Download Year 9 Unit Plan 2016

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