Irene Mccormack Catholic College

Irene McCormack Catholic College

Mathematics Learning Area

Year 9 Mathematics

Course 1 Program

2017

Resource Materials

Assessments

SEMESTER ONE
TESTS (3) / 24%
EPW (2) / 16%
EXAM (Semester 1 Content Only) / 8%
SUB TOTAL / 48%
SEMESTER TWO
TESTS (3) / 24%
EPW (2) / 16%
EXAM (Semester 1 & 2 Content) / 12%
SUB TOTAL / 52%
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, andmodellingpractical situationsinvolving 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

Year 9 Mathematics Course 1 Program

Term 1

Week / Content / Australian Curriculum Content
Descriptor / Exercises and Resources / Assessments
Probability
1 / Review of Probability from year 8 / · Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)
· 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)
1- 4 / Understanding probability.
Probability events.
Representing probability
Venn diagrams and Two-way tables / · List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225)
· Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292)
Week / Content / Australian Curriculum Content
Descriptor / Exercises and Resources / Assessments
Financial mathematics
5-6 / Percentages review.
Buying and selling / · Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187)
· Solve problems involving profit and loss, with and without digital technologies (ACMNA189) / EPW 2: Project, Cost of Living
Test 1
(Week 5)
7 / 1.5 Simple interest / · Solve problems involving simple interest (ACMNA211)
Pythagoras’ theorem
8 - 10 / Pythagoras’ theorem and right-angled triangles
Finding the length of the hypotenuse
Finding the length of a shorter side
Applications of Pythagoras’ theorem / · Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222) / Test 2
(Week 9)

Term 2

Week / Content / Australian Curriculum Content
Descriptor / Exercises and Resources / Assessments
Algebra
1-2 / Introducing index laws using variables
More index laws and index properties
(Not negative or fractional indices)
Scientific notation including negative indices and time scales / · Apply index laws to numerical expressions with integer indices (ACMNA209)
· Express numbers in scientific notation (ACMNA210) / Project Due
Week / Content / Australian Curriculum Content
Descriptor / Exercises and Resources / Assessments
NAPLAN
2-4 / Revise basic skill for NAPLAN & do practice questions / Past NAPLAN papers & texts / EPW 2: Problem solving
Algebra
4 / Expanding brackets / · Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)
5 / Factorising using common factors / · Factorise algebraic expressions by identifying numerical factors (ACMNA191)
Measurement
6 / Area
Including composites and sectors / · Calculate the areas of composite shapes (ACMMG216)
6 - 7 / Surface area
(NO pyramids) / · 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) / Test 3
(Week 6)
7 - 8 / REVISION
8 / EXAMS / EXAM
Measurement
9 - 10 / Volume and capacity
(No pyramids) / · 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) / 4.4
Term 3
Week / Content / Australian Curriculum Content
Descriptor / Exercises and Resources / Assessments
Linear relationships
1 - 3 / Coordinate geometry
Direct Proportion / · Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (ACMNA214)
· Find the midpoint of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)
· Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208) / Test 4
(Week 3/4)
4 - 5 / Gradient
Sketching linear graphs using the gradient and y-intercept
Vertical and horizontal graphs / · Find the gradient of a line on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)
· Sketch linear graphs using the coordinates of two points (ACMNA215)
Trigonometry
6 - 7 / Similarity and similar triangles
Solving problems using similar triangles / · Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220)
· Solve problems using ratio and scale factors in similar figures (ACMMG221) / EPW 3
8 - 9 / Using trigonometry to find side lengths / · Apply trigonometry to solve right-angled triangle problems (ACMMG224) / Test 5
(Week 8/9)
10 / Using trigonometry to find angles
Applications of trigonometry / · Apply trigonometry to solve right-angled triangle problems (ACMMG224)

Term 4

Week / Content / Australian Curriculum Content
Descriptor / Exercises and Resources / Assessments
Statistics
1 / Review of Basic calculations / · Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171)
· Describe and interpret data displays using median, mean and range (ACMSP172)
1 - 2 / Investigating data
Interpreting data / · Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228) / EPW 4
2 - 3 / Statistics from grouped data
Comparing data sets / · Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282)
· Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283)
Non-linear graphs
4 - 5 / Quadratic: Sketching parabolas
Exponential: Sketch Graphs / · Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296) / Test 6
CAMINO CAMP WILL OCCUR IN WEEKS 6
7 / REVISION
8 - 9 / REVISION
EXAM / EXAM
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.