Strand: / Statistics and Probability / Substrand: / Probability
Rationale: / A good understanding of experimental probability (or relative frequency) will help students predict future outcomes. Students can then compare this with the theoretical probability of the event. This unit works best if practical, hands-on activities can be applied. / Teacher:
Outcomes: / Review of earlier work from Stage 4 and selections from:
Probability[Stages 5.1, 5.2]
A student:
•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)
•calculates relative frequencies to estimate probabilities of simple and compound events (MA5.1-13SP)
•describes and calculates probabilities in multi-step chance experiments (MA5.2-17SP) / Dates taught: / ______to ______
Teacher reflection
Strengths
Content statements: / •Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’ or ‘or’ (ACMSP226)
•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) / Weaknesses
Resources: / •Foundation worksheets• Challenge worksheets
•Drag-and-drop activities • GeoGebra activities
•Excel activities
Literacy: / chance event
complementary event
compound events / equally likely outcomes
experimental probability
mutuallyexclusiveevents
non-mutually exclusive events
outcomes / probability
random
relative frequency
sample
sample space / simulation
subjective probability
survey
theoreticalprobability
trial / Other
Student book / eBook / Content dot points / Register / Technology / Resources and suggestions
4:01The language of probability / Drag-and-drop
Maths terms 4 / Revise the language of probability on p. 84.
Students need to be familiar with a standard pack of cards. Bring a few packs into the classroom so students understand what a ‘deck’, ‘suit’, ‘royal card’ etc. look like.
Investigation 4:01–Rolling dice (p. 87). This investigation involves students having two dice each.
Make use of Maths terms 4. (p.111)
4:02Experimental probability / •repeat a chance experiment a number of times to determine the relative frequencies of outcomes
•predict the probability of an event from experimental data using relative frequencies / GeoGebra
Rolling a single dice a large number of times
Excel
Theoretical and experimental probabilities / Explain that experimental probability is based on observing a sample and is also known as relative frequency. Direct students to the blue box for a formal definition on p. 88.
Foundation worksheet 4:02– Experimental probability
Investigation 4:02– Tossing a coin (p. 91). This investigation involves students having a coin.
Encourage students to recognise that probability estimates become more stable as the number of trials increases.
Observe the photo on p. 91 and discuss the question in pairs.
4:03Theoretical probability / •identify theoretical probabilities as being the likelihood of outcomes occurring under ideal circumstances / Excel
Chance experiments / Foundation worksheet 4:03– Theoretical probability
Challenge worksheet 4:03–Probability: An unusual case
Read and discuss the cartoon (p. 92) and the photo (p. 94).
Investigation 4:03– Chance experiments (p. 97). This investigation involves students having a dice and a deck of cards.
Give students opportunity to recognise and explain differences between relative frequency (experimental probability) and theoretical probability in a simple experiment.
4:04Mutually and non-mutually exclusive events / •calculate probabilities of events, including events involving 'and', 'or' and 'not', from data contained in Venn diagrams representing two or three attributes,
•calculate probabilities of events, including events involving 'and', 'or' and 'not', from data contained in two-way tables / Drag-and-drop
Pack of cards
Rolling two dice / Ensure students grasp the difference between mutually and non-mutually exclusive events. Do this by reading through the explanation on p. 98.
Investigation 4:04– Chance happenings (p. 101). This investigation involves students having access to blank spinners, media releases and travel statistics.
4:05Using diagrams and tables / Design a Venn diagram and corresponding two-way table based on your class. E.g. Who has a Facebook account and Twitter account?
Fun spot 4:05– What are Dewey decimals? (p. 104)
4:06Two-step chance experiments / •sample, with and without replacement, in two-step chance experiments
•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 / Excel
Two-step chanceexperiments / Discuss the meaning of ‘without replacement’ and how this impacts the probability.
Investigation 4:06– Two-step chance experiments (p. 110). This investigation requires students having four blank identical pieces of paper and a container to put them in.
Review / Diagnostic test 4– Use the right-hand column to assist in remediation when errors occur. (p. 112)
Assignment 4A– Exam-style questions for revision (p. 113)
Assignment 4B–Working mathematically problems (p.114)
Assignment 4C– Use this cumulative revision to review previous topics. (p. 115)
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Australian Signpost Mathematics New South Wales 9 Stages 5.1–5.2 Teaching Program — Chapter 4
Copyright © Pearson Australia 2013 (a division of Pearson Australia Group Pty Ltd)ISBN 978 1 4860 0053 1