MYP Subject Groups

Course Content

	Number	Algebra	Geometry / Trignometry	Statistics & Probability	Discrete Mathematics
M1	Students should be able to: investigate problems involving several operations on natural numbers and rational numbers apply algorithms to integers in various situations compare rational numbers in different forms learn to estimate with whole numbers.	Students should be able to: express the rule for algorithms in symbolic language investigate problems with one missing term including examples from geometry calculate the value of the variable.	Students should be able to: investigate problems involving triangles investigate problems involving convex quadrilaterals investigate problems involving the perimeter or the area of certain polygons investigate problems involving straight lines or angles create figures by means of isometric transformations.	Students should be able to: interpret tables and graphs construct tables and graphs calculate averages.	Students should be able to: perform set operations with whole numbers find the cardinality of sets.

M2	Students should be able to: investigate problems involving ratios and rates investigate problems involving proportions and percentages investigate problems with squares and square roots estimate with rational numbers rounding numbers	Students should be able to: demonstrate their understanding of the concept of an expression carry out basic operation on expressions (+, -, ×, ÷) translate one representation of a situation into another (rules, graphs, tables of values) sequences and number patterns (patterns- graphing-algebraic equations) investigate first-degree equations (expressions not containing x²) investigate problems using a table of values or a graph.	Students should be able to: investigate problems involving polygons investigate problems involving circles (circumference and area) volume and surface area of regular prisms. investigate problems involving enlarging or reducing a figure- scaling create figures by means of isometric transformations in the Cartesian plane.	Students should be able to: calculate the probability of an event in a simple situation investigate probabilities sample space diagrams use Venn diagrams to investigate problems.	Students should be able to: perform set operations with rational numbers find the cardinality of sets locate paths and tours set notation

M3	Students should be able to: work with rational numbers approximate some rational and irrational numbers ( investigate ) accuracy standard form perform and discuss problem-solving strategies investigate problems involving cubes and cube roots.	Students should be able to: determine the dependent variable and independent variable in a variety of situations represent rules that apply to given situations in various ways investigate problems where a linear relationship exists between variables convert an algebraic situation into an equivalent expression using basic operations investigate first-degree in equations.	Students should be able to: investigate problems by applying Pythagoras'theorem create figures using composites of transformations describe, identify and prove some composites of transformations create solids by rotating or translating figures investigate problems involving solids investigate problems related to the area or volume of solids. introduce sin and cos (right angled triangles only)	Students should be able to: investigate problems involving situations represented by a one-variable statistical distribution derive qualitative information about a distribution using mean, median, mode and range	Students should be able to: to work with a logic table. defining number system probability tree diagrams

M4	Use practical situations. Four rules for calculations with whole numbers, decimals, fractions, order of operations and brackets. Meaning of dividing by a fraction/decimal, Give approximations to specified number of S.F's and D.P's and rounding off answers to reasonable accuracy according to the context. Give appropriate upper and lower bounds to solutions of simple problems. Finding the percentage of a quantity, express one quantity as a percentage of another, % increase or decrease Give definitions of different number types and concepts. Principal of ratio, direct & indirect proportion in algebraic form, Simple interest and simple problems involving compound interest; common measures of rate. Dividing a quantity into a given ratio. Use of scales in practical situations. Increase; decrease a quantity by a given ratio.	Use letters to generalise numbers and express algebraically. Substitution and transform simple formula. Manipulate directed number, use brackets and extract common factors Factorising simple expressions; Solve simple linear equations in one and two unknowns. Solve simple linear inequalities; Use and interpret graphs in practical situations including conversion graphs, distance - time graphs and travel graphs; Develop the concept of gradient and be able to calculate it as well as the length of a line given two points. Use the form of the equation for a straight line, y = mx + c. Use to solve simultaneous equations. Recognise different types of graphs - straight line, quadratic.	Investigate the sum of the internal angles in polygons and extend to problems involving regular polygons. Investigate properties of circles including tangents to circles and cyclic quadrilaterals and use findings in solving problems. Recognise symmetry in two and three-dimensional shapes including prisms and pyramids. Look at symmetry in circles with application to chords and tangents. Understand the concept of locus and apply the following situations: Given distance from a point, straight line. Equidistant from two points and two intersecting straight line graphs. Use of protractor, construct simple geometrical figures. Construct angle bisectors & perpendicular bisectors. Understand the concept of �loci'and be able to draw the loci for various situations. Read and make scale drawings. Relate increase/decrease in lengths of similar shapes to corresponding increase/decrease in areas and volumes. Use Pythagoras and trig ratios to solve right-angled triangles. Three figure bearings. Understand the concept of angle of elevation & depression.	Review statistics concepts noted in the core section of the syllabus. Discuss the concept of discrete, continuous and grouped data. Construct and read histograms with equal intervals. Construct and use cumulative frequency diagrams; estimate the median, percentiles, quartiles and inter-quartile ranges; calculate an estimate of the mean for grouped and continuous data, identify the modal class for a grouped frequency distribution. Scatter graphs and correlation together wit line of best fit. Revise the concept of probability. Use tree diagrams and possibility diagrams to solve problems. Use correct notation	Students should be able to investigate problems involving optimal solutions, perform and discuss problem-solving strategies.

M4 Extended	In addition to the objectives above: Reverse %; Compound interest by use of the formula; Finding general formula for number sequences using intuitive and algebraic methods. Recognise square, cubic, and triangular numbers in a sequence.	Quadratic factorisation - all four types; Algebraic fractions - addition & subtraction, multiplication and division, more complicated equations; Quadratic equations by factorisation & formula. Draw quadratic graphs and use them to solve quadratic equations.	Proof of congruence. Circle properties - angles in the same segment, tangent and chord theorems, angles in the alternate segment, and tangents to the circle from a point. More complex loci. Develop and use sine, cosine and area sine rules including proof. Apply above rules to 2 - dimensional problems including angle of elevation and depression. Simple trig equations 0 - 360 degrees	Histograms with unequal intervals using the concept of frequency density. Find the equation of the line of best fit in correlations Measures of spread including std deviation and variance. Conditional probability	Students should be able to investigate problems involving optimal solutions, and perform and discuss a variety of problem-solving strategies.

M5	Review standard index form. Operations with fractions. Limits of error; Give appropriate upper and lower bounds to solutions of simple problems. Simple interest and simple problems involving compound interest; common measures of rate.	Review changing the subject including more complex formulae. Finding and justifying or proving general rules/formulae for sequences. Function definition and notation, use of the notation definition as a mapping. Draw up graphs for different functions by substituting values into the functions and developing co-ordinate points. Use intersection points to solve systems of equations. Distance-time and speed time graphs, Vector algebra.	Develop and use sine, cosine and area sine rules including proof. Apply above rules to 2 - dimensional problems including angle of elevation and depression. Simple trig equations 0 - 360 degrees. Perform calculations involving the circumference and area of a circle, the area of a parallelogram, trapezium and the volume of solids with uniform cross-sectional area(prisms) Reflect simple plane figures in horizontal and vertical lines; rotate simple plane figures about the origin, vertices or mid-points of the edges of the figures, through multiples of 90�; construct given translations and enlargements of simple plane figures; recognise and describe reflections, rotations, translations and enlargements.	Histograms with unequal intervals using the concept of frequency density. Probability of exclusive and combined events. Use tree diagrams and possibility diagrams to solve problems. Use correct notation.	Students should be able to investigate problems involving networks.

M5 Extended	In addition to the above: Find error and % error; Finding general formula for number sequences using intuitive and algebraic methods up to geometric sequences; Recognise square, cubic, and triangular numbers in a sequence;	Inverse functions & composite functions. Fractional indices; Quadratic solutions by completing the square; Estimate the gradient at a point by drawing suitable tangents; Analyse the quadratic function; Include reciprocal and exponential graphs.	Solve problems involving arc length and sector areas as a fraction of the circumference and area of a circle. Volumes of pyramids, cones and spheres. Simple trig identities: Transformations and matrices (including inverse matrices) combination of transformations. Be able to give precise descriptions of descriptions of transformations.	Measures of spread including normal distribution and standard deviation and variance. Conditional probability.	Students should be able to investigate problems involving networks and directed networks and classify and describe topological objects including the Möbius strip.