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YEAR 9 MATHEMATICS UNIT: TERM 1 YEAR 9 UNIT OVERVIEW: PROBABILITY ASSESSMENT: EXAM UNIT DETAILS: Sample Space Experimental Probability Theoretical Probability (Lists, Tree Diagrams, Tables, Venn Diagrams) (relative frequency and expected values) (independent events, multiple events, complementary events, dependent events with and without replacement) Success Criteria PROBABILITY Strand Australian Curriculum Statement Construct sample spaces for single-step experiments with equally likely outcomes ACMSP167 (7) Assign probabilities to the outcomes of events and determine probabilities for events ACMSP168 (7) Identify complementary events and use the sum of probabilities to solve problems ACMSP204 (8) Represent such events in twoway tables and Venn diagrams and solve related problems ACMSP292 (8) List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays Assign probabilities to outcomes and determine No Learning Goal (I know I’ve got it when I can successfully complete the following exercises and teach someone else the concepts) 1 Describe and represent probability of an event. 2 Apply experimental probability formula to calculate the relative frequency of an event. 3 To construct a sample space using a list and calculate the theoretical probability 4 Construct a sample space using a table and/or tree diagram and calculate the theoretical probability of an event. Handout - 9 MQ Ex. 10A Handout – 9 MQ Ex. 10B Handout – 9 MQ Ex. 10C Handout – 9 MQ Ex. 10E 5 Handout – 10MQ Identify complementary events and apply sum of probabilities to calculate the probability of an event Ex. 10B and the probability of a complementary event. 6 Construct Venn Diagrams to calculate the probability of events occurring. 7 Define and identify independent and dependent events. Dwyer Textbook Ex. 14.8 Yr 8 Dwyer – Ex. 18.3 Handout – 10 Dwyer Ex. 8.3 Additional Extension Exercises Simpler Option Dwyer Textbook Chapter 14 Extra Option Handout – 10MQ Ex. 10A Handout – 10MQ Ex. 10D Dwyer Textbook Ex. 14.12 Year 8 Dwyer Ex. 18.9, 18.10 Chapter Review Ex. 14.14, 14.15 Maths Quest 1 YEAR 9 MATHEMATICS probabilities for events ACMSP225 Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’ or ‘or’ ACMSP226 8 Apply knowledge of sample space to calculate the probability of dependent events. Handout – 10 Dwyer Ex. 8.4 Handout – 10 Dwyer Ex. 8.5, 8.6 9 Apply probability formula and Venn Diagrams to calculate conditional probability. Chapter 9 Maths Quest 2 Chapter 10 Maths Quest 3 Chapter 10 YEAR 9 MATHEMATICS UNIT: TERM 2 YEAR 9 UNIT OVERVIEW: NAPLAN, PYTHAGORAS AND TRIGONOMETRY ASSESSMENT: EXAM UNIT DETAILS: Problem Solving Pythagoras Similar Triangles Trigonometry (NAPLAN, ICAS, Problem Solving) (is a triangle square, finding the hypotenuse and a shorter side, applications) (understanding, finding a side, investigation towards trigonometry) (finding the angle, side on top, side on bottom, applications) Success Criteria PYTHAGORAS AND TRIGONOMETRY NUMERACY Strand Australian Curriculum Statement NAPLAN and Problem Solving Resilience and independent thinking Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles ACMMG222 Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right angled triangles ACMMG223 Apply trigonometry to solve right angled triangle problems ACMMG224 No Learning Goal (I know I’ve got it when I can successfully complete the following exercises and teach someone else the concepts) 1 2 3 4 5 6 7 8 Apply numeracy concepts to solve problems. Explore Pythagorean Triads Understand and apply Pythagoras’s Theorem to identify if a triangle is ‘square’. Apply Pythagoras’s Theorem to calculate the hypotenuse of a right angle triangle. Apply Pythagoras’s Theorem to calculate a shorter side of a right angle triangle. Apply Pythagoras’s Theorem to calculate the length of a line on a Cartesian Plane. Calculate the side of a triangle using similar triangles. Identify the sides of a right angle triangle in relation to an angle. Additional Extension Exercises Past NAPLAN test papers Past ICAS test papers NAPLAN prep sets Problem Solving for Dummies Dwyer Textbook Ex. 7.1 Dwyer Textbook Ex. 7.2 Dwyer Textbook Ex. 7.3, 12.1, 17.1 Dwyer Textbook Ex. 7.4, 12.2 Dwyer Textbook Ex. 7.5 Dwyer Textbook Ex. 8.5, 8.6, 8.7 Dwyer Textbook Ex. 7.10 Ex. 8.11 Ex. 12.12 Ex. 17.12 Dwyer Textbook Ex. 12.3 Chapter Review Ex. 7.13, 7.13 Ex. 8.13, 8.14 Ex. 12.14, 12.15 Ex. 17.14, 17.15 YEAR 9 MATHEMATICS 9 10 11 12 13 14 Investigate and understand trigonometric ratios of a right angle triangle. Dwyer Textbook Ex. 12.4 Apply trigonometry (sin, cos, tan) to calculate the angle in a right angle triangle. Apply trigonometry (sin, cos, tan) to calculate the unknown side in a right angle triangle (when the unknown is the numerator in the ratio). Apply trigonometry (sin, cos, tan) to calculate the unknown side in a right angle triangle (when the unknown is the denominator in the ratio). Determine the correct trig ration to calculate the angles and sides of right angle triangle problems. Define and use terms of bearings, angles of elevation and depression to solve problems. Dwyer Textbook Ex.12.5, 17.2, 17.3, 17.4 Dwyer Textbook Ex. 12.6 Dwyer Textbook Ex. 12.7 Dwyer Textbook Ex. 17.5, 17.6, 17.7, 17.8 Pearson Mathematics Ex. 2.1 to 2.5 Ex. 7.1 to 7.5 YEAR 9 MATHEMATICS UNIT: TERM 3 YEAR 9 UNIT OVERVIEW: ALGEBRA AND LINEAR RELATIONSHIPS ASSESSMENT: EXAM UNIT DETAILS: Algebra Linear and Non-Linear Relationships (index laws, expanding and factorising, solving) (linear and quadratic equations and graphs, distance and midpoints) Success Criteria PATTERNS AND ALGEBRA Strand Australian Curriculum Statement Extend and apply the index laws to variables, using positive integral indices and the zero index ACMNA212 Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate, including factorisation and solving ACMNA213 Find the distance between two points located on a Cartesian plane using a range of strategies including graphing software ACMNA214 Find the gradient of a line segment (interval) on the Cartesian plane using a range of strategies, No Learning Goal (I know I’ve got it when I can successfully complete the following exercises and Additional Extension Exercises teach someone else the concepts) 1 Review calculating integers. 2 Simplify algebra using index laws. 3 Simplify algebraic expressions. 4 Expand the brackets using the distributive law. 5 Factorise an algebraic expression. 6 Expand binomial expressions. 7 Factorise terms from within terms. 8 Solve equations to calculate the unknown variable. 9 Find the rule for a linear equation. 10 Sketch linear graphs. 11 Sketch non-linear graphs. Dwyer Textbook Ex. 18.1, 18.2, 18.3 Dwyer Textbook Ex. 11.1 to 11.9 Dwyer Textbook Ex. 18.5, 18.6, 18.7, 18.8 Dwyer Textbook Ex. 18.9, 18.10 Dwyer Textbook Ex. 18.11, 18.12 Dwyer Textbook Ex. 18.13 Dwyer Textbook Ex. 18.14 Pearson Textbook Ex. 5.1 Dwyer Textbook Ex. 4.2, 4.3 Dwyer Textbook Ex. 4.4, 4.5 Dwyer Textbook Ex. 4.6, 4.7 Simple Option Chapter 2 instead of Chapter 18 Dwyer Textbook Ex 11.19 Ex. 2.16 Ex. 18.18 Ex. 4.12 Chapter Review Ex. 11.21, 11.22 Ex 2.18, 2.19 Ex. 18.20, 18.21 Ex. 4.14, 4.15 Ex 16.15, 16.16 Pearson Mathematics Ex. 3.1 to 3.8 Ex. 9.2 YEAR 9 MATHEMATICS including graphing software ACMNA294 Sketch linear graphs using the coordinates of two points ACMNA215 12 Find the distance between two points on a graph. 13 Calculate the midpoint of a line segment. 14 Calculate the gradient of a line. 15 Apply formulas to calculate the gradient, midpoint and length of a line. Dwyer Textbook Ex. 16.1, 16.2 Dwyer Textbook Ex. 16.3, 16.4, 16.5 Dwyer Textbook Ex.16.6, 16.7 Dwyer Textbook Ex. 16.8, 16.9 Maths Quest 3 Chapter 4 YEAR 9 MATHEMATICS UNIT: TERM 4 YEAR 9 UNIT OVERVIEW: MEASUREMENT ASSESSMENT: EXAM UNIT DETAILS: Measurement (area, surface area and volume, capacity) Success Criteria MEASUREMENT Strand Australian Curriculum Statement Express numbers in scientific notation ACMNA210 Calculate the areas of composite shapes ACMMG216 Calculate the surface area and volume of cylinders and solve related problems ACMMG217 Solve problems involving the surface area and volume of right prisms ACMMG218 No Learning Goal (I know I’ve got it when I can successfully complete the following exercises and Additional Extension Exercises teach someone else the concepts) Dwyer Textbook Ex. 11.10, 11.12, 11.14, 11.15 Dwyer Textbook Ex. 3.1, 13.1 1 Convert between ordinary numbers and scientific notation. 2 Review the formulas to calculate area. 3 Apply formula to calculate the area of composite Dwyer Textbook Ex. 3.2, 13.2 shapes. Apply formula to calculate the area of a sector of a circle. Handout 4 5 Apply formula to calculate the surface area of right prisms. 6 Apply formula to calculate the surface area of cylinders. Dwyer Textbook Ex. 3.5 Dwyer Textbook Ex. 3.6, 3.7, 3.8 7 Apply formula to calculate the area of shapes to solve problems. 8 Convert units of volume and capacity. 9 10 Apply formula to calculate the volume of prisms. Apply formula to calculate the volume of shapes to solve problems. Dwyer Textbook Ex. 3.9 Dwyer Textbook Ex. 13.3 Dwyer Textbook Ex. 13.4, 13.5 Dwyer Textbook Ex. 13.6 Dwyer Textbook Ex. 3.13, 3.14 Ex. 13.10 Chapter Review Ex. 3.16, 3.17 Ex. 13.12, 13.13 Pearson Mathematics Ex. 4.2, 4.3, 4.4