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impossible certain
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DRAFT-‐This is a work in progress. MAG wriAng project 2012-‐2013
• Many games use a tossed coin (heads and tails) to decide who will go first eg.cricket • A spinner or coin toss provides an equal likelihood of choice
Part 2 • In student learning journal create a word bank
ü record the word probability as related to the word probable
ü likely to chance something will happen is very good
ü equally likely to chance is just as good that either of two things will happen
• Ask students to come up with their own definiAon of the word chance
• Use a spinner and model a graphic representaAon that represents this meaning
• ParAcipants will oOen use the ‘best of three’ idea to
increase the likelihood of an outcome-‐discuss whether this is likely to result in a fairer result • In maths we oOen use symbols-‐introduce students to
capital P as the maths symbol for probability-‐demonstrate how to write the probability of
tossing a coin and having it land on heads P(H)
Part 3 • Using the following experiments determine the outcome
(possible result) e.g. A spinner has 4 equal sectors coloured yellow, blue, green and red. What is the probability of landing on purple aOer spinning the spinner? It is impossible to land on purple since the spinner does not contain this colour.
• P (purple) = 0/4 = 0
• Students complete in learning journal. A teacher
chooses a student at random from a class of 30 girls. What is the probability that the student chosen is a girl?
• A glass jar contains 5 red, 3 blue, and 2 green jelly beans. If a jelly bean is chosen at random from the jar, then which of the following is an impossible event?
• Choosing a red jelly bean (A) • Choosing a blue jelly bean (B) • Choosing a yellow jelly bean (C) • None of these (D)
• A spinner has 7 equal sectors numbered 1 to 7. If you spin the spinner, then which of the following is a certain event?
• Landing on a number less than 7 (A) • Landing on a number less than 8 (B) • Landing on a number greater than 1 (C) • None of these (D)
Australian Curriculum Year 4 ACMSP092 Describe possible everyday events and order their chances of occurring ACMNA071 InvesAgate and use the properAes of odd and even numbers ACMNSP095 Select and trial methods of data collecAon, including survey quesAons and recording sheets Key Idea Probability is the chance or possibility that an event will happen.
Resources Pigs Might Fly by Emily Rodda, and Vocab Cards Random outcome generators, spinners, coins, dice Introductory Ac@vity Process-‐Review Probability Words In pairs imagine it is the first day of the school holidays. • You ask your mum or dad or friend whether you
can go to the park today. • What sorts of things might they say in reply? • Can you pick out the words which tell you how
likely is it that you will actually go to the park in each case?
• Can you put these words in an order from 'never' at one end to 'yes' at the other? (pair, pair, share)
4.1.6 Math Word Wall: familiar, unfamiliar, possible, impossible, event, order, chance, ‘least likely’, ‘most likely’, predict, compare, certain, uncertain, ‘equally likely’, ‘most likely’, ‘less likely’, likelihood, ‘chance experiment’, random, impossible, perhaps, chance
1. Ac@vity Process-‐Fair Choices Resources:hfp://nrich.maths.org/8426/index?nomenu=1
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• If a number is chosen at random from the following list
• what is the probability that it is a prime number?
• 2, 3, 5, 7, 11, 13, 17, 19 Ac@vity Process Recognising ‘unpredictability’ of some events Resources: Pigs Might Fly by Emily Rodda, Paper strips, 2 envelopes • Read chapter 1 aloud to class-‐The story opens with a
statement ‘I wish something would happen’. Rachel thinks her life ‘lacks, excitement….the challenge of the unlikely event, the unexpected’
• Sandy a family friend comes to visit and brings a drawing of Rachel astride a unicorn with several flying pigs. She wishes ‘things like that did happen to her, but believe it is apparently impossible’. Sandy tells her that ‘nothing that you imagine is totally impossible, it might be unlikely’
• Discuss the role of imaginaAon in likely and unlikely events
• Ask students to write a ‘wish’ e.g. ‘animals could speak’ on a strip of paper and place it in one of two envelopes marked likely or unlikely
• Open the envelopes with class wishes and sort them into
• Discuss the choices made when sorAng the wishes • What might vary your results?
impossible possible maybe
• Decide on range of the scale 1-‐5
• Listen/Look for word clues in the text. eg. havoc or disaster
• Use a dicAonary to look for synonyms which are equivalent in meaning to the chosen word. eg. havoc = chaos, confusion, catastrophe, disorder, loss.
• ‘had to wear a bag of fish and chips on his or her head in public at all @mes’
• Ask student to think of everyday events and compare them to the imaginary ones in the story eg. ‘wear bag of fish and chips’ with ‘no hat no play rule’
• Use a Venn diagram to sort the events into three categories-‐students to choose and jusAfy choice eg. certain, likely, unlikely
Ac@vity Process-‐’Pigs Might Fly’ Resources: Probability vocabulary cards developed in probable words • Write the statement ‘Pigs Might Fly’on the board and ask
students to brainstorm ideas about the likelihood of an unlikely/likely event happening.
• Record phrases and words randomly • Ask students to choose a spot across the room which
represents
how likely they feel this event might occur (use brainstorm ideas) • Ask students to explain why their choice is reasonable,
using appropriate language e.g. It is impossible for pigs to fly as they don’t have wings.
Part 2 • Retell with class a newspaper report from USA ‘ABC News
reported that a 300-‐pound pot-‐bellied pig flew on a US Airways flight from Philadelphia to Seafle because the animal was deemed a therapeuAc companion pet.’ The pig was recognised by the airline as a service animal that the owner could not fly without.
• Ask students if this would change where they are standing? • ‘Pigs might fly’ is a figure of speech that uses comparison to
such an extent as to suggest complete impossibility. Other examples are 'It is easier for a camel to pass through the eye of a needle...' and 'Make a mountain out of a molehill'.
• Lewis Carroll also used this figure of speech in Alice's Adventures in Wonderland, "I've a right to think," said Alice sharply... "Just about as much right," said the Duchess, "as pigs have to fly.”
Ac@vity process-‐’’PimpleboLom Theory Disaster’
Choose a scale criteria to idenAfy the UEF (unlikely Event Factor level of events during the Pimplebofom Theory Diaster. Display text of pages 36-‐42 on IWB/iPad/paper copy for students
impossible certain unlikely likely
catastrophe
chaos
loss
disorder
confusion
had to wear a bag of fish and chips on his or her head in public at all 9mes’
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How can I demonstrate my soluAon?
Apps for demonstra9ng
learning using screencas9ng Digital Learning-‐Assessment Probability Chance TLF ID S5111 This interacAve resource is a game in which the student responds to quesAons about idenAfying the possible outcomes of everyday events and predicAng their chances of occurring. The student chooses a quesAon and then selects a matching Ale that
What might the event be?’
The event is 1/3.
What do I know about probability?
What kind of problem is it? Look for clues by working backwards from the answer.
Extension and Varia@ons (opportunity to work with small groups who might need further instrucAon, pracAce or extension)
1. iPad App-‐Probability
2. Create a Visual DicAonary
• Using the PicCollage App
• Create a visual diary entry
• This acAvity can be used for
assessment
Contexts for Learning
Inves@ga@on-‐Likely Events Focus on FISH problem solving ‘The probability of an event is 1/3. What might the event be?’
Answers the quesAon. Immediate feedback is given, and, when the answer is correct, the Ale turns over to reveal part of a picture. There is an accompanying PDF worksheet that orders the chances of possible everyday events and invesAgates events that have an even chance of the desired outcome occurring.
Slushy Sludger TLF ID L115 Use a vending machine to squirt coloured 'slushies' into ice-‐cream cones. Work out which 'sludge events' are possible and then choose a matching probability word. Self Assessment Learning Journal. Use the resource ‘Take a Moment’ by Kath Murdock Model a ‘think aloud’ using either ‘Pavers & Pathways’ or ‘Pat on the Back’. Ask students to complete one
Background
As with all concept formaAon, it's important that learners meet fundamental ideas informally, well in advance of formal teaching. In terms of probability these fundamental ideas are those of fairness, and the familarisaAon of the language of chance.
Khan Academy Videos:
hfp://www.khanacademy.org/math/probability/v/basic-‐probability
Basic Probability
Simple Probability
Links to other MAGs
Certain Likely Unlikely
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