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Sparks
24: Probability
Place the outcomes suggested on a number line.
Add more if appropriate.(Use 3 parallel number lines,
if useful, to show equivalence between fractions,
decimals and percentages.) |
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Understand and use the probability
scale from 0 to 1.
- Find and justify probabilities
based on equally likely outcomes in simple contexts
- Identify all the possible mutually exclusive outcomes
of a single event
- Decide on relevant data for an enquiry and possible
sources |
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probability
chance
likelihood
outcome
event
certain
equally likely
random
probability line
data
data collection sheet
experiment |
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1. Collect examples
from pupils of events that are likely, certain,
no chance (etc); record on probability line.
Which probabilities of
outcomes can you describe more accurately?
(eg: heads on 1 die: fifty-fifty: ½).
Which probabilities of outcomes can't you describe
with a fraction? Why?
Highlight need for equally likely outcomes.
2. Bag of coloured counters – show counters.
Probability of each colour?
Record on number line.
Working definition of probability
of an event?
3. OHS
HD5b/2: Counter Cheating
Bag of 20 coloured counters. Don't show (6 sevens,
8 fives, 4 three, 2 ones).
'I have 20 counters in
the bag. 6 sevens, 8 fives, 1 three and 5 ones.'
Am I telling the truth?
Whole class experiment: complete table. Discuss
difference between theoretical and experimental
probability. |
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Finding
Theoretical Probability
1. Activities to find probabilities (counters, cards,
dice, coins …)
Eg: 1 – 49 bingo
game: Probability (fraction) of:
a) 44? b) a number in 20's? c) a number greaterthan
10? d) an odd number?
Position the fractions on a probability scale. Express
probabilities as fraction, decimal or percentage.
2. Discuss possible investigations,
such as Counter Cheating:
Working in pairs, place 10 counters using 4 different
numbers in a bag. Pupil 1 tells partner how many
of each number, and explains theoretical probability
for each number.
Pupil 2 chooses 1 counter at a time without looking,
replaces counter and records outcome in table, such
as in:
OHS
HD5b/2: Counter Cheating
Repeat 50 times.
Pupil 2 compares theoretical
and experimental probability, and decides whether
pupil 1 is cheating. Reverse roles.
Winner: pupils with most correct decisions.
Make some initial decisions about how to plan and
collect data to answer this question for next lesson. |
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What
is the probability of:
a red or black card?
a green card?
(defines 0: impossible and 1: certain)
a red card?
(even chance, ½ )
a 4 of hearts?
any 4?
any heart?
not a heart?
not a 4?
(using 1 – P(n) rule)
Use number line if helpful, and link to FDP equivalences. |
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- Plan how to collect
and organise small sets of data
- Design a data collection sheet or questionnaire
to use in a simple survey
- Collect data from a simple experiment and record
in a frequency table
- Estimate probabilities based on this data. |
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data
data collection sheet
experiment
outcome
event |
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Review decisions
made from previous lesson.
Check understanding of data collection process.
Agree on timing. |
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Deciding,
Planning & Collecting
Investigation such as Counter
Cheating (above):
- Finalise deciding and planning. Record briefly,
eg: on flow chart.
- Design data collection sheet.
- Collect data on data collection sheet. |
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Summarise main stages
for a statistical enquiry:
- decide on relevant data;
- research possible sources
(including newspapers, Internet, library,
survey);
- plan data collection sheet;
- collect data using sheet;
- calculate statistics;
- display using charts & diagrams;
- interpret;
- conclusion;
- & report findings. |
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