Math Games

7.S.1

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.

7.G.1

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.

7.G.5

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.

7.G.7

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

7.N.1

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.

7.N.2

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".

7.N.3

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".

7.N.4

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.

7.N.5

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.

7.N.7

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).

7.N.8

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.