Year 9 Mathematics Pathway 2 Program 2024 PDF

YEAR 9 MATHEMATICS PATHWAY 2 PROGRAM 2024 CONTENT DESCRIPTIONS RESOURCE KEYWORDS ASSESSMENT Review: in italics, Extension in fade Pythagoras’ Theorem...

YEAR 9 MATHEMATICS PATHWAY 2 PROGRAM 2024 CONTENT DESCRIPTIONS RESOURCE KEYWORDS ASSESSMENT Review: in italics, Extension in fade Pythagoras’ Theorem : Calculating hypotenuse TERM Investigate Pythagoras’ Theorem and its application PM 9 and sides (9) 1 to solving simple problems involving right-angled Chapter 2 : Surds approximation (9) Weeks triangles (ACMMG222) (9) 2.1 – 2.5 : Application problems (9) 1–2 : Pythagoras triples (9) START NAPLAN REVISION Using units of measurement Find perimeters and areas of parallelograms, : Circumference and arc trapeziums, rhombuses and kites (ACMMG196) (8) length of circle (8) : Perimeter of triangle and Use formulas to solve problems involving quadrilateral (8) circumference and area (ACMMG197) (8) : Area of triangle, Develop formulas for volumes of rectangular and quadrilateral and circle (8) triangular prisms and prisms in general : Volume of prism in general (ACMMG198) (8) (8) PM 9 Weeks Calculate areas of composite shapes (ACMMG216) : Area of sector (9) Chapter 4 2 – 5 (9) : Area of composite shapes 4.1 – 4.4 (9) Calculate the surface area and volume of cylinders : Surface area of prisms and and solve related problems (ACMMG217) (9) cylinders (9) Solve problems involving the surface area and : Volume of prisms and volume of right prisms (ACMMG218) (9) cylinders (9) : Inverse calculations (9) Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids : Surface area and volume (ACMMG242) (10) of composite solids (10) Real numbers Test 1 Use index notation with numbers to establish the : Index law with numbers (8) index laws with positive integral indices and the zero : Zero index (8) Week 6 index (ACMNA182) (8) : Index law with variables Apply index laws to numerical expressions with Tuesday (9) integer indices (ACMNA209) (9) 5th March : Negative indices (9) Extend and apply the index laws to variables, using : Simplify numerical (Area, SA, Weeks positive integer indices and the zero index PM 9 expressions using index Volume, 6 – 9 (ACMNA212) (9) Chapter 3 laws (9) Pythagoras’ 3.1 – 3.3 Express numbers in scientific notation (ACMNA210) Theorem) : Scientific notation (9) (9) : Express in terms of Investigate very small and very large time scales positive powers (9) NAPLAN and intervals (ACMMG219) (9) WEEKS 7 – 9 : Simplify algebraic Simplify algebraic products and quotients using expressions using index index laws (ACMNA231) (10) laws (10) Week Money and financial mathematics PM 9 : Percentage increase & 9 Solve problems involving the use of percentages, Chapter 1 decrease (8) including percentage increases and decreases, with 1.1, 1.2 : Profit and loss calculation and without digital technologies (ACMNA187) (8) (8)  CONTENT DESCRIPTIONS RESOURCE KEYWORDS ASSESSMENT Review: in italics, Extension in fade TERM PM 9 : Express amount as Solve problems involving profit and loss, with and 2 Chapter 1 percentage (8) without digital technologies (ACMNA189) (8) Weeks 1.5 1 – 2 Solve problems involving simple interest : Using I=PRT (9) (ACMNA211) (9) : Inverse simple interest questions (9) Statistics and Probability Identify complementary events and use the sum of : Complementary events (8) probabilities to solve problems (ACMSP204) (8) : Probability language (8) : Two-way tables and Venn Describe events using language of ‘at least’, diagrams (8) exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’ (ACMSP205) (8) : Use fractions, decimals or percentages to describe Represent events in two-way tables and Venn probability and relative diagrams and solve related problems (ACMSP292) frequency (9) (8) : Calculate experimental Calculate relative frequencies from given or probability of two steps Investigation collected data to estimate probabilities of events events (9) PM 9 1 : Calculate theoretical Weeks involving ‘and’ or ‘or’ (ACMSP226) (9) Chapter 8 8.6 – 8.7 probability of two steps 2 – 5 List all outcomes for two-step chance experiments, Week 3 events with or without both with and without replacement using tree replacement (9) Tuesday diagrams or arrays. Assign probabilities to : Use tree diagrams to list 30th April outcomes and determine probabilities for events sample spaces (9) (ACMSP225) (9) : Use probability tree diagrams (9) Describe the results of two- and three-step chance Sadler experiments, both with and without replacements, Unit 2C : Calculate probability of assign probabilities to outcomes and determine Chapter 2 three step events with and probabilities of events (ACMSP246) (10) without replacement (10) Unit 2D Use the language of ‘if...then’, ‘given’, ‘of’, ‘knowing : Mutually exclusive events Chapter 2 that’ to investigate conditional statements and (10) identify common mistakes in interpreting such : Write and calculate language (ACMSP247) (10) conditional probability (10) Patterns and algebra Extend and apply the distributive law to the : Distributive law (8) expansion of algebraic expressions (ACMNA190) (8) PM 9 : Expand brackets and Test 2 Chapter 3 collect like terms (8) Factorise algebraic expressions by identifying 3.5 – 3.6 : Factorise numerical factors numerical factors (ACMNA191) (8) Week 6 (8) Simplify algebraic expressions involving the four Sadler : Simplify algebraic Tuesday operations (ACMNA192) (8) Blue expression (+, -, ×, ÷) (8) 21st May Chapter 9 Solve linear equations using algebraic techniques (ACMNA194) (8) (Simple Weeks PM 9 : Binomial expansion (9) Interest, 6 – 8 Apply the distributive law to the expansion of Chapter 3 Indices, algebraic expressions, including binomials, and 3.7, 3.8, Scientific collect like terms where appropriate (ACMNA213) 3.4 : Factorise by grouping in Notation, (9) pairs (10) Probability) : Factorise by algebraic factors (10) : Transpose and substitute  CONTENT DESCRIPTIONS RESOURCE KEYWORDS ASSESSMENT Review: in italics, Extension in fade Weeks Expand binomial products and factorise monic into formulas (10) 6 – 8 quadratic expressions using a variety of strategies : Trinomial factorisation Cont. (ACMNA233) (10) with a=1 (10) : Difference of two squares Factorise algebraic expressions by taking out a (DOPS) (10) common algebraic factor (ACMNA230) (10) Substitute values into formulas to determine an unknown (ACMNA234) (10) Linear relationships : Plotting points from rules Plot linear relationships on the Cartesian plane with (8) and without the use of digital technologies : Solve linear equations (8) (ACMNA193) (8) : Distance between two Solve linear equations using algebraic and graphical points (9) techniques. Verify solutions by substitution : Midpoint between two (ACMNA194) (8) points (9) : Gradient (9) Find the distance between two points located on : Sketch linear functions the Cartesian plane using a range of strategies, given slope and y-intercept including graphing software (ACMNA214) (9) or given x & y- intercepts Weeks Find the midpoint and gradient of a line segment (9) 9 – 11 (interval) on the Cartesian plane using a range of : Determine linear rule strategies, including graphing software from table of values or PM 9 (ACMNA294) (9) graphically (9) Chapter 5 : Interpret graph of linear Sketch linear graphs using the coordinates of two 5.1 – 5.8 relationships (9) points and solve linear equations (ACMNA215) (9) : Simplify algebraic fractions Apply the four operations to simple algebraic TERM (10) fractions with numerical denominators (ACMNA232) 3 : Determine the rule given (10) Weeks (10) 1 – 2 Solve linear equations involving simple algebraic - Gradient and y intercept fractions (ACMNA240) (10) - Gradient and a point - Two points Solve problems involving linear equations, including - Parallel gradient those derived from formulas (ACMNA235) (10) - Perpendicular gradient Solve linear simultaneous equations, using graphical : Solve linear algebraic techniques (ACMNA237) (10) fraction equations (10) : Solve simultaneous Solve problems involving parallel and perpendicular equations graphically (10) lines (ACMNA238) (10) Weeks Geometric reasoning Test 3 3 – 6 Identify corresponding, alternate and co-interior : Angles and parallel lines angles when two straight lines are crossed by a (7) Week 3 transversal (ACMMG163) (7) : Congruency conditions of triangles (8) Tuesday Develop the conditions for congruence of triangles : Properties of 30th July (ACMMG201) (8) PM 9 quadrilaterals (8) Establish properties of quadrilaterals using Chapter 6 (Algebra, congruent triangles and angle properties, and solve 6.1, : Enlargement (9) Linear related numerical problems using reasoning 6.3 - 6.6 : Similarity conditions of Relationship) (ACMMG202) (8) triangles (9) : Ratio and scale factors (9)  CONTENT DESCRIPTIONS RESOURCE KEYWORDS ASSESSMENT Review: in italics, Extension in fade Use the enlargement transformation to explain : Correct mathematical similarity and develop the conditions for triangles notation and language (9) to be similar (ACMMG220) (9) : Similar triangle problems Weeks (9) Solve problems using ratio and scale factors in 3–6 similar figures (ACMMG221) (9) : Formulate proof for Cont. congruent triangles (10) Formulate proofs involving congruent triangles and : Formulate proof for similar angle properties (ACMMG243) (10) triangles (10) Trigonometry : Name sides in a right Use similarity to investigate the constancy of the angled triangle using a sine, cosine and tangent ratios for a given angle in reference angle (9) right-angled triangles (ACMMG223) (9) : Using sine, cosine and tangent ratios (9) Apply trigonometry to solve right-angled triangle problems (ACMMG224) (9) : Determine unknown sides PM 9 and angles using Weeks Chapter 7 7 – 8 Solve right-angled triangle problems including those trigonometry (9) involving direction and angles of elevation and 7.1 – 7.5 : Trigonometry problems depression (ACMMG245) (10) (9) : Simple bearings, angle of depression and elevation (10) Data representation and interpretation Investigate the effect of individual data values, : Types of data (8) including outliers, on the mean and median : Effects of outlier (8) (ACMSP207) (8) Investigate techniques for collecting data, including : Collect data and analyse Weeks census, sampling and observation (ACMSP284) (8) secondary data (9) 9 – 10 Investigate reports of surveys in digital media and : Construct back-to-back elsewhere for information on how data were stem-and-leaf plots (9) obtained to estimate population means and : Construct back-to-back medians (ACMSP227) (9) histograms (9) Test 4 : Describe shape of the TERM Identify everyday questions and issues involving at data distribution (9) 4 least one numerical and at least one categorical Week 9 : Compare and contrast Weeks variable, and collect data directly and from PM 9 Tuesday 10th mean, median, mode and 1–2 secondary sources (ACMSP228) (9) Chapter 8 September range (9) 8.1 – 8.4 Construct back-to-back stem-and-leaf plots and (Geometric histograms and describe data, using terms Reasoning, including ‘skewed’, ‘symmetric’ and ‘bi-modal’ Trigonometry) (ACMSP282) (9) Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283) (9) Determine quartiles and interquartile range : Determine quartiles and (ACMSP248) (10) IQR (10) Construct and interpret box plots and use them to : Construct box plots (10) compare data sets (ACMSP249) (10)  CONTENT DESCRIPTIONS RESOURCE KEYWORDS ASSESSMENT Review: in italics, Extension in fade Investigation 2 Weeks Exam Revision Week 3 3–5 Tuesday 22nd October Linear and Non-linear relationships : Application rates (9) : Direct proportion graphs Solve problems involving direct proportion. Explore (9) PM 9 the relationship between graphs and equations : Graph parabolas and Chapter 9 corresponding to simple rate problems interpreting information, 9.6, 9.1, (ACMNA208) (9) specifically x & y- 9.4 intercepts, turning point Exam Graph simple non-linear relations with and without and line of symmetry (9) Weeks the use of digital technologies and solve simple : Graph circles given center Week 5 5 – 8 related equations (ACMNA296) (9) and radius (9) Tuesday 5th November Expand binomial products and factorise monic : Trinomial factorisation quadratic expressions using a variety of strategies PM 9 with a=1 (10) (ACMNA233) (10) Chapter 9 : Difference of two squares 9.2 Solve simple quadratic equations using a range of (DOPS) (10) strategies (ACMNA241) (10) : Null factor law, solving quadratics (10) Money and financial mathematics : Derive compound interest Sadler Connect the compound interest formula to repeated idea (10) Purple applications of simple interest using appropriate : Use compound interest Chapter 2 digital technologies (ACMNA229) (10) formula (10) : Salary, commission, wages Weeks Calculate weekly or monthly wage from an annual (11) 9 – 10 salary, wages from an hourly rate, including situations involving overtime and other allowances PM 9 and earnings based on commission or piecework Chapter 1 (Apps 1.1.1) (11) 1.3, 1.4, 1.7 Resources PM 9 – Coffey, D., Pearson Mathematics 9, Pearson Australia Group Pty Ltd. Sadler Blue – Sadler, A.J., Understanding Mathematics – a resource series for West Australian Secondary Schools – Resource 2. Sadler Purple – Sadler, A.J., Understanding Mathematics – a resource series for West Australian Secondary Schools – Resource 4. Sadler Unit 2C – Sadler, A.J., A book for Unit 2C of the West Australian Mathematics course of study. Mathspace – www.mathspace.co