Math Games

Number Systems; N: the set of natural numbers, N = {1,2,3,4...}; Z: the set of integers, including 0; Q: the set of rational numbers; R: the set of real numbers; R/Q: the set of irrational numbers
• The binary operations of addition, subtraction multiplication and division and the relationships between these operations, beginning with whole numbers and integers. They explore some of the laws that govern these operations and use mathematical models to reinforce the algorithms they commonly use. Later, they revisit these operations in the context of rational numbers and irrational numbers (R/Q) and refine, revise and consolidate their ideas. Students learn strategies for computation that can be applied to any numbers; implicit in such computational methods are generalisations about numerical relationships with the operations being used.
• Students articulate the generalisation that underlies their strategy, firstly in the vernacular and then in symbolic language.
• Problems set in context, using diagrams to solve the problems so they can appreciate how the mathematical concepts are related to real life. Algorithms used to solve problems involving fractional amounts.

Indices
• Binary operations of addition, subtraction, multiplication and division in the context of numbers in index form.

Applied arithmetic
• Solving problems involving, e.g., mobile phone tariffs, currency transactions, shopping, VAT and meter readings.
• Making value for money calculations and judgments.
• Using ratio and proportionality.

Applied measure
• Measure and time.
• 2D shapes and 3D solids, including nets of solids (two-dimensional representations of three-dimensional objects).
• Using nets to analyse figures and to distinguish between surface area and volume.
• Problems involving surface area and volume.
• Modelling real-world situations and solve a variety of problems (including multi-step problems) involving surface areas, and volumes of prisms and cylinders.
• Students learn about the circle and develop an understanding of the relationship between its circumference, diameter and pi.

Sets
• Set language as an international symbolic mathematical tool; the concept of a set as being a well-defined collection of objects or elements. They are introduced to the concept of the universal set, null set, sub-set, cardinal number; the union, intersection, set difference operators, and Venn diagrams. They investigate the properties of arithmetic as related to sets and solve problems involving sets.

Synthesis and problem-solving skills
• explore patterns and formulate conjectures
• explain findings
• justify conclusions
• communicate mathematics verbally and in written form
• apply their knowledge and skills to solve problems in familiar and unfamiliar contexts
• analyse information presented verbally and translate it into mathematical form
• devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions

Synthetic Geometry
• Axioms
• Theorems
• Corollaries
• Constructions

Transformation Geometry
• Translations, central symmetry and axial symmetry.

Co-ordinate Geometry
• Co-ordinating the plane.
• Properties of lines and line segments including midpoint, slope, distance and the equation of a line in the form: y - y1 = m(x - x1) y = mx + c; ax + by + c = 0 where a, b, c, are integers and m is the slope of the line
• Intersection of lines.
• Parallel and perpendicular lines and the relationships between the slopes.

Trigonometry
• Right-angled triangles: theorem of Pythagoras.
• Trigonometric ratios
• Trigonometric ratios in surd form for angles of 30°, 45° and 60° Right-angled triangles
• Decimal and DMS values of angles.

Synthesis and problem-solving skills
• explore patterns and formulate conjectures
• explain findings
• justify conclusions
• communicate mathematics verbally and in written form
• apply their knowledge and skills to solve problems in familiar and unfamiliar contexts
• analyse information presented verbally and translate it into mathematical form
• devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions.

Generating arithmetic expressions from repeating patterns
• Patterns and the rules that govern them, and so construct an understanding of a relationship as that which involves a set of inputs, a set of outputs and a correspondence from each input to each output.

Representing situations with tables, diagrams and graphs
• Relations derived from some kind of context -- familiar, everyday situations, imaginary contexts or arrangements of tiles or blocks. They look at various patterns and make predictions about what comes next.

Finding Formulae
• Ways to express a general relationship arising from a pattern or context.

Examining algebraic relationships
• Features of a relationship and how these features appear in the different representations.
• Constant rate of change: linear relationships.
• Non-constant rate of change: quadratic relationships
• Proportional relationships

Relations without Formulae
• Using graphs to represent phenomena quantitatively.

Expressions
• Using letters to represent quantities that are variable.
• Arithmetic operations on expressions; applications to real life contexts.
• Transformational activities: collecting like terms, simplifying expressions, substituting, expanding and factoring.

Equations and Inequalities
• Using a variety of problem solving strategies to solve equations and inequalities. They identify the necessary information, represent problems mathematically, making correct use of symbols, words, diagrams, table and graphs.

Synthesis and problem-solving skills
• explore patterns and formulate conjectures
• explain findings
• justify conclusions
• communicate mathematics verbally and in written form
• apply their knowledge and skills to solve problems in familiar and unfamiliar contexts
• analyse information presented verbally and translate it into mathematical form
• devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions

Counting
• Listing outcomes of experiments in a systematic way.

Concepts of probability
• The probability of an event occurring: student progress from informal to formal descriptions of probability.
• Predicting and determining probabilities.
• Difference between experimental and theoretical probability.

Outcomes of simple random processes
• Finding the probability of equally likely outcomes.

Statistical reasoning with an aim to becoming a statistically aware consumer
• The use of statistics to gather information from a selection of the population with the intention of making generalisations about the whole population. They consider situations where statistics are misused and learn to evaluate the reliability and quality of data and data sources.

Finding, collecting and organising data
• Formulating a statistics question based on data that vary allows for distinction between different types of data.

Representing data graphically and numerically
• Methods of representing data. Students develop a sense that data can convey information and that organising data in different ways can help clarify what the data have to tell us. They see a data set as a whole and so are able to use fractions, quartiles and median to describe the data.
• Mean of a grouped frequency distribution.

Analysing, interpreting and drawing conclusions from data
• Drawing conclusions from data; limitations of conclusions.

Synthesis and problem-solving skills
• explore patterns and formulate conjectures
• explain findings
• justify conclusions
• communicate mathematics verbally and in written form
• apply their knowledge and skills to solve problems in familiar and unfamiliar contexts
• analyse information presented verbally and translate it into mathematical form
• devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions.

Functions
• The meaning and notation associated with functions.

Graphing functions
• Interpreting and representing linear, quadratic and exponential functions in graphical form.

Synthesis and problem-solving skills
• explore patterns and formulate conjectures
• explain findings
• justify conclusions
• communicate mathematics verbally and in written form
• apply their knowledge and skills to solve problems in familiar and unfamiliar contexts
• analyse information presented verbally and translate it into mathematical form
• devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions