions.

Converting BetweenDecimals and Fractions.

MYP1 Maths UNITC: Statistics

Relationships Representation

Sciences:Patterns


Studying the basicelements ofStatistics, we areable to betterunderstand andinterpret our world

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsii. apply the selected mathematicssuccessfully when solvingproblemsiii. solve problems correctly in avariety of contextsiii. interpret information to makescientifically supportedjudgments.

D: Applying mathematics in real-life contexts

i. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solutioniv. explain the degree of accuracyof a solutionv. describe whether a solutionmakes sense in the context of theauthentic real-life situation

Content:Samples and Populations

Categorical Data

Graphs of Categorical Data

Numerical Data

Mean or Average

Mode and Median

MYP1 Maths UNIT5: Paper andPencil

Form RepresentationSpace

Design:Form



Architecture andDesign are directapplications ofMathematics in areal life situation.

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsii. apply the selected mathematicssuccessfully when solvingproblems



Self-management

Skills:(Maths & Design) Points andLines;

(Maths) Angles (Angles at aPoint or on a Line);

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Globalization andsustainability

iii. solve problems correctly in avariety of contextsi. demonstrate awareness of theart form studied, including the useof appropriate language


C: Creating the solutionii. demonstrate excellent technicalskills when making the solution

III. Organization skills (Maths) Vertically OppositeAngles;

(Maths & Design) BisectingAngles;

(Maths & Design) Polygons;

(Maths) Triangles;

(Maths) Quadrilaterals;

(Design) Visual Language;

(Design) Tools Usage

(Visual Arts) image analysis

(visual Arts) geometricalreproduction



knowledge, skills)MYP2 Maths UNIT1: Integer, Powerand Roots!

Form QuantityRepresentation


Being able torepresent differentforms of quantitieshas helpedhumans exploreand describe ourplanet



i. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solutioniv. explain the degree of accuracyof a solution


ThinkingX. Transfer skills

Content:POSITIVE AND NEGATIVENUMBERS: Integer

- Opposites

- Adding and subtractingnegatives

- Multiplying and dividingnegatives

- Combined operations

POWERS AND ROOTS:

- Powers, Logaritms andRoots

- How to find the square rootof a number by hand

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v. explain whether a solutionmakes sense in the context of theauthentic real-life situation

- Roots as fractional powers

- Properties of roots

- Operation with roots

- Negative powers

Skills:Performing the operation ofmultiplication, division,addition and subtractionwith integer

Performing the operation ofmultiplication, division,addition and subtractionwith powers and roots

Applying mathematicalstrategies to solve problemsinvolving integers

Defining, comparing andordering integers

MYP2 Maths UNIT2: Be Rational

Relationships EquivalenceRepresentation


The discovery ofdifferent butequivalentrepresentations ofrational numbercan leads to abetterunderstanding ofrelationshipbetween differentAreas ofMathematics.


B: Investigating patternsi. select and apply mathematicalproblem-solving techniques todiscover complex patternsii. describe patterns asrelationships and/or general rulesconsistent with findingsiii. verify and justify relationshipsand/or general rules

C: Communicating


SocialII. Collaboration skills

Content:- Place Value (review)

- Converting betweendecimals and fractions

- Rounding decimalnumbers

- Placing decimal numberson a number line

- Comparing decimalnumbers

- Adding and Subtractingdecimal numbers

- Multiplying and dividing by

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i. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsii. use appropriate forms ofmathematical representation topresent informationiii. move between different formsof mathematical representationiv. communicate complete andcoherent mathematical lines ofreasoningv. organize information using alogical structure

powers of 10

- Multiplying anddividing decimal numbers

- Understandingpercentages

- Relationship betweenpercentages, fractions anddecimal numbers

- Interchanging number form

Skills:Interpreting ratios torepresent relations betweenquantities

Transforming fractions topercentages and decimals

Interpreting ratios torepresent relations betweenquantities

Percentages Relationships QuantityRepresentation


The use ofpercentages astool to investigatethe distribution ofnatural resourceson Earth and howthese are locatedthrough thepopulations canbe useful torepresent andcommunicaterelationshipsamong quantities.



i. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selected

ResearchVI. Information literacy skills

Content:- Understandingpercentages

- The definition ofPercentage

- One quantity as apercentage of another

- Finding a percentage of aquantity

- Percentage increase ordecrease

- Finding a percentage

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mathematical strategiessuccessfully to reach a solutioniv. explain the degree of accuracyof a solutionv. explain whether a solutionmakes sense in the context of theauthentic real-life situation

change

- Relationship betweenpercentages, fractions anddecimal numbers

- Interchanging number form

- Graphical representation ofpercentages

- Real-life applications ofpercentages (statistics)

Skills:Interpreting ratios torepresent relations betweenquantities

Transforming fractions topercentages and decimals

Real-life applications ofpercentages (statistics)

Graphical representation ofpercentages

The use of the threelanguages in differentcontexts

Mathematicallanguage andrepresentation

Form EquivalenceSimplification


Producingequivalent formsthroughsimplification canhelp to explainand solve puzzles


C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral and


Content:Elements of Algebraiclanguage

Patterns and Models inAlgebra

Letters to representvariables, parameters and/orunknown objects.

Skills:

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written explanationsii. use appropriate forms ofmathematical representation topresent informationiii. move between different formsof mathematical representationiv. communicate complete andcoherent mathematical lines ofreasoningv. organize information using alogical structure

Use of letters to representvariables, parameters and/orunknown objects.

Use of letters (as variables /parameters / unknown) towrite general statements inAlgebraic language

Transformations betweenalgebraic representations

Interpretation of differentalgebraic representations

writing and simplifyingalgebraic expression

MYP2 Maths UNIT5: Pythagoras'sScribbles

Logic MeasurementSpace


Pythagoras'stheorem is theproof that logicalreasoning can giveus higherunderstanding ofmeasurement ofthe Natural spacearound us.



ThinkingX. Transfer skills

Content:POLYGONS:

- Quadrilaterals

- Angles of a quadrilateral

- Areas of polygons

- Areas of composite figures

PYTHAGORAS'STHEOREM:

- Pythagoras Theorem

- Euclid's Theorems

Skills:Find the perimeter and areaof different 2-dimensionalshapes

Solving problems with2-dimensional shapes

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MYP2 UNIT 6:Mathematics:Statistics

Communities ModelRepresentation

Identities andrelationships

Communities canbe representedthroughmathematicalmodelling able todescribe theirlifestyle.

C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsii. use appropriate forms ofmathematical representation topresent informationiii. move between different formsof mathematical representationiv. communicate complete andcoherent mathematical lines ofreasoningv. organize information using alogical structure


Content:Numerical DataMean or Average

Mode and Median

Frequency Tables andDiagram

Data Collection

Dependent and IndependentVariables

Skills:Be able to recognizedependent an Independentvariables and report them ona frequency FrequencyDiagram

Calculate Mean Mode andMedian of Collected data

Collect Data

excel



knowledge, skills)MYP 3. Unit 1:Arithmetic

Form ChangeQuantity


Values ofquantities can bechanged from oneform to another,allowing one todescribe systemsin moreconvenient andintuitive ways.



i. identify relevant elements ofauthentic real-life situations


Content:sets of numbersoperations with fractionsand BEDMASproperties of powers androotsscientific notation and metricmultipliers

Skills:understanding thedifferences between natural,

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ii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solutioniv. explain the degree of accuracyof a solutionv. explain whether a solutionmakes sense in the context of theauthentic real-life situation

integer, rational andirrational numbers

converting between differentrepresentations of numbers

performing calculationsinvolving big and smallnumbers without calculator

estimations based on realdata

MYP3 - Unit a -2DGeometry: circles

Form MeasurementRepresentation


The form of acircle isrepresented aspoligon with aninfinite number ofsides and pi hasbeen invented torepresent themeasure of acircunferencebased on itsdiameter.Irrationality of pi:it's not a fraction!better toapproximate orcalculate exactly,using calculators?



i. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solutioniv. explain the degree of accuracyof a solutionv. explain whether a solutionmakes sense in the context of theauthentic real-life situation



Content:definition of radiuslenght of a circumnferencepiarea of a circlearc lenghtarea of a sector

Skills:being able to draw a circlegiven the diameter

measuring the amplitude ofan angle using the protractor

MYP3. Unit 2:Algebra, equationsand functions

Relationships GeneralizationModel


Models framespecific problemsinto the generalbroad picture, thusallowing one tounderstandrelationships andpredict the

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsii. apply the selected mathematicssuccessfully when solvingproblemsiii. solve problems correctly in a

Self-managementV. Reflection skills


Content:monomials and polynomialslinear equationssystems of linear equationsand pure quadraticequationsfunctions

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evolution ofsystems.

variety of contextsB: Investigating patterns

i. select and apply mathematicalproblem-solving techniques todiscover complex patternsii. describe patterns asrelationships and/or general rulesconsistent with findingsiii. verify and justify relationshipsand/or general rules

C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsii. use appropriate forms ofmathematical representation topresent informationiii. move between different formsof mathematical representationiv. communicate complete andcoherent mathematical lines ofreasoningv. organize information using alogical structure



Skills:Understanding the power ofcreating models usingvariables instead of numbers

Moving between differentform of representation usingalgebra

Translating real-life problemsinto mathematical problems

Solving real-life problems

Understanding the relationbetween variables

Predicting the evolution ofthe dependent variableknowing its functional form

Myp3 unit b:coordinates

Relationships ModelRepresentation


Relationshipbetween valuesand exactpositions of pointsallows to represent

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsii. apply the selected mathematics

Self-managementIII. Organization skills

Content:Cartesian coordinatesDistance Between TwoPointsFormulae for the areas of

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in a graphgeometricalshapes and tocommunicatepositions in orderto be oriented inspace andrepresent naturaland humanlandscape

successfully when solvingproblemsiii. solve problems correctly in avariety of contexts



triangles and quadrilaterals.Midpoint of a segmentEquation of a Straight Line

Skills:Students will be able to usecontent in order model andunderstand problems

Setting up equations tomodel a problem, thensolving them with algebraictechniquesBeing ableto decompose complicatedshapes into simple ones.Being able to reflect on theproperties of right triangles(Pythagoras' theoremmostly)Understand how to drawhow to draw the graph of aline, find some points, checkif the line passes through agiven point, and interpretgeometrically the slope andthe cutoff.

Myp3 Unit c: solidshapes

Relationships GeneralizationMeasurement


Generalizingrelationshipsbetweenmeasurement canhelp analyze andgenerate products,process andsolutions


C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsii. use appropriate forms ofmathematical representation topresent information


Content:Three-dimensional shapes,surface area and volume:

Cube

Rectangular Solids orCuboids

Prism

Pyramid

Cylinder

Cone

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iii. move between different formsof mathematical representationiv. communicate complete andcoherent mathematical lines ofreasoningv. organize information using alogical structure

Sphere

Composite shapes

MYP 3. Unit 3:Probability

Logic ModelPattern


The analysis ofpatterns in datacan drive decisionmaking towardslogical solutions.





Content:Experimental VS theoreticalprobabilityIndependent VS dependenteventsCalculating probability ofcombined eventsUsing diagrams and chartsto model and understandprobabilityStatistics: measure of centerand spread, graphs andcharts

Skills:Understand whether twoevents are dependent orindependent according tothe specific situation.

Using probability to modelreal-life situations

Interpreting charts and treediagrams

Using differentrepresentations to performstatistical analysis



knowledge, skills)MYP 4. Unit 1:Arithmetics andAlgebra

Form GeneralizationModel


The process ofabstraction givesform to modelswhich generalize a

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situations

Self-managementIII. Organization skillsV. Reflection skills

Content:review of sets of numbersand properties of powersInteger and rational indexes

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variety ofsituations.

ii. apply the selected mathematicssuccessfully when solvingproblemsiii. solve problems correctly in avariety of contexts

B: Investigating patternsi. select and apply mathematicalproblem-solving techniques todiscover complex patternsii. describe patterns as generalrules consistent with findingsiii. prove, or verify and justify,general rules


i. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solutioniv. justify the degree of accuracy ofa solutionv. justify whether a solution makessense in the context of theauthentic real-life situation

radicals and surds(Extended: proof that squareroot of 2 is irrational)revision monomials andpolynomialsexpansion lawsfactorization of polynomials(Extended: Ruffini's theorem)algebraic fractionsrearranging formulae

Skills:being able to classifynumbers

understanding theconnection between powersand radicals

proving statements right orwrong

using algebra to providegeneral models

using formulae to predictresults

MYP 4. Unit 2:Relations andfunctions

Relationships EquivalenceModel


Exploring andunderstanding therelationshipsbetween quantitiesmay predict futureevolution ofdifferent systems.

C: Communicatingi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsii. use appropriate forms ofmathematical representation topresent informationiii. move between different formsof mathematical representationiv. communicate complete,coherent and concisemathematical lines of reasoningv. organize information using alogical structure



Content:Cartesian product of twosetsRelations between quantitiesand their representationsDomain and range ofrelationsFrom relations to functionsFunction notationComposite functionsInverse functionSpecial functions: constant,direct, linear, quadratic andinverse proportionality

Skills:

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Identifying dependent andindependent variables

Moving between differentforms of representations andmathematical notations

Being able to select and usesoftware to analyse data

Representing and solvingreal-life problems withfunctions

Predicting the evolution ofsystems using functions

MYP 4. Unit 3:Geometry

Logic ModelRepresentation


Efficienttheoretical modelsrepresent theproblem andorganize theprocess to reach asolution in a logicand rigorous way.



C: Communicatingii. use appropriate forms ofmathematical representation topresent informationiv. communicate complete,coherent and concisemathematical lines of reasoningv. organize information using alogical structure


ThinkingIX. Creative thinking skills

Content:knowledge of the 2Dcoordinate systemdistance between two pointsmidpoint, gradient, interceptequation of a lineparallel and perpendicularlinesdistance between a pointand a lineVectors: definition,properties and operations.

Skills:Being able to model real-lifephenomena with equationsof lines and to representthem graphically

Familiarizing with online andoffline graphic calculators(Geogebra, GDC)

Exploting coordinategeometry to investigate real-life problems in groups

understanding how straight

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i. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solution

lines can be used torepresent physicalphenomena which aredescribed by linearlydependent variables

MYP 4 IDU Unit:Air Pollution

InterdisciplinaryUnitMathematics

Global interaction ConsequencesEnvironment

Mathematics:MeasurementRepresentation


The impact ofglobalization haslead to increasedconcerns aboutenvironmentalsustainability.Global interactionsamongcommunities canbe analyzed froma statistical pointof view throughmeasurementsand datarepresentation inorder to betterunderstand theconsequences ofdaily life-style onthe environment.

Sciences - SciencesC: Communicating

iii. move between different formsof mathematical representationiv. communicate complete,coherent and concisemathematical lines of reasoningi. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsii. use appropriate forms ofmathematical representation topresent informationv. organize information using alogical structure.


iv. justify the degree of accuracy ofa solutioni. identify relevant elements ofauthentic real-life situationsii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selectedmathematical strategiessuccessfully to reach a solutionv. justify whether a solution makessense in the context of theauthentic real-life situation.

Mathematics - MathematicsA: Knowing and understanding

i. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsii. apply the selected mathematics



Content:Mathematics:

discrete and continuousdatadata representationevaluating centre and errorof a distributioncumulative dataspread and standarddeviationfive-number summary andbox-and-whisker plot

Skills:understanding the differencebetween discrete andcontinuous data and how togroup them whenperforming statisticalanalysis

finding the most effectiveway to graphically representdata

learning how statistics canbe used to extractinformation in differentcontexts

investigating real-lifesituations with statisticalanalysis

learning new tools: from

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successfully when solvingproblemsiii. solve problems correctly in avariety of contexts

online software to GDCcalculator

comparing, evaluating andpredicting using statistics



knowledge, skills)MYP5: Unit 1:Mathematics:Revision of lastyear topics

Communication Equivalence Identities andrelationships

This is not a unit ofwork as it issupposed to beaccording to theMYP philosophy;it's a recordkeeping of therevision workwhich has beendone during thefirst two weeks ofschool. Therewon't be anysummative task,only formativework will takeplace in classduringcollaborativelessons: teacherwith students andstudents withstudents will solveproblems, reflect,ask forclarifications,assessthemeselves

A: Knowing and understandingi. select appropriate mathematicswhen solving problems in bothfamiliar and unfamiliar situationsiii. solve problems correctly in avariety of contexts

algebraB: Investigating patterns

ii. describe patterns as generalrules consistent with findings

use appropriate mathematicalconcepts and skills to solveproblems in both familiar andunfamiliar situations, includingthose in real-life contextsC: Communicating

i. use appropriate mathematicallanguage (notation, symbols andterminology) in both oral andwritten explanationsiii. move between different formsof mathematical representationiv. communicate complete,coherent and concisemathematical lines of reasoning

select and apply general rulescorrectly to make deductions andsolve problems, including those inreal-life contexts.D: Applying mathematics in real-life contexts

ii. select appropriate mathematicalstrategies when solving authenticreal-life situationsiii. apply the selected


Self-managementIII. Organization skillsIV. Affective skillsV. Reflection skills

Skills:Knowledge & Skills TBD

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mathematical strategiessuccessfully to reach a solution

statistics and probabilitynumbergeometry and trigonometrydiscrete mathematics

MYP5: Unit 2:Mathematics:Algebra

FormRelationships

Simplification Personal andcultural expression

The language ofAlgebra canenhance both theunderstanding ofreal life situationsand the problemsolving, translatingor modelling intowell organized,simpler andequivalentstructures(equations,inequalities..) whatis expressed inwords as arelationshipbetween two ormore quantities.






Self-managementIII. Organization skillsIV. Affective skillsV. Reflection skills


Social

Skills:Simultaneous equations,quadratic equations.

Inequalities: linear andquadratic

Sets of inequalities (linearonly and linear combinedwith quadratic; not morethan three inequalities perset)

Exponential equations

Surds: defintions, laws ofmultiplication, division;taking out a factor, likesurds, addition andsubtraction of like surds,rationalization ofdenominators

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MYP5:Mathematics -Unit 1 - Geometry

Form MeasurementPattern

Other:Space


Understandingform and shapepatterns enhancecreativity andgives access toNature's beauty.






Content:Part One- TRIGONOMETRY

Unit Circle: definition of sine,cosine and tangent of anangle and First FundamentalIdentity;sine, cosine and tangent ofsome special acute angles(30°, 45°, 60°) andassociated arcs;inverse trigonometricfunctions using GDC (only indegrees)resolution of right triangles(SOH, CAH and TOA) bothwith and without GDC;applying SOH, CAH andTOA to figures that can bedecomposed into righttriangles;2D trigonometry (direct andinverse) problems involvingperimeter, area, inradius,circumradius and anglebisectors;3D trigonometry (direct andinverse) problems.

Part Two - PARABOLASIN THE CARTESIANPLANE

Definition of a parabola as aconic section;definition of a parabola as ageometric locus of points;standard equation of aparabola with axis parallel tothe y-axis in the Cartesianplaneconcavity of a parabola,coordinates of the focus of aparabola,

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coordinates of the vertex ofa parabola,equation of the directrix of aparabola,equation of the axis ofsymmetry of a parabola,coordinates of the point ofintersection of a parabolaand the y-axis,coordinates of the point(s) ofintersection of a parabolaand the x-axisgraphing a parabola in theCartesian planequadratic inequalities: agraphical approach;mutual position of a straightline and a parabola:condition of tangencyequation of the two straightlines tangent to a parabolaand passing through a pointexternal to the parabolaitself,equation of the straight linetangent to a parabola at apoint of the parabola itselffamilies of parabolas;coordinate geometry directand inverse problemsinvolving parabolas/straightlines;real-world applications ofparabolas.

Part Three -CIRCUMFERENCES INTHE CARTESIAN PLANE

Definition of a circumferenceas a geometric locus ofpoints;equation of a circumferencein the Cartesian plane:center-radius equation of a



circumference,general equation of acircumference,intersections of acircumference with the axes;mutual position of a straightline and a circumference:condition of tangency:equation of the straight linetangent toa circumference at a point ofthe circumference itself;families of circumferences;coordinate geometry directand inverseproblems involvingcircumferences/parabolas/straight lines.real-world applications ofcircumferences.

Skills:Applying geometry to reallife situations.

Solving problems usingbasic trigonometricidentities.

Solving problems aboutparabolas in the CartesianPlane

Solving problems aboutcircumferences in theCartesian Plane

Part One -TRIGONOMETRY

Solving exercises byapplying basic trigonometricidentities (First FundamentalIdentity and definition oftangent);solving problems about right



triangles by using SOH, CAHand TOA both withoutcalculator (if special anglesare involved) and with thehelp of a GDC;solving 2D and 3D direct/inverse geometry problemswhere the involved figurescan be decomposed intoright triangles.

Part Two - PARABOLASIN THE CARTESIANPLANE

Recognizing the equation ofa parabola in the Cartesianplane;finding the coordinates ofthe vertex of a parabola;finding the coordinates ofthe focus of a parabola;finding the equation of theaxis of symmetry of aparabola;finding the equation of thedirectrix of a parabola;finding the points ofintersection of a parabolawith the axes;graphing a parabola in theCartesian plane;finding the points ofintersection of a parabolaand a given line, if there areany;finding the equations of thelines tangent to a parabolaand passing through a pointexternal to the parabolaitself;finding the equation of theline tangent to agiven parabola at a point ofthe parabola itself;



finding the equation of aparabola given someconditions on it;applying quadratics to real-life situations;solving coordinate geometryproblems involving points,lines and parabolas;solving a quadraticinequality graphically.

Part Three -CIRCUMFERENCES INTHE CARTESIAN PLANE

Recognizing the equation ofa circumference in theCartesian plane;finding the center of acircumference given itsequation;finding the radius of acircumference given itsequation;finding the points ofintersection of acircumference with the axes,if there are any;graphing a circumference inthe Cartesian plane;finding the point ofintersection of a parabolaand a given line, if there areany;finding the equation of a linetangent to a circumferenceat a point of thecircumference itself;finding the equation of acircumference given someconditions on it;applying circumferences toreal-life situations;solving coordinate geometryproblems involving points,



lines, parabolas andcircumferences.

MYP5:Mathematics -Unit 2 - Algebra

Relationships EquivalenceGeneralization

Other:Model


Models asgeneralizations ofthe relationshipsbetween variables.





SocialII. Collaboration skills


Content:Part One - QUADRATICEQUATIONS (in R)

Discriminant (delta) of aquadratic trinomial and realsolutions of a quadraticequation via quadraticformula;solutions of specialpolynomial equations ofdegree higher than two vianull product law;real-life applications ofquadratic equations (seeUnit 1, Part Two).

Part Two - REALINTERVALS,INEQUALITIES AND SETSOF SIMULTANEOUSINEQUALITIES,DOMAINS OFFUNCTIONS

Real Intervals:formal definition of interval:examples andcounterexamples;classification of intervals(left/right open/closed,bounded/unbounded);set-builder notation vsinterval notation;graphical representation ofintervals on the real line;union and intersection of(two or more) intervals.Inequalities in R:addition, subtraction,multiplication and divisionproperties of

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inequalities; equivalentinequalities.linear inequalities: algebraicand graphical approach;quadratic inequalities:algebraic and graphicalapproach (see Unit 1, PartTwo);inequalities of degree higherthan two via signs diagram.Systems of (two or more)simultaneous inequalities.Domain of functions of onereal variable:conditions of existencefor rational functions;conditions of existence forirrational functions;conditions of existence forlogarithmic functions.

Part Three - EXPONENTAND LOGARITHMS:

Rational exponents (review);definition of logarithm andconditions of existence onits base and argument;properties of logarithms(product rule, quotient rule,power rule and change ofbase formula);exponential and logarithmicfunctions and their graphs inthe Cartesian plane;exponential and logarithmicequations;real-life problems involvingexponents and logarithms:exponential growth anddecay problems.

Skills:Using algebra to provide



general models.

Setting up equations tomodel a problem, thensolving them with algebraictechniques.

Part One - QUADRATICEQUATIONS (in R)

Solving quadratic equationsboth factoring and applyingthe quadratic formula;solving polynomialequations of degree higherthan two by factoring;solving real-life problemsinvolving quadraticequations.

Part Two - REALINTERVALS,INEQUALITIES AND SETSOF SIMULTANEOUSINEQUALITIES,DOMAINS OFFUNCTIONS

Operating with intervals andinterval notation;solving linear and quadraticinequalities;solving polynomialinequalities of degree higherthan two by factoring andusing sign diagrams;solving inequalitiesgraphically;solving systems of (two ormore) simultaneousinequalities;finding the domain ofrational, irrational andlogarithmic functions.



Part Three - EXPONENTAND LOGARITHMS:

Calculating easy logarithmsby hand;operating with logarithmsand their properties (productrule, quotient rule, powerrule and change of baseformula);solving exponential andlogarithmic equations bothby hand and using the GDC;solving real-life problemsinvolving exponents andlogarithms: exponentialgrowth and decay problems.

Are you a goldenperson?CorrelationMYP5: Unit 4:Mathematics:Statistics:Bivariate Analysis

FormRelationships

Model Orientation inspace and time

The unit purposeis develop theknowing andunderstanding ofcorrelationbetween two anyvariables in termsof type andstrength, followedby the applicationof this newknowledge to realife context and toService activity.




ThinkingVIII. Critical thinking skillsX. Transfer skills

Skills:Knowledge about linearmodelling that has beenacquired during the previousunit: visualizing theinformation

knowledge about creatingdiagrams making use ofExcel

Knowledge about the use ofthe Graphic DisplayCalculator to findparameters relevant to thetask developments

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i. identify relevant elements ofauthentic real-life situationsiv. justify the degree of accuracy ofa solutionv. justify whether a solution makessense in the context of theauthentic real-life situation

MYP5: Unit 5:Mathematics:Geometry andTrigonometryMYP5:Mathematics -Unit 3 - Statisticsand Probability

Logic ModelRepresentation

Other:Pattern


Both through therepresentation of amodel and logicthe process ofdata-drivedecision making isfacilitated.




Content:Part One - BIVARIATESTATISTICS

Graphical representation ofbivariate data: 2DScatterplots;linear correlationPearson's CorrelationCoefficient: strength anddirection of a linearcorrelation;locus of means;equation of the line of bestfit using GDC;interpolation andextrapolation.

Part Two - THEORETICALPROBABILITY (*)

Sample space and definitionof theoretical probability ofan event;Venn diagrams andprobability tree diagrams;conditional probability andLaw of total probability.

(*) This could be the last

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part of the MYP5Mathematics program but itis possible it will not beaddressed in class due tolack of time.

Skills:Collecting, organizing,analyzing, and interpretingnumerical data.

Communicating statisticalinformation effectively.

Determining the likelihood ofan event, as well asdetermining potential risk.

Part One - BIVARIATESTATISTICS

Displaying data in ascatterplot;finding the locus of meansusing a GDC;calculating the Pearson'sCorrelation Coefficient usinga GDC;finding the equation of theline of best fit using a GDC;interpolating between thepoles;extrapolating outside thepoles.

Part Two - THEORETICALPROBABILITY

Calculating the probability ofan event using the definitionof theoretical probability ofan event.drawing Venn Diagrams andcalculating probabilitiesstarting from them.



drawing probability treediagrams and calculatingprobabilities from them.calculating the probability ofan event A given that theevent B has occurred(conditional probability)applying the Law of totalprobability in easysituations.



mathematics - mathematics subject group overview · 2019-12-17 · mathematics (myp 1) unit title...

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