Download Year 10 Course Outline

Year 10 Mathematics – General Program Overview
Topic(s)
Assessment
Weeks 1 – 4
Simple and Compound Interest
Test 1 – N&A
Investigation 1 – N&A
Weeks 5 – 9
Right Triangle Trigonometry
Test 2 – M&G
Investigation 2 – M&G
Weeks 1 – 4
Formulae and Solving Equations
Test 3 – N&A
Week 5
Semester One Exam
Exam – N&A and M&G
Week 6 – 10
Simultaneous Equations and Exponential Functions
Test 4 – N&A
Weeks 1 – 2
Univariate Statistics
Investigation 3 – S&P
Weeks 3 – 5
Probability
Test 5 – S&P
Weeks 6 – 10
Surface Area & Volume
Test 6 – M&G
Weeks 1 – 2
Bivariate Data
Investigation 4 – S&P
Weeks 3 – 5
Similar & Congruent Triangles
Test 7 – M&G and S&P
Weeks 6 - 10
Year 11 Preparation
Term 1
Term 2
Term 3
Term 4
Term 1, Weeks 1 – 4
Number: Simple and Compound Interest
Finance
 Review of decimals and
percentages
 Review finding
percentages of
quantities / expressing
quantities as a
percentage
Connect the compound interest formula to repeated applications
of simple interest using appropriate digital technologies
(ACMNA229)
EM Chapter 3
MQ Chapter 16
Dwyer Chapter 11
PM Chapter 1
B
– Complex loan and investment calculations
– Uses inverse calculations to solve for the principal in
compound interest
C


– Uses simple and compound interest formulae
– Rearrange the Simple Interest formula and use these to find P,
R&T
– Repeated use of simple interest to calculate compound interest
– Uses a variety of time formats (days/weeks/months etc) and
compounding frequency (annually, monthly, weekly etc)
Simple Interest formula
& related calculations
Compound Interest
formula
D
– Uses simple interest for all calculations
Number and Algebra mini-test (week 3)
Number and Algebra Test 1 (end of wk 4)
ClickView Resources:
https://clickv.ie/w/yxqf (Interest, Loans and Credit)
Number and Algebra
Investigation 1 (wk 3)
Term 1, Weeks 5 – 9
Measurement: Right Triangle Trigonometry
Right Trigonometry
 Review of Pythagoras’
theorem
 Review of
Trigonometry ratios
 Angle of elevation and
depression
Solve right angled triangle problems including those involving direction
and angles of elevation and depression (ACMMG245))
B
– Draws diagrams for word problems involving elevations
– Uses multiple steps to solve problems, including combinations of ratios
and Pythagorean Theorem
EM Chapter 4
MQ Chapter 5
Dwyer Chapter 12
PM Chapter 5
C
– Selects and uses the correct ratios to calculate unknown angles
D
– Selects and uses the correct ratios to calculate unknown sides
Measurement mini-test (wk 7)
M&G Test 2 (end of wk 9)
ClickView Resources:
Measurement and Geometry
Investigation 2 (wk 7)
https://clickv.ie/w/-yrf (Pythagorean Theorem: An Introduction)
Term 1, Week 10 & Term 2, Weeks 1 – 4
Algebra: Formulae and Solving Equations
Solving Linear Equations
 Techniques for solving
linear equations
Formulas
 Substitution into
formulas
 Solve linear equations
resulting from
formulas
Substitute values into formulas to determine an unknown (ACMNA234)
Solve problems involving linear equations, including those derived from
formulas (ACMNA235)
B
– Substitutes into formulas, identifying the form of the resulting equation,
and selects the appropriate method of solution.
C
– Substitutes into formulas and solves the resulting linear equation.
D
– Substitutes values into formulas to determine an unknown.
Algebra mini-test (wk 2)
Number & Algebra Test 3 (end of wk 4)
ClickView Resources:
https://clickv.ie/w/D0rf (Substituting Values into Formulae)
Term 2, Week 5
Semester One Exam
Number & Algebra and Measurement & Geometry
EM Chapter 1
MQ Chapter 4
Dwyer Chapter 2
PM Chapter
Term 2, Weeks 6 – 10
Algebra: Simultaneous Equations and Exponential Functions
Solving Simultaneous
Equations
 Graphical (including
using CAS calcs)
 Substitution
 Elimination
Solve linear simultaneous equations, using algebraic and graphical
techniques including using digital technology (ACMNA237)
Explore the connection between algebraic and graphical representations
of … exponentials using digital technology as appropriate (ACMNA239)
Dwyer Chapter 2
EM Chapter 3
MQ Chapter 20
Dwyer Chapter 14
PM Chapter 1
B
–
–
–
–
Distinguish between the rules of different exponential functions
Sketches exponential functions
Applies transformations to exponential functions
Graphs a pair of linear relations given in a variety of ways, writes the
simultaneous solution and justifies algebraically.
– Uses algebraic techniques (elimination and substitution) to solve a pair
of simultaneous linear equations.
Exponential Functions
 Rules from tables
 Graphing
 Simple growth and
decay applications
C
– Can identify the algebraic form of an exponential function
– Can identify the graphical form of an exponential function
– Graphs a pair of simple linear relations and writes the simultaneous
solution.
D
– Writes the simultaneous solution when given a graph of a pair of linear
relations.
Algebra mini-test (wk 8)
Number & Algebra Test 4 (end of wk 10)
ClickView Resources:
https://clickv.ie/w/P1rf (Simultaneous Equations on a Golf Course)
https://clickv.ie/w/i2rf (Basketballs, Parabolas and Circles)
PM Chapter 9
Term 3, Weeks 1 – 2
Statistics: Univariate Data
Univariate Data
 Boxplots
 IQR
 Median, Quartiles
 Outliers
Determine quartiles and interquartile range (ACMSP248)
Construct and interpret box plots and use them to compare data sets
(ACMSP249)
B
– Calculates the 5 number summary and uses it to draw B&W plots
– Identify outliers using UQ/LQ ± 1.5 x IQR
– Compares data on parallel B&W plots drawn from primary and
secondary data
ABS Census at School
website for extensive
resources
EM Chapter 9
MQ Chapter 13
Dwyer Chapter 13
PM Chapter 7
C
– Calculates quartiles & IQR for collected and/or real data
– Compares data sets by referring to the shape of the B&W plot
D
– Calculates quartiles for a small range of ordered data
Statistics mini-test (wk 2)
Statistics and Probability Test 5 (end of wk 5)
ClickView Resources:
Statistics Investigation 3
(Start wk 2, finish wk 3)
https://clickv.ie/w/A3rf (Sampling, Surveyng and Data Analysis)
https://clickv.ie/w/-3rf (Histograms and Dot Plots of Gym Membership)
Term 3, Weeks 3 – 5
Probability: Compound Events
Compound Events
 Two and three step
experiments
Describe the results of two- and three-step chance experiments, both
with and without replacements, assign probabilities to outcomes and
determine probabilities of events. Investigate the concept of
independence (ACMSP246)
B
– Lists outcomes for multi step experiments, with and without replacement
and assigns probabilities to the outcomes
– Uses two way tables to determine the probability of compound events
– Uses Venn diagrams to determine the probability of compound events
C
– Lists outcomes for multi step experiments
– Calculates probabilities for multi step experiments
– Events with outcomes that aren’t equally likely
D
– Lists outcomes for two step experiments
– Calculates probabilities for two step experiments
Probability mini-test (wk 4)
Statistics and Probability Test 5 (end of wk 5)
ClickView Resources:
https://clickv.ie/w/y4rf (Taking a Chance - Key Probability Concepts)
EM Chapter 8
MQ Chapter 12
Dwyer Chapter 8
PM Chapter 11
Term 3, Weeks 6 – 10
Measurement: Surface Area & Volume
Surface Area & Volume
 Surface area and
volume of prisms,
cylinders and
composite solids.
Solve problems involving surface area and volume for a range of prisms,
cylinders and composite solids (ACMMG242)
B
– Draws diagrams from word problems
– Solves problems involving composite solids made up of prisms
– Solves problems with non-right triangular prisms, where height needs to
be calculated first
C
– Uses appropriate formula to calculate SA & Vol of prisms (& prism like
shapes);
– rectangular prisms
– other quadrilateral prisms (trapezium or rhombus on the base etc)
– right triangular prisms
– cylinders
D
– Calculate SA & Vol of simple right prisms only
Surface Area mini-test (wk 7)
Volume mini-test (wk 9)
Measurement & Geometry Test 6
(end of wk 10)
ClickView Resources:
https://clickv.ie/w/S0pf (Surface Area of Solids)
EM Chapter 6
MQ Chapter 6
Dwyer Chapter 3
Term 4, Weeks 1 – 2
Statistics: Bivariate Data
Bivariate Data
 Scatterplots
 Direction, strength
Line of best fit
Evaluate statistical reports in the media and other places by linking claims
to displays, statistics and representative data (ACMSP253)
Use scatter plots to investigate and comment on relationships between two
numerical variables (ACMSP251)
EM Chapter 9
MQ Chapter 14
MQ Chapter 15
MQ Chapter 23
Dwyer Chapter 18
PM Chapter 7
Investigate and describe bivariate numerical data where the independent
variable is time (ACMSP252)
B
– Draws trend lines by eye, using mean point
– Uses trend line to make predictions
– Comments on reliability of predictions made from data, uses terms like
extrapolation and interpolation
– Describes relationships in bivariate and time series data in terms of
direction and strength
– Investigate some real world data from relevant social issues
C
– Describes the trend in the data when independent variable is time
– Describes the statistical relationship between two continuous variables
– Evaluates statistical reports from real world sources
D
– Draws a scatterplot for bivariate data
Bivariate data mini-test (wk 2)
M&G and S&P Test 7 (end of wk 5)
ClickView Resources:
https://clickv.ie/w/65rf (Scatterplots and Gym Training)
Statistics
Investigation 4 (wk 2)
Term 4, Weeks 3 – 5
Geometry: Similar & Congruent Triangles
Similarity and Congruence
 Similarity rules for
triangles
 Congruence rules for
triangles
 Using properties to
determine unknowns
Formulate proofs involving congruent triangles and angle properties
(ACMMG243)
Apply logical reasoning, including the use of congruence and similarity,
to proofs and numerical exercises involving plane shapes (ACMMG244)
B
– Draws a diagram to represent a familiar situation with similar triangles
and uses ratios to determine unknown values
– Draws a diagram from given information to determine congruence or
similarity
C
– Use SAS, SSS, AAS & RHS to determine congruence
– Use ratios and angles to determine similar triangles
D
– Use congruence to calculate unknowns in triangles
– Use ratios in similar triangles to determine unknowns
Geometry mini-test (wk 4)
M&G and S&P Test 7 (end of wk 5)
ClickView Resources:
https://clickv.ie/w/c6rf (Proving Congruent Triangles)
https://clickv.ie/w/96rf (Congruence and Similarity in Plane Shapes)
EM Chapter 2
MQ Chapter 10
Dwyer Chapter 17
PM Chapter 8
Term 4, Weeks 6 – 10
Year 11 Preparation
Select relevant content from the following areas (required for Applications and Essentials)
 Identifying types of numbers – counting, whole, integers
 Working with fractions – addition, subtraction, multiplication & division
 Rule of order
 Working with numerical indices, square and other roots
 Scientific Notation
 Rounding to various levels of accuracy
 Ratios – expressing situations as ratios, simplifying, problem solving
 Rates – best buys, comparing rates, expressing in simplest form
 Applications of percentages – percentage of an amount, one value as the percentage of the total,
commission
 Using formulae
 Area and perimeter of rectangle, triangle, parallelogram, trapezium, circle
 Using technologies – CAS calculators
SEMETER TWO
SEMESTER ONE
YEAR 10, 2017
MATHEMATICS ASSESSMENT SCHEDULE
ASSESSMENT
ITEM
Investigation 1 N&A
Test 1
N&A
Investigation 2 M&G
Test 2
M&G
Test 3
N&A
Exam 1 N&A,M&G
Test 4 Simul-Eg and
Exponentials N&A
Investigation 3 S&P
Test 5
S&P
Test 6
M&G
Investigation 4 S&P
Test 7MG & SP
Exam 2
Observation
Formative tests, etc
Term
Week
Weight
T1
T1
T1
T1
T2
T2
T2
wk 3
wk 4
wk 8
wk 9
wk 4
wk5
wk10
5%
7%
5%
7%
7%
12%
7%
T3
T3
T3
T4
T4
T4
wk2
wk 5
wk 10
wk 2
wk 5
5%
6%
6%
5%
4%-4%
15%
5%
total
100%