Irene McCormack Catholic College
Mathematics Learning Area
Year 9 Mathematics
Course 2 Program
2017
Resource Materials Pearson Mathematics 9 (Student eBook) Excel Year 9 Revision and Exam Workbook Mathspace
Assessments
SEMESTER ONE
TESTS (3) 21%
EPW (2) 14%
EXAM (Semester 1 Content Only) 10%
SUB TOTAL 45%
SEMESTER TWO
TESTS (3) 21%
EPW (2) 14%
EXAM (Semester 1 & 2 Content) 20%
SUB TOTAL 55%
YEAR TOTAL 100% Year 9 Level Description
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this year level:
Understanding includes describing the relationship between graphs and equations, simplifying a range of algebraic expressions, explaining the use of relative frequencies to estimate probabilities, and the use of the trigonometric ratios for right-angle triangles
Fluency includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments and developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms
Problem Solving includes formulating, and modelling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry, and collecting data from secondary sources to investigate an issue
Reasoning includes following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs
2 Year 9 Mathematics Course 2 Program Term 1
Exercises Australian Curriculum Content Week Content and Assessments Descriptor Resources Probability Review of Probability from Identify complementary events and use the sum of 9.5,9.6 year 8 probabilities to solve problems (ACMSP204) (Y8P) 14.1 (XL) 1 Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and' (ACMSP205) Understanding probability. List all outcomes for two-step chance experiments, 8.5 (Y8P) both with and without replacement using tree 8.6 (Y8P) Probability events. diagrams or arrays. Assign probabilities to 8.7 (Y8P) outcomes and determine probabilities for events 9.7 (Y9P) Representing probability (ACMSP225) EPW 1: 1- 3 Calculate relative frequencies from given or 14.2 (XL) Investigation Venn diagrams and Two- collected data to estimate probabilities of events 14.3 (XL) Probability way tables involving 'and' or 'or' (ACMSP226) 14.8 (XL) Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292)
Financial mathematics Percentages review. Solve problems involving the use of percentages, Recall 1 including percentage increases and decreases, with 1.1(Y9P) Buying and selling and without digital technologies (ACMNA187) 1.2 (Y9P) EPW 2: 3 - 4 Project, Cost Solve problems involving profit and loss, with and 5.5 (XL) of Living without digital technologies (ACMNA189)
Simple interest Solve problems involving simple interest Half-time 1 1.5 (Y9P) (ACMNA211) 5-6 5.1 (XL) 5.2 (XL) 5.3 (XL) Pythagoras’ theorem Pythagoras’ theorem and Investigate Pythagoras’ Theorem and its Recall 2 right-angled triangles 2.1 (Y9P) application to solving simple problems involving 2.2 (Y9P) Finding the length of the right angled triangles (ACMMG222)r 2.3 (Y9P) hypotenuse Half-time 2 2.4 (Y9P) Test 1 7-9 Finding the length of a (Week 5) shorter side Ch4 (XL)
Applications of Pythagoras’ theorem
Algebra Introducing index laws Extend and apply the index laws to variables, using Recall 3 using variables positive integer indices and the zero index 3.1 (Y9P) (ACMNA212) 3.2 (Y9P) More index laws and index Apply index laws to numerical expressions with Test 2 properties 10 integer indices (ACMNA209) (Week 9) (Not negative or fractional Ch3 (XL) indices)
3 Term 2
Australian Curriculum Content Exercises Week Descriptor and Content Assessments Resources
Algebra Scientific Express numbers in scientific notation (ACMNA210) Ch6 (XL) notation including 3.3 (Y9P) 1 negative indices Investigate very small and very large time scales and and time scales interval (ACMMG219)
Apply the distributive law to the expansion of algebraic 3.5 (Y9P) Expanding Half-time 3 2 brackets expressions, including binomials, and collect like terms Project Due where appropriate (ACMNA213) 3.6 (Y9P)
Factorising using Factorise algebraic expressions by identifying numerical 3.7 (Y9P) common factors factors (ACMNA191) 3.8 (Y9P) 3 Factorising by grouping in pairs
Measurement Area Calculate the areas of composite shapes (ACMMG216) Recall 1 Including 4.2 (Y9P) 4 composites and 13.1, 13.2 sectors (XL) Calculate the surface area and volume of cylinders and Half-time 4 Surface area solve related problems (ACMMG217) 4.3 (Y9P) 5 (NO pyramids) Solve problems involving the surface area and volume of 13.4,13.5 right prisms (ACMMG218) (XL) Calculate the surface area and volume of cylinders and 4.4 (Y9P) Volume and solve related problems (ACMMG217) Test 3 6 capacity 13.8, 13.9 Solve problems involving the surface area and volume of (Week 4/5) (No pyramids) right prisms (ACMMG218) (XL)
7-8 REVISION
8 EXAMS EXAM
Linear relationships Solving linear solve linear equations (ACMNA215) Recall 1 equations 5.1 (Y9P) 5.2 (Y9P) EPW 3: Travel 9 - 10 Solving problems Graphs using linear Ch9 (XL) equations
4 Term 3 Exercises Australian Curriculum Content Week Content and Assessments Descriptor Resources Linear relationships Coordinate Find the distance between two points located on a 5.3 (Y9P) geometry Cartesian plane using a range of strategies, including 5.4 (Y9P) graphing software (ACMNA214) Half-time 5 Find the midpoint of a line segment (interval) on the 9.6 (Y9P) Cartesian plane using a range of strategies, including graphing software (ACMNA294) Ch7 (XL) 1 -2 Direct Proportion Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
Gradient Find the gradient of a line on the Cartesian plane using a 5.5 (Y9P) range of strategies, including graphing software 5.6 (Y9P) Sketching linear (ACMNA294) 5.8 (Y9P) graphs using the Sketch linear graphs using the coordinates of two points gradient and y- Ch8 (XL) and solve linear equations (ACMNA215) Test 4 3 - 4 intercept (Week 3) Vertical and horizontal graphs
Trigonometry Properties of Classify triangles according to their side and angle 6.4 (Y9P) Triangles properties (ACMMG165) 5 Demonstrate that the angle sum of a triangle is 180° Transformations (ACMMG166) Review and enlargement Similarity and Use the enlargement transformation to explain similarity 6.5 (Y9P) similar triangles and develop the conditions for triangles to be similar 6.6 (Y9P) (ACMMG220) 6 - 7 Solving problems Ch12 (XL) using similar Solve problems using ratio and scale factors in similar triangles figures (ACMMG221)
Using Apply trigonometry to solve right-angled triangle 7.3 (Y9P) trigonometry to Half-time 7 Test 5 8 problems (ACMMG224) find side lengths CH10 (XL) (Week 7/8)
Using Apply trigonometry to solve right-angled triangle 7.4 (Y9P) trigonometry to problems (ACMMG224) 7.5 (Y9P) find angles 9 - 10 Applications of trigonometry
5 Term 4
Australian Curriculum Content Exercises Week Descriptor and Content Assessments Resources
Statistics Review of Basic Calculate mean, median, mode and range for sets of Ch15 (XL) calculations data. Interpret these statistics in the context of data (ACMSP171) 1 Describe and interpret data displays using median, mean EPW 4 and range (ACMSP172)
Investigating Identify everyday questions and issues involving at least Recall 8 data one numerical and at least one categorical variable, and 8.1 (Y9P) collect data directly from secondary sources (ACMSP228) 8.2 (Y9P) 2 Interpreting data 15.7 (XL)
Statistics from Construct back-to-back stem-and-leaf plots and 8.3 (Y9P) grouped data histograms and describe data, using terms including 8.4 (Y9P) ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282) Half-time 8 3-4 Comparing data Compare data displays using mean, median and range to sets describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283) Non-linear graphs Quadratic Graph simple non-linear relations with and without the Recall 9 relationships 9.1 (Y9P) use of digital technologies and solve simple related 9.3 (Y9P) 4 - 5 Test 6 Sketching equations (ACMNA296) parabolas using extension transformations
CAMP WILL OCCUR IN WEEK 6
Exponentials and Graph simple non-linear relations with and without the 9.4 (Y9P) 9.5 (Y9P) 7 hyperbolas use of digital technologies and solve simple related equations (ACMNA296)
7 REVISION
REVISION 7 - 9 EXAM EXAM
6 Year 9 Achievement Standard
Number and Algebra By the end of Year 9, students solve problems involving simple interest. Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and non-linear relations. Measurement and geometry They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of right- angled triangles. Statistics and probability Students compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data. Students calculate relative frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes. They construct histograms and back-to-back stem-and-leaf plots.
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