Math Games

Data analysis
• 1.1 analysis and interpretation of:
- tables
- bar graphs
- pictograms
- line graphs
- pie charts
• 1.2 purposes and uses, advantages and disadvantages of the different forms of statistical representations
• 1.3 explaining why a given statistical diagram leads to misinterpretation of data
• 1.4 Construct tables, bar graphs, pictograms, line graphs and pie charts from given data.
• 1.5 Work collaboratively on a task to:
- collect and classify data
- present data using an appropriate statistical representation (including the use of software)
- analyse data
• 1.6 Compare various statistical representations and justify why a particular representation is more suitable than others for a given situation.
• 1.7 Use data to make informed decisions, predictions and inferences.

Angles, triangles and polygons
• 1.1 right, acute, obtuse and reflex angles
• 1.2 vertically opposite angles, angles on a straight line, angles at a point
• 1.3 angles formed by two parallel lines and transversal: corresponding angles, alternate angles, interior angles
• 1.4 properties of triangles
• 1.5 investigate the properties relating the sides and angles of a triangle, e.g. form triangles with different lengths to discover that the sum of two sides is greater than the third side, and that the longest side is opposite the largest angle.

Mensuration
• 5.1 area of parallelogram and trapezium
• 5.2 problems involving perimeter and area of plane figures
• 5.3 volume and surface area of prism and cylinder
• 5.4 conversion between cm² and m², and between cm³ and m³
• 5.5 problems involving volume and surface area of composite solids
• 5.6 Make connections between the area of a parallelogram and that of a rectangle, and between the area of trapezium and that of a parallelogram, e.g. using paper folding/cutting.
• 5.7 Identify the height corresponding to any given side of a triangle or quadrilateral that is taken as the base.
• 5.8 Visualise and sketch 3D shapes from different views.
• 5.9 Visualise and draw the nets of cubes, cuboids, prisms and cylinders for the calculation of surface area.

Problems in real-world contexts
• 7.1 solving problems in real-world contexts (including floor plans, surveying, navigation, etc) using geometry
• 7.2 interpreting the solution in the context of the problem
• 7.3 identifying the assumptions made and limitations of the solution
• 7.4 Work on tasks that incorporate some or all elements of the mathematical modelling process

Numbers and their operations
• 1.1 primes and prime factorisation
• 1.2 finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
• 1.3 negative numbers, integers, rational numbers, real numbers and their four operations
• 1.4 calculations with calculator
• 1.5 representation and ordering of numbers on the number line
• 1.6 use of <, >, ≥, ≤
• 1.7 approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation)
• 1.8 Classify whole numbers based on their number of factors and explain why 0 and 1 are not primes.
• 1.9 Discuss examples of negative numbers in the real world.
• 1.10 Represent integers, rational numbers and real numbers on the number line as extension of whole numbers, fractions and decimals respectively.
• 1.11 Use algebra discs or the AlgeDisc application in AlgeTools to make sense of addition, subtraction and multiplication involving negative integers and develop proficiency in the 4 operations of integers.
• 1.12 Work in groups to estimate quantities (numbers and measures) in a variety of contexts, compare the estimates and share the estimation strategies.
• 1.13 Compare follow-through errors arising from intermediate values that are rounded to different degrees of accuracy.
• 1.14 Make estimates and check the reasonableness of answers obtained from calculators.

Ratio and proportion
• 2.1 comparison between two or more quantities by ratio
• 2.2 relationship between ratio and fraction
• 2.3 dividing a quantity in a given ratio
• 2.4 ratios involving rational numbers
• 2.5 equivalent ratios
• 2.6 writing a ratio in its simplest form
• 2.7 problems involving ratio
• 2.8 Discuss and explain how ratios are used in everyday life.
• 2.9 Use the concept of equivalent ratios to find a:b:c given the ratios a:b and b:c
• 2.10 Make connections between ratios and fractions, use appropriate mathematical language to describe the relationship, and use algebra to solve problems, e.g. "The ratio A to B is 2:3" can be represented as: A 2x B 3x The ratio 2:3 means "2 units to 3 units", "A is 2/3 of B", or "B is 3/2 of A".

Percentage
• 3.1 expressing one quantity as a fraction or decimal
• 3.2 expressing one quantity as a percentage of another
• 3.3 comparing two quantities by percentage
• 3.4 percentages greater than 100%
• 3.5 increasing/decreasing a quantity by a given percentage (including concept of percentage point)
• 3.6 finding percentage increase/decrease
• 3.7 reverse percentages
• 3.8 problems involving percentages
• 3.9 Collect examples of percentages from newspapers and magazines and discuss the meaning of percentage in each example.
• 3.10 Examine bills and receipts, ect. to find examples of the uses of percentages, e.g. discount, service charge, GST and other taxes and check the calculated values.
• 3.11 Make connections between percentages and fractions/decimals, e.g. "25% of a quantity is 1/4 of the quantity". "20 % of x is 0.2x".
• 3.12 Discuss misconceptions, e.g. "A is 5% more than B, then B is 5% less than A".

Rate and Speed
• 4.1 relationships between distance, time and speed
• 4.2 writing speed in different units (e.g. km/h, m/min, m/s and cm/s)
• 4.3 concepts of average rate, speed, constant speed and average speed
• 4.4 conversion of units (e.g. km/h to m/s)
• 4.5 calculation of speed, distance or time given the other two quantities
• 4.6 problems involving rate and speed
• 4.7 Discuss examples of rates e.g. currency exchange rates, interest rates, tax rates, rate of rotation and speed.
• 4.8 Find out and compare the speeds of bicycles, cars, trains, aeroplanes and spaceships and their respective units to have a sense of their magnitude.
• 4.9 Explain the difference between average speed and constant speed and also explain why average speed is not the average of speeds.

Algebraic expressions and formulae
• 5.1 using letters to represent numbers
• 5.2 interpreting notations:
- ab as a x b
- a/b as a ÷ b or a x 1/b
- a² as a x a, a³ as a x a x a, a²b as a x a x b,...
- 3y as y + y + y or 3 x y
- 3(x + y) as 3 x (x + y)
- 3 + y/5 as (3 + Y) ÷ 5 or 1/5 x (3 + y)
• 5.3 evaluation of algebraic expressions and formulae
• 5.4 translation of simple real-world situations into algebraic expressions
• 5.5 recognising and representing patterns/relationships by finding an algebraic expression for the nth term
• 5.6 addition and subtraction of linear expressions
• 5.7 simplification of linear expressions such as 2(x - 3y) 4x - 2(3x - 5) 3(x - y) - (2y + x)- y
• 5.8 Use spreadsheets, e.g. Microsoft Excel, to
- explore the concept of variables and evaluate algebraic expressions.
- compare and examine the differences between pairs of expressions, e.g. 2n and 2 + n, n² and 2n, 2n² and (2n)².
• 5.9 Use algebra discs or the AlgeDisc application in AlgeTools to make sense of and interpret linear expressions with integral coefficients, e.g. 4x - 3y and -3(x-2).
• 5.10 Use the AlgeDisc application in AlgeTools to construct and simplify linear expressions with integral coefficients.
• 5.11 Work in groups to select and justify pairs of equivalent expressions.
• 5.12 Write algebraic expressions to express mathematical relationships, e.g. for the statement "There are 3 times as many boys as girls", if we let x be the number of girls, then the number of boys is 3x. This can also be written as b= 3g, where b and g are the number of boys and girls respectively.
• 5.13 Explore number patterns and write algebraic expressions to represent the patterns.

Equations and inequalities
• 7.1 concepts of equation
• 7.2 solving linear equations with integral coefficients in one variable
• 7.3 formulating a linear equation in one variable to solve problems
• 7.4 Use the virtual balance in AlgeTools to explore the concepts of equation and to construct, simplify and solve linear equations with integral coefficients.
• 7.5 Use the AlgeBar application (for whole numbers) in AlgeTools to formulate linear equations to solve problems (Students can draw models to help them formulate equations).

Problems in real-world contexts
• 8.1 solving problems based on real-world contexts:
- in everyday life (including travel plans, transport schedules, sports and games, recipes, etc)
- involving personal and household finance (including simple interest, taxation, instalments, utilities bills, money exchange, etc)
• 8.2 interpreting and analysing data from tables and graphs, including distance-time and speed-time graphs
• 8.3 interpreting the solution in the context of the problem
• 8.4 identifying assumptions made and the limitations of the solution
• 8.5 Examine and make sense of data in a variety of contexts (including real data presented in graphs, tables and formulea/equations).
• 8.6 Work on tasks that incorporate some or all of the elements of the mathematical modelling process.