SYLLABUS GRID MATHS QUEST FOR WESTERN AUSTRALIA BOOK 3. Exercises/Investigations

Transcription

1 SYLLABUS GRID MATHS QUEST FOR WESTERN AUSTRALIA BOOK 3 Cluster: Appreciating Mathematics (AM) Outcome 1 Confidence in mathematics Outcome 2 Contextualise mathematics AM 2.6 Uses familiar mathematical ideas to represent, describe and explain some features of their world. History of mathematics: Srinivasa Ramanujan ( ) Career profile: Peter Richardson History of mathematics: Richard Dedekind Career profile: Anna Wojcik Career profile: Jim Elliott Career profile: Donna Pullen Career profile: Mike Matheson Career profile: Graham de Hoedt History of mathematics: Leonhard Euler

2 Cluster: Working Mathematically (WM) Outcome 3 Mathematical strategies Outcome 4 Apply and verify Outcome 5 Reason mathematically WM 3.6 Partitions a problem into sub-problems to help guide its investigation and uses problemsolving strategies that include identifying and working on related problems or sub-problems. Plotting irrational numbers on the number line Braking distances Recurring surds Standard paper sizes What s our money worth overseas? Many hands make light work! The building problem Mouse pad dimensions What s the problem? How many cockatoos and kangaroos? Cat and mouse problem Cramer s rule for simultaneous equations Concert hall seating Flying dolphin Finding intercepts and turning points using a graphics calculator Catch this! The path of a golf ball Bicycle helmets A growing investment Water tank worries The cosine ratio Satellite height Which way do I go? Problems collating data Non-random sampling Misuse of graphs Standard deviation Conducting a statistical inquiry Footy card collecting Hit or sit? Traversable or not traversable? Sprouts Tourist attractions

3 WM 4.6 Looks back and asks if the mathematics chosen was helpful, the assumptions reasonable and the solution a good one. WM 5.6 Makes generalisations by abstracting common mathematical features from situations or data, tests by making varied and/or systematic checks of additional cases, and understands that only counter-examples are conclusive. Leonardo s observations Equal or not equal? Simultaneous equations in 3 unknowns Comparing volumes of pyramids and prisms Volume and capacity Patchwork sewing Who owns the gold coins? Explain these tricks How many paths in a network? The bridges of Königsberg Recurring surds Focus on proportion Musical notes Further exponential graphs Standard paper sizes revisited Teardrops A trendy problem Long jump to the top

4 Cluster: Number (N) Outcome 6 Understand numbers Outcome 7 Understand operations Outcome 8 Calculate N 6.6 Reads, writes, says and understands the meaning, order and relative magnitude of positive and negative rational numbers, ratios, familiar rates and numbers expressed with integer powers. N 6.7 Reads, writes and moves freely between real numbers, including powers and roots, rates, recurring decimals and decimal approximations for irrational roots. N 7.6 Understands the meaning, use and connections between the four operations on positive and negative rational numbers, ratios and familiar rates and numbers expressed with integer powers, and uses this understanding to choose appropriate operations. N 7.7 Understands the meaning, use and connections between the four operations on various forms of real numbers, including powers and roots, rates, recurring decimals and decimal approximations for irrational roots, and uses this understanding to choose appropriate operations. Ex 2A Direct proportion Ex 6A Index laws Ex 6B Negative indices Teardrops Ex 1B Finite and recurring decimal numbers Plotting irrational numbers on the number line Ex 1D Simplifying surds Ex 6C Fractional indices Ex 1A Operations with fractions Ex 2D Partial proportion Many hands make light work! Ex 2E Inverse proportion The building problem Focus on proportion Ex 2F Identifying the type of proportion Ex 1C Irrational numbers Ex 6C Fractional indices

5 N 8.6 Calculates with positive and negative numbers, decimals, fractions, ratios and integer powers, using mostly mental strategies, including those for frequently-used fractions and percentages of amounts. N 8.7 Undertakes efficient computations on numbers of any size, including fractional powers and scientific notation, rearranging formulae to facilitate computation and quoting results to an appropriate degree of accuracy. Ex 1A Operations with fractions Ex 2A Direct proportion Ex 2B Direct proportion the constant of proportionality Ex 2C Direct proportion and ratio or rate Leonardo s observations What s our money worth overseas? Ex 2D Partial proportion Many hands make light work! Ex 2E Inverse proportion The building problem Focus on proportion Ex 2F Identifying the type of proportion Ex 6A Index laws Ex 6B Negative indices Ex 6D Further use of the index laws Braking distances Ex 1E Addition and subtraction of surds Ex 1F Multiplication and division of surds Recurring surds Ex 1G Writing surd fractions with a rational denominator Standard paper sizes Ex 6C Fractional indices Ex 6D Further use of the index laws

6 Cluster: Measurement (M) Outcome 9 Understand units and direct measure Outcome 10 Indirect measure Outcome 11 Estimate M 9a.6 Decides what measurements are needed in order to complete practical tasks and ensures that units used are consistent with each other and with any formula used. M 9b.6 Makes or collects measurements to planned levels of accuracy and integrates measurement information from several sources in order to complete practical tasks. M 10b.5 Understands and uses scale factors and the effect of scaling linear dimensions on lengths, areas and volumes of figures and objects produced on grids and with cubes. M 10a.6 Understands and applies directly length, area and volume relationships for polygons and circles, prisms and pyramids. M 10b.6 Understands and uses similarity and Pythagoras theorem to solve problems involving triangles and scale drawing. Teardrops Volume and capacity The cosine ratio Which way do I go? Tourist attractions Volume and capacity Ex 7E Length, area and volume changes with dilations Ex 7A Perimeter Ex 7B Area Teardrops Ex 7C Total surface area Ex 7D Volume and capacity Water tank worries Maths Quest for Western Australia Book 2

7 M 10b.7 Understands and uses similarity relationships in and between figures and objects, including the trigonometric ratios. M 11.6 Estimates in situations in which it is sensible to do so, including where direct measurement is impossible or impractical, and judges whether estimates and measurements are reasonable. The cosine ratio Ex 8A Trigonometric ratios Ex 8B Using a calculator Ex 8C Using trigonometric ratios to find side lengths Ex 8D Using trigonometric ratios to find angles Ex 8E Applications of trigonometry Satellite height Patchwork sewing Ex 8F Trigonometry and bearings Which way do I go? Ex 8G Graphs of y = sin? and y = cos? Comparing volumes of pyramids and prisms Water tank worries

8 Cluster: Chance and Data (C&D) Outcome 12 Understand chance Outcome 13 Collect and process data Outcome 14 Interpret data C&D 12.6 Estimates probabilities and proportions based on primary or secondary data collection and assigns probabilities for one- and two-stage events by reasoning about equally-likely outcomes. C&D 12.7 Estimates probabilities, proportions, means and medians based on primary and secondary data collection and assigns probabilities using complementarity and independence. C&D 13a.6 Plans experiments, surveys and secondary data collection, collaboratively and independently, checking that data are recorded and organised correctly, including those in databases. C&D 13b.6 Displays and summarises data to show location and variability, including situations where some grouping of data is required, in order to compare data sets and to show relationships in one data set. C&D 13b.7 Displays and summarises data to show location, variability and association, and links displayed data with measures of location, variability and association. Ex 10A Probability of single events Explain these tricks Ex 10D Two-way tables and tree diagrams Ex 10F Subjective probability Ex 10A Probability of single events Ex 10B Complementary events Ex 10C Mutually exclusive events Ex 10E Independent and dependent events Footy card collecting Hit or sit? Problems collating data Ex 9A Collecting data Non-random sampling Conducting a statistical inquiry A trendy problem Ex 9B Presenting categorical and discrete data Ex 9C Representing data grouped into class intervals Ex 9D Measures of central tendency Conducting a statistical inquiry Who owns the gold coins? Ex 9F Bivariate data Ex 9G Lines of best fit Ex 9E Measures of spread Conducting a statistical inquiry Who owns the gold coins?

9 C&D 14.6 Interprets, makes comparisons and describes relationships in collected and published data from tables, diagrams, plots, graphs, text, summary statistics and databases, distinguishing between sample and population data. C&D 14.7 Selects and interprets information from a wide range of collected and published data to construct arguments to support or refute positions taken. Misuse of graphs Conducting a statistical inquiry Who owns the gold coins? Ex 9G Lines of best fit Ex 9E Measures of spread Ex 9F Bivariate data Ex 9G Lines of best fit A trendy problem Long jump to the top

10 Cluster: Space (S) Outcome 15 Represent spatial ideas Outcome 16 Reason geometrically S 15a.5 Uses coordinates, bearings and scale on maps and plans and in descriptions of locations and paths. Identifies the essential features of a location or arrangement needed to serve a purpose and represents them in networks and other diagrams. S 15a.6 Visualises, sketches and describes paths and regions that satisfy specified conditions. Uses networks and other diagrams to represent the order of, and paths between, locations. S 15b.6 Interprets and meets specifications requiring the accurate construction and placement of figures and objects, including manipulating shapes and arrangements mentally. S 15c.6 Visualises, produces and accurately describes specific translations, reflections, rotations and dilations. S 16.6 Analyses, describes and applies properties of, and relationships between, the classes of figures that can be reasoned about in terms of the properties of triangles and parallel and intersecting lines. Ex 8F Trigonometry and bearings Which way do I go? Ex 11A What is a network? Ex 11B Basic properties of networks Ex 11C Application of networks to problemsolving Sprouts The bridges of Königsberg Tourist attractions Ex 8F Trigonometry and bearings Which way do I go? Traversable or not traversable? Ex 11B Basic properties of networks Ex 11C Application of networks to problemsolving How many paths in a network? Ex 11D Paths and circuits part I Ex 11E Paths and circuits part II Ex 11F Networks and maps Tourist attractions Cat and mouse problem Ex 7E Length, area and volume changes with dilations Maths Quest for Western Australia Book 2

11 Cluster: Algebra (A) Outcome 17 Functions Outcome 18 Expressing generality Outcome 19 Equivalence, equations and inequalities A 17a.6 Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope. A 17b.6 Recognises and represents at least linear and square relationships in tables, symbols and graphs and describes informally how one quantity varies with the other. A 17a.7 Plots, sketches and interprets graphs in four quadrants, considering local and global features, including maxima and minima and cyclical changes. A 17b.7 Recognises and represents at least linear, reciprocal, exponential and quadratic functions in tables, symbols and graphs, and describes the assumptions needed to use these functions as models. Ex 4A Graphical solution of simultaneous equations How many cockatoos and kangaroos? Cat and mouse problem Ex 5D Plotting parabolas Ex 2A Direct proportion Ex 2D Partial proportion Ex 4A Graphical solution of simultaneous equations How many cockatoos and kangaroos? Ex 5D Plotting parabolas Ex 5E Sketching parabolas using the basic graph of y = x 2 Ex 5F Sketching parabolas of the form y = ax 2 + bx + c The path of a golf ball Bicycle helmets Ex 8G Graphs of y = sin? and y = cos? Ex 2E Inverse proportion Ex 5E Sketching parabolas using the basic graph of y = x 2 Ex 5F Sketching parabolas of the form y = ax 2 + bx + c Ex 6E Exponential functions and their graphs Further exponential graphs Ex 6F Modelling exponential growth and decay A growing investment

12 A 18a.6 Classifies number patterns which are linear, square or involve a power of a whole number; interprets, constructs and clarifies rules for describing them; and applies them to familiar or concrete situations. A 18b.6 Uses and interprets basic algebraic conventions for representing situations involving a variable quantity. A 18b.7 Uses and interprets algebraic conventions for representing generality and relationships between variables and establishes equivalence using the distributive property and inverses of addition and multiplication. A 19.6 Explains why two linear expressions are equivalent; sets up equations to represent one constraint in a situation; solves equations of the form ax + b = cx + d and ax 2 + bx = c using guess, check and improve and graphical methods; and solves linear equations using analytical methods. Maths Quest for Western Australia Book 2 Ex 6A Index laws Ex 3A Expanding algebraic expressions Ex 3B Factorising using common factors Ex 3C Factorising expressions with two or four terms Ex 3D Factorising expressions with three terms Mouse pad dimensions Ex 3E Mixed factorising practice Ex 3F Simplifying algebraic fractions Equal or not equal? What s the problem? Ex 3G Adding and subtracting algebraic fractions Ex 6B Negative indices Ex 6C Fractional indices Ex 6D Further use of index laws Standard paper sizes revisited Musical notes Ex 5D Plotting parabolas Ex 5E Sketching parabolas using the basic graph of y = x 2 Finding intercepts and turning points using a graphics calculator Catch this!

13 A 19.7 Sets up equations and inequalities that represent one or two constraints in a situation; solves equations using guess, check and improve and graphical methods; solves linear equations, quadratic equations and pairs of simultaneous linear equations analytically; and generates complete sets of numbers or number pairs that satisfy the constraints of an inequality. Ex 3H Algebraic applications Ex 4A Graphical solution of simultaneous equations How many cockatoos and kangaroos? Ex 4B Algebraic solutions of simultaneous equations elimination method Simultaneous equations in 3 unknowns Ex 4C Algebraic solutions of simultaneous equations substitution method Cramer s rule for simultaneous equations Ex 4D Problem solving using simultaneous equations Concert hall seating Ex 5A Solving quadratic equations by factorising Ex 5B Solving quadratic equations using the quadratic formula Ex 5C Using the discriminant Flying dolphin Ex 5F Sketching parabolas of the form y = ax 2 + bx + c Catch this! The path of a golf ball Bicycle helmets Standard paper sizes revisited A growing investment