Download Chapter 4: Probability

Chapter 4: Probability
Stage 5.2 – Year 10
Unit length: 2 weeks
Strand:
Statistics and Probability
Substrand:
Rationale:
Students will develop a good understanding of experimental probability (or
relative frequency) while engaging in practical activities illustrating
probability. Students will learn to predict future outcomes and can compare
this with the theoretical probability of the event.
Teacher:
Outcomes:
Review of earlier work from Stage 4 and selections from:
Probability [Stage 5.2]
Dates taught:
A student:
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Content
statements:
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selects appropriate notations and conventions to communicate
mathematical ideas and solutions (MA5.2-1WM)
interprets mathematical or real-life situations, systematically applying
appropriate strategies to solve problems (MA5.2-2WM)
constructs arguments to prove and justify results (MA5.2-3WM)
describes and calculates probabilities in multi-step chance experiments
(MA5.2-17SP)
List all outcomes for two-step chance experiments, with and without
replacement, using tree diagrams or arrays; assign probabilities to
outcomes and determine probabilities for events (ACMSP225)
Describe the results of two- and three-step chance experiments, with
and without replacement, assign probabilities to outcomes, and
determine probabilities of events; investigate the concept of
independence (ACMSP246)
Use the language of ‘if … then’, ‘given’, ‘of ’, ‘knowing that’ to investigate
conditional statements and to identify common mistakes in interpreting
such language (ACMSP247)
Probability
________ to ________
Teacher reflection
Strengths
Weaknesses
Australian Signpost Mathematics New South Wales 10 Stages 5.1–5.2 Teaching Program — Chapter 4
Copyright © Pearson Australia 2014 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0054 8
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Resources:
•
•
•
Literacy:
complementary
event
dependent events
experimental
probability
independent
events
Foundation worksheet
Interactive lessons
Video
• Drag-and-drop activities
• Tutorial
multiplication rule
mutually
exclusive events
outcomes
probability
random
relative
frequency
sample space
theoretical
probability
trial
Other
two- and threestep chance
experiments
Australian Signpost Mathematics New South Wales 10 Stages 5.1–5.2 Teaching Program — Chapter 4
Copyright © Pearson Australia 2014 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0054 8
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Student book / eBook
4:01
4:02
Probability and
language
Two-step chance
experiments
Content dot points
• calculate probabilities of events where a
condition is given that restricts the sample
space, eg given that a number less than 5
has been rolled on a fair six-sided die,
calculate the probability that this number
was a 3
> describe the effect of a given condition
on the sample space, eg in the above
example, the sample space is reduced
to {1,2,3,4} (Communicating, Problem
Solving, Reasoning)
• evaluate the likelihood of winning a prize in
lotteries and other competitions (Problem
Solving, Reasoning)
Register
Technology
Drag-and-drop
Maths terms 4
Theoretical
probability
Interactive lesson
Mutually exclusive
events
• sample, with and without replacement, in
two-step chance experiments, eg draw two
counters from a bag containing three blue,
four red and one white counter
> compare results between an
experiment undertaken with
replacement and then without
replacement (Reasoning)
• record outcomes of two-step chance
experiments, with and without
replacement, using organised lists, tables
and tree diagrams
• calculate probabilities of simple and
compound events in two-step chance
experiments, with and without replacement
> explain the effect of knowing the result
of the first step on the probability of
events in two-step chance
experiments, with and without
replacement (Communicating,
Reasoning)
Australian Signpost Mathematics New South Wales 10 Stages 5.1–5.2 Teaching Program — Chapter 4
Copyright © Pearson Australia 2014 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0054 8
Resources and suggestions
Review the language of probability as
seen on p. 75.
Foundation worksheet 4:01Probability review
Investigation 4:01 – Probabilities
given as odds (p. 80). This
investigation can be used to discuss
the deceptive uses of probability in
gambling.
Discuss the difference between an event
involving replacement and an event
without replacement.
Apply relative frequency to predict future
experimental outcomes.
Design a device to produce a desired
relative frequency eg a four-coloured
circular spinner.
Investigation 4:02 – Experimental
probability without replacement (p. 84)
3
4:03
4:04
4:05
Three-step chance
experiments
The probability of
two- and three-step
events
The multiplication
rule for multi-step
events
• sample, with and without replacement, in
three-step chance experiments, eg draw
three counters from a bag containing three
blue, four red and one white counter
• record outcomes of three-step chance
experiments, with and without
replacement, using organised lists, tables
and tree diagrams
Encourage students to use a variety of
ways to display the possible outcomes
for an event: tree diagrams, lists, tables
etc.
• calculate probabilities of simple and
compound events in three-step chance
experiments, with and without replacement
> use knowledge of complementary
events to assist in calculating
probabilities of events in multi-step
chance experiments (Problem Solving)
Allow students to discover the quicker
method of finding the number of
outcomes by using the multiplying
technique.
• distinguish informally between dependent
and independent events
> explain the difference between
dependent and independent events
using appropriate examples
(Communicating, Reasoning)
• recognise that for independent events P(A
and B) = P(A) x P(B)
Have students repeat an experiment a
number of times to determine the
relative frequency of an event,
recognising that estimates become more
stable as the number of trials increases.
Investigation 4:04 – What is the chance
of a boy and a girl? (p. 94)
Interactive lessons
Independent events
(1)
Independent events
(2)
Distinguish between independent events
and dependent events. (p. 95)
Fun spot 4:05 – The Monty Hall
problem (p. 100)
Video
Combined
probability –
independent
Australian Signpost Mathematics New South Wales 10 Stages 5.1–5.2 Teaching Program — Chapter 4
Copyright © Pearson Australia 2014 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0054 8
4
4:06
The multiplication
rule for dependent
events
• critically evaluate conditional statements
used in descriptions of chance situations
>
describe the validity of conditional
statements used in descriptions of
chance situations with reference to
dependent and independent events,
eg explain why if you toss a coin and
obtain a head, then the probability of
obtaining a head on the next toss
remains the same (Communicating,
Reasoning)
>
identify and explain common
misconceptions related to chance
experiments, eg explain why the
statement 'If you obtain a tail on each
of four consecutive tosses of a coin,
then there is a greater chance of
obtaining a head on the next toss' is
incorrect (Reasoning)
Review
Highlight the difference between
independent and dependent events
when drawing tree diagrams
Make use of Maths terms 4. (p. 108)
Diagnostic test 4 – Use the right-hand
column to assist if further review is
required. (p. 109)
Assignment 4A – Exam-style questions
for revision (p. 111)
Assignment 4B – Working
mathematically problems (p. 112)
Assignment 4C – Use this cumulative
revision to review previous topics.
(p. 113)
Australian Signpost Mathematics New South Wales 10 Stages 5.1–5.2 Teaching Program — Chapter 4
Copyright © Pearson Australia 2014 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0054 8
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