Vertical Planner Subject: Mathematics Year level: MYP 1 Unit Title Key Concept Related Concept Global Context Statement of Inquiry MYP subject group objectives/assessment Number Systems and number properties Relationships System Generalization Pattern Orientation in and time Discovering and finding patterns in systems, time and can lead to a better understanding, make generalizations and building Number Test Ai, ii, iii B: i, ii Organization skills: Bring necessary equipment and supplies to class Keep an organized and logical system of information files/notebooks Number systems, odd numbers, even numbers, prime numbers Order of operations, rounding numbers, estimation and approximation Keep and use a planner for assignments Fractions, decimals and percentages Measurement and volumes Systems Form Equivalence Simplification Change Model Representation Measurement Orientation in and time Knowing how operations work and their relation with change increases our understanding of systems The surface area of your hand can be mathematically modeled by different 2D-shapes (triangles, rectangles, circles) Fractions, decimals and percentages Test Ai, ii, iii B i, ii Real Life Problem C i, ii, iii, iv D I, ii, iii Measurement Test Ai, ii, iii Real life Problem C i, ii, iii, iv D I, ii, iii, iv, v Communication skills Understand and use mathematical notation Affective skills Practise focus and concentration Practise bouncing back after adversity, mistakes and failure Representing fractions Fractions of regular shapes Equal, simplifying fractions Comparing fraction sizes Improper fractions and mixed numbers Constructing, representing decimal numbers, ordering, rounding decimals, converting decimals to fractions and fractions to decimals Percentages, converting percentages to fractions and decimals to percentages Plotting numbers on a line Units of measurement, reading scales, length conversions, perimeter, scale diagrams, area, conversion of units, the area of different shapes, volume Algebra and patterns Relationships Pattern Equivalence Justification Generalization Algebra follows a logical system of reasoning using variables to represent the unknown and thus resulting in making generalizations and justifications. Algebra Test Ai, ii, iii Test Communication skills Organise and depict information logically Patterns, variables and notation, algebraic form, the value of an expression, substituting into formulae
C i, ii, iii, iv Statistics Relationships Quantity, representation Throughout history, mathematics has evolved to include symbolic representation of quantities and functions that describe increasingly complex in our world. Statistics Test Ai, ii, iii Real World Problems Test C i, ii, iii, iv D I, ii, iii, iv, v Research skills Collect and analyse data to identify solutions and make decisions Process data and report results Data collection and representation Categorical data, graphs on categorical data, Numerical data Mean or average In-school survey
Vertical Planner Subject: Mathematics Year level: MYP 2 Unit Title Key Concept Related Concept Global Context Statement of Inquiry MYP subject group objective(s) Numbers & their properties Development Culture, change, quantity Angles Aesthetics Measurement, representation expression expression The development of number systems in different cultures in centuries past has changed towards the one decimal system that we use today. Tessellations can be found in both ancient and modern decoration, for example tiling and wall paper designs. Number test A i, ii,iii - Numberlines Angles test Organisation communication Types of numbers, factors & multiples, positive and negative numbers, rounding and estimation 4 operations on whole numbers (divisibility tests), Order of operations Index notation, Square and cube numbers, roots of whole numbers types of angles, using a protractor, Types of triangle, quadrilateral, polygon Angles in a triangle, quadrilateral Fractions, Decimals, Percentages Relationships Equivalence and quantity Length & Area Aesthetics Measurement, representation, Form Patterns and Models Volume & Capacity Circles & Statistics Communicatio n Aesthetics Communities Patterns, Form, Relationships Measurement, representation, form Generalization Justification, representation relationship Orientation in time and Orientation in time and Fairness and development Equivalent values expressed as fractions, decimals and percentages can be used to describe and calculate the relationship between quantities and rates. 2D shapes can be used to find the area of a country on a map. Symbols are a vital part of everyday life and can be used effectively to communicate a message The human body can be modeled by 3D mathematical shapes Statistically there are more red sweets made than other colours. D i, ii, iii, iv, v C I, ii, iii, iv, v A i,ii, iii B I, ii, iii, iv, v C iii C i, ii, iii, iv v D i, ii, iii, iv, v C i, ii, iii, iv, v D i,ii, iii thinking Creative thinking Communication Communication, Reflection Know: fractions, decimals and percentages rates, ratios, proportions, simple interest Understand: Numbers have meaning in relation to other numbers, there is a meaningful relationship between interest rate, principal, length of loan and total payment Do: Calculating percentages and finding simple interest, discounts and commissions Perimeter, Units of length, units of area. Converting units Area of square, rectangle, triangle, parallelogram, trapezium Area of compound shapes, Number sequences, nth term, Substituting into formulae, creating formulae from words Finding a pattern and solving a practical problem Simplifying expressions, Index notation in algebra, Evaluating algebraic expressions Volume of cube, cuboid, prism & pyramid Converting units of volume Units of Mass and Capacity Surface area of a cuboid Parts of a circle, Pi, Circumference & area, Cylinders Data collection, mean, mode, median & range, Pie charts, line graphs, stem & leaf diagram, Raise awareness of maths with Pi day activities
Equations Relationships Equivalence, representation Systems, patterns Scientific and technical innovation Two sides of an equation will always balance and you can use this to find an unknown quantity. B iii, iv, v C iii Communication correlation Writing equations, Solving equations with x on one side Simplifying and solving equations
Vertical Planner Subject: Mathematics Year level: MYP 3 Unit Title Key Concept Related Concept Global Context Statement of Inquiry MYP subject group objectives /Assessment Number Development Systems Generalization Orientation in time and The development of systems lead to generalizations of time and Numbers Test A ii, iii Test Organisation Bring necessary equipment and supplies to class Keep an organized and logical system of information files/notebooks Types of numbers; Natural numbers N, Integers Z, Rational numbers Q, Prime numbers, square numbers, cubed numbers, index notation, standard form Order of operations using Integers, fractions and decimals Ratio Keep and use a planner for assignments Percentage Systems Equivalence, Change Model expression Equivalent values expressed as fractions, decimals and percentages can be used to describe and calculate the relationship between quantities and rates Percentages Test B i, ii Real Life Problem Test C i, ii D i, ii, iii Collaboration Delegate and share responsibility Manage and resolve conflict and work collaboratively in teams Working with 1% (unitary method) Finding X% of Y Percentage increase and decrease, percentage change Reverse percentage Simple and compound interest Algebraic Expressions and Solving Equations Logic Pattern, representation, simplification Logical patterns can be represented in various ways and simplify them helps better understanding. Algebra Test A i, ii Patterns B i, ii C i, ii Organisation, Set goals that are challenging and realistic Changing word problems to algebraic expressions, Substitution, Simplification distributive law, expanding brackets working with surds (radicals) Rearranging algebraic expressions: Changing the subject of the formula
Unit Title Key Concept Related Concept Global Context Statement of Inquiry MYP subject group objectives /Assessment Indices Communication quantity representation, simplification Scientific and technical innovation Representing different quantities, especially in science, can be made simpler and thus eases communication Indices Test A i, ii, B ii, iii, iv, v C i, ii Critical thinking Laws of indices Scientific notation (standard form) Decimal places and significant figures Linear Graphs Aesthetics Representation system Two unknowns can be found by creating systems of simultaneous equations Graphs and Simultaneous Equations Test A ii, iii Real-Life Problems Test C ii, iii D i, ii, iii transfer Equation of a linear graph y = mx+c Sketching graphs by identifying the y-intercept and gradient Graphing using a set of points Finding the equation of a line from the graph or given two points Simultaneous equations: graphical and algebraic methods Square root functions Length, Area & Volume Logic Justification, Measurement identity Logic is a powerful tool for justifying what we discover through measurement and observation Area and Volume Test C i, ii Creative thinking Units of Measurement and their conversions Perimeter and Area of basic and composite shapes Circumference and area of a circle Surface area of objects with curved surfaces (cylinders, spheres) Volume and capacity of cube, cuboid, cylinder and sphere. Volume and capacity of combined objects Problem Solving Raising awareness of maths through Pi day activities Polygons, similarity & congruence communities Pattern, model, representation Orientationin time and Many geometric proofs date back to the days of the great Greek philosophers Polygons, Similarity & Congruence Test C i, ii, iii, iv, v Reflection Word problems, involving algebraic expressions Angles at a point, angles on a straight line, angles on parallel lines Angles in a triangle, quadrilateral & polygon (Interior and exterior angles) Transformations, Similarity & congruence Deductive reasoning & geometric proof
Vertical Planner Subject: Mathematics Year level: MYP 4 Unit Title Key Concept Related Concept Global Context Statement of Inquiry MYP subject group objectives/assessment Sets & Venn diagrams Connections Representation systems Venn diagrams give a visual representation of data sets that interact with each other. Sets and Venn diagram test A i,ii, iiii Critical thinking Practise observing carefully in order to recognise problems Number sets Set notation Mutually exclusive sets Venn diagrams Probability and Probability using Venn diagrams Indices and Exponential Functions Development Change, Model pattern Fairness and development The spread of many diseases can be modelled by an exponential function Indices (& Logarithms) Maths & medicine investigation iv, v C I, ii, iii Draw reasonable conclusions and generalisations Research Present information in a variety of formats Process data and report results Select appropriate digital tools based on specific tasks Simplifying surds Scientific notation (standard form) Laws of indices Integer Exponents Evaluating numbers with integer exponents Exponential equations Fractional exponents - Using the rules of indices to simplify numerical expressions involving radicals and exponents Logarithms Evaluating the logarithm of a number and simplifying numerical expressions Using the laws of logarithms Number Bases performing operations with numbers in different bases Coordinate Geometry Connections Change System Scientific and technical innovation Different methods for representing and solving equations have been used over time by different cultures. Graphs & simultaneous equations test A ii, iii B I, ii, iii, iv, v transfer Distance between two points Midpoint of a line Vertical and horizontal lines, equation of a straight line Simultaneous Equations: solving graphically and algebraically
Solving Linear Equations Form Representation Equivalence Pattern Orientation in time and When a problem can be expressed as an algebraic equation then manipulation of the equation to an equivalent form can allow you to find a value or set of values that satisfy the equation. Equations test A iii, iv Real world graphs D I, ii, iii, iv, v Communication, Organise and depict information logically Understand and use mathematical notation Solving linear equations and linear inequalities Money and investment problems Motion problems Quadratic Equations and Quadratic Graphs Connections Patterns simplification The flight of an object is modeled by a quadratic equation Parabolas can be found in the real world all around us Quadratic equations test A i, ii Expansion, iv, Parabolas in the real world C ii, iii, iv, v D ii, iii, iv, v Collaboration Use and interpret a range of disciplinespecific terms and symbols Make inferences and draw conclusions Factorizing quadratic expressions Solving quadratic equations by factorizing and by using the quadratic formula Drawing quadratic functions and identifying characteristics such as the axis of symmetry, maximum and minimum points Transforming quadratic functions using the form f(x) = a(x h) 2 + k Solving quadratic equations by completing the square Completing the square to draw the graph, using the vertex (h, k) Circle Geometry Development Representation system Scientific and technical innovation Coordinate systems have been developed for 2D and 3D, but may theoretically work in 4D Circle Geometry Test A i, ii B i, ii Collaboration Angles in Circles Circle Theorem Length of Chords Measure of angles and arcs Perimeter and area of sectors Mensuration Aesthetics Model Quantity identity Packaging is generally designed to minimise surface area and maximise volume Area and volume test Organisation Percentage error in measurements Perimeter, area, surface area & volume review Optimization Optimizing Area and Perimeter Pythagoras and Trigonometry connections Generalization, Justification change Scientific and technical innovation Trigonometric ratios were used before the invention of calulators, how is that possible? Formative assessment criteria A and D Collaboration Pythagoras Theorem Pythagorean triples Properties of similar triangles Properties of congruent triangles Trigonometric Ratios Bearings Sine and Cosine Rules
Vertical Planner Subject: Mathematics standard and extended Year level: MYP5 Unit Title Key Concept Related Concept Global Context Statement of Inquiry MYP subject group objectives/assessment Number and Algebra Change Equivalence, generalization Equivalence forms for a certain context A B I,ii,iii C I,ii,iii,iv,v Communication Give and receive meaningful feedback Use intercultural understanding to interpret communication Inequalities - Expressing the solution set of a linear inequality on the number line (as well as set notation) Algebraic Fractions Simplifying algebraic fractions and solving equations involving algebraic fractions Linear programming Expansion laws Factorization Binomial expansion Solving non-linear inequalities Radicals, Advanced trigonometry Identity Justification, measurement Orientation in and time In tune with trigonometry Real life problem C, D I,ii,iii,iv,v Test A I,Ii,iii Collaboration skills Help others to succeed Listen actively to other perspectives and ideas Stamdard and s Radicals Trigonometric ratios in right-angled triangles 2- and 3-dimensional problems area of a triangle A = ½ absinc Sine and cosine rules The unit circle Multiples of 30 and 45 degrees Trigonometric equations Modeling with sine functions Trigonometric identities Functions & sequences Systems Representation, simplification Fibonacci was a genius! C, B i-iii Reflection skills Develop new skills, techniques and strategies for effective learning Identify strengths and Number Sequences and recurrence Predicting the next term in a number sequence (linear, quadratic, triangular, Fibonacci)
weaknesses of personal learning strategies (self-assessment) Functions - Types of functions: linear, quadratic, exponential, sine and cosine Domain and range Transformations of functions and Transforming a figure by rotation, reflection, translation and enlarging Inverse function and composite functions Transformation of Functions Describing and analysing transformed logarithmic rational (of the form f(x) = 1/x), and sine and cosine Example: f(x) = a sin(bx c) + d Arithmetic and Geometric Series Statistics & probability communication Change, justification expression C i-v D i-v Transfer skills Apply skills and knowledge in unfamiliar situations Inquire in different contexts to gain a different perspective Graphical analysis and representation (pie charts, histograms, line graphs, scatter plots, box-and- whisker plots) Data collection Constructing and Interpreting graphs Drawing the line of best fit Population Sampling Selecting samples and making inferences about populations Measures of central tendency/location (mean, mode, median, quartile, percentile) Calculating the mean, median and mode, and choosing the best measure of central tendency Measures of dispersion (range, interquartile range) for discrete and continuous data Calculating the interquartile range Probability of an event Probability of independent, mutually exclusive and combined events
Probability of successive trials Calculating probabilities of simple events, with and without replacement Calculating probabilities of independent events, mutually exclusive events and combined events Solving problems using tree diagrams and VennDiagrams Standard deviation Making inferences about data given the mean and standard deviation Conditional probability Calculating Conditional Probability