Teaching and Learning Plan – Permutations, Combinations & Probability
Lesson Title: Code-Breaker
Prior Knowledge:
Students should have covered the fundamental principle of counting before attempting
this activity.
Students do not require any prior knowledge of probability before beginning this
topic. The content has been designed as a general introduction to probability. Students
should have a general knowledge of Arithmetic before the lesson begins. The teacher
will also have to prepare for this class in advance by teaching general information
about a pack of cards, e.g. How many suits, names of suits, how many black cards,
red cards, Kings, Queens etc.
Learning Outcomes:
All pupils will be able to:
Arrange the letters and numbers in the code exercise to come up with a number of
possible permuations.
Count the number of cards in a certain suit/character to come up with the maximum
number of those cards that could be selected from a deck.
Some pupils will be able to:
Arrange the letters and numbers in the code exercise to come up with a ALL possible
permuations.
Derive an expression to represent the probability of choosing a certain suit/character
card when one card only is chosen from a deck.
A few pupils will be able to:
Come up with the formula for discovering the number of permutations possible from
a given set of data.
Derive an expression to represent the probability of choosing a more specific type of
card
(e.g. red Queen), when one card only is chosen from a deck.
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New Vocabulary:
Suit
Spades
Diamonds
Hearts
Clubs
Probability
Chance
Permutations
Arrangements
Limitations
Selections
Resources:
o
Sets of Colour-coded letter and number cards for the code-breaking activity.
o
(approximately 14 sets per group of 3 students)
o
Code-breaker activity sheet.
o
Sets of
4 number cards for the ATM pin activity.
o
(approximately 25 sets per group of 3 students)
o
ATM pin activity sheet.
o
Flashcards for terminology and symbols.
o
Deck of cards (one per 3 students).
o
Giant deck of cards
o
Deck of cards activity sheet.
Possible misconceptions/difficulties for students:
Students may have the misconception that codes cannot begin with the number zero.
They may have difficulty in bringing a logical method to the code exercise.
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Key teaching strategies for this topic:
The key strategies required to teach this topic are active, hands-on learning (students
dealing out cards, constructing codes, physically doing exercises during the lesson),
appealing to the students’ multiple intelligences (visual, kinaesthetic, logical),
constructivism (building on any prior general knowledge the students have of
pin-
codes, atm codes, chance, probability etc.).
Real life context:
This activity is very relevant to everyday life: Students selecting an atm code, mobile
phone pin code, security alarm code etc., and realising the number of permutations
available to them.

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- Spring '17
- Jane Smith