1) The document outlines a lesson plan for a Grade 11 mathematics class on probability. It includes details on the topic, duration, learners, and classroom. 2) The pre-interactive phase involves eliciting prior knowledge on probability terms and concepts. Learners are expected to recall definitions and notations for mutually exclusive, inclusive, independent, and dependent events as well as complements. 3) The interactive phase engages learners in a probability problem using a deck of cards to distinguish between inclusive and exclusive events, and dependent and independent events. Learners draw and interpret a Venn diagram to represent the problem.

1. Lesson Planning
Subject: Mathematics Grade: 11
Date: 04 September 2015 Start: 9:30 End: 10:15
Lesson duration: 45 min
Topic: Probability
THE PRE-INTERACTIVE PHASE INVITATION PHASE
1. SITUATION ANALYSIS
WHO? - Ms. Ntshangase, Ms Ndlela, Ms Zulu and Mr Nonjola are experienced Student teachers. Their Grade 11 learners are all
second language English speakers. The class is a bit diverse containing both boys and girls from different cultural backgrounds and
there are Christians within. None of the learners is experiencing learning barriers. The student teachers realize that their learners have
sufficient background knowledge from Grade 10 on the terminology around probability.
WHERE? – In a classroom furnished in a way to facilitate class discussion. Learners sit as individuals which is ideal for the student
teachers to implement class discussion.
WHEN? – 30 minutes after 9 am, namely 9:30 – 10:15 am (45 min)
2. BASELINE/PRIOR KNOWLEDGE
The prior knowledge that learners should have?
 That the probability of an event is a real number between 0 and 1 that describes how likely it is that an event will occur.
 That two or more events are mutually exclusive when they have no outcomes in common.
Denoted as 𝑃( 𝐴 ∪ 𝐵) = 𝑃( 𝐴) + 𝑃( 𝐵)
 That two or more events are inclusive when they have outcomes in common.
Denoted as 𝑃( 𝐴 ∪ 𝐵) = 𝑃( 𝐴) + 𝑃( 𝐵) − 𝑃(𝐴 ∩ 𝐵)
 That two events are independent if the occurrence of one has no effect on the occurrence of the other, thus the probability of
the intersection of the events is equal to the product of the probability of the first event and the second event.
Denoted as 𝑃( 𝐴 ∩ 𝐵) = 𝑃( 𝐴). 𝑃(𝐵)
 And they are dependent if the occurrence of one event has effect on the occurrence of the other, thus the probability of the
intersection of the events is not equal to the product of the probability of the first event and the second event.

2. Denoted as 𝑃( 𝐴 ∩ 𝐵) ≠ 𝑃( 𝐴). 𝑃(𝐵)
 The complement of an event is the collection of all outcomes in the sample space that are not in an event.
Denoted as 𝑃( 𝐴′) = 1 − 𝑃(𝐴)
Teacher’s Activity Learner’s Activity
 Questions to ask to elicit prior knowledge
 We are going to use lotto tickets to invite learner’s
contribution that will lead us to discuss about the
probability of an event and other terms around
probability.
 What do learners understand by the probability of
an event?
 What other terms have they learnt about the
probability of events?
 Explain the terms that they have recalled and
provide with a mathematical notation which
represent the term.
 Possible answers expected
The prior knowledge that learners should have?
 The probability of an event is a real number between 0 and
1 that describes how likely it is that an event will occur.
 Two or more events are mutually exclusive when they have
no outcomes in common.
Denoted as 𝑃( 𝐴 ∪ 𝐵) = 𝑃( 𝐴) + 𝑃( 𝐵)
 Two or more events are inclusive when they have outcomes
in common.
Denoted as 𝑃( 𝐴 ∪ 𝐵) = 𝑃( 𝐴) + 𝑃( 𝐵) − 𝑃(𝐴 ∩ 𝐵)
 Two events are independent if the occurrence of one has
no effect on the occurrence of the other, thus the probability
of the intersection of the events is equal to the product of
the probability of the first event and the second event.
Denoted as 𝑃( 𝐴 ∩ 𝐵) = 𝑃( 𝐴). 𝑃(𝐵)
 And they are dependent if the occurrence of one event has
effect on the occurrence of the other, thus the probability of
the intersection of the events is not equal to the product of
the probability of the first event and the second event.
Denoted as 𝑃( 𝐴 ∩ 𝐵) ≠ 𝑃( 𝐴). 𝑃(𝐵)
 The complement of an event is the collection of all
outcomes in the sample space that are not in an event.
Denoted as 𝑃( 𝐴′) = 1 − 𝑃(𝐴)

3. 3. LESSON OUTCOMES
 Minds-on lessonoutcomes-
 At the end of the lesson- learners will know the difference between mutually exclusive and inclusive
events.
 Learners will know the difference between dependent and independent events.
 Learners will know what is meant by the complement of an event.
 Hands-on lessonoutcomes-
 At the end of the lesson- learners will be able to calculate the probability of an event.
 Learners will be able to analyze the given data and interpret it on a Venn diagram
 Learners will be able to identify and use the correct formula to calculate the probability of mutually exclusive, inclusive,
complementary, dependent and independent events.
 Hearts-on lessonoutcomes-
 At the end of the lesson- learners will be able to appreciate that probability applies to many instances of life
chances and they can make use of it to make their important future decisions.
THE INTERACTIVE LESSON PHASE (engagement with new content phase)
1. INTRODUCTION (ATTENTION FOCUS)
 What activity?
 Class discussion is used as learners engage with a probability problem such as the following
- One card is selected from a standard deck of 52 playing cards. What is the probability that the card is either a
heart or a face card? (Are events inclusive or exclusive?)
- Draw a Venn diagram to represent the above event.
- Are events of selecting either a heart or a face card dependent or independent?
- What is the complement of selecting a heart card?
- What is the complement of selecting a face card?

4.  How?
Teacher’s activity Learner’s activity
 The teacher will give out the question for
class discussion.
 Learners read the question problem.
 To activate the minds of the learners
Teacher’s activity Learner’s activity
 With the help of the learners we will
interpret the problem at hand using a real
deck of 52 cards.
 Post a prepared Venn diagram on the board
after the learners have got it right which
reflects the event where we were using a deck
of 52 cards with the help of the learners.
 Help and Watch while the teacher interpret
and demonstrates the problem at hand using a
deck of real cards.
 Learners observe the Venn diagram and help
to answer the following questions.

5. CONTENT (CoRe)
IMPORTANT MATHEMATICS IDEAS / CONCEPTS
a. What we intend the learners to know about the idea.
Big idea 1 Big idea 2 Big idea 3
 They can find the probabilities
of events.
 Find the probabilities of
mutually exclusive or inclusive
events.
 Find the probabilities of independent or
dependent events.
 Find the probability of the
complement of an event.
b. Why is it important for students to know this?
Big idea 1 Big idea 2 Big idea 3
 As you grow up you need to
think about your actions and
what the consequences of these
actions will be, thus it is
important to know how to use
probability when you make
decisions about your future.
 There are several major industries that
big users of probability, the first of
those is the gambling, sports and games
industry. E.g. probability applies to
many games of chance, you can
calculate probabilities that relate to the
game of roulette.
 A basic understanding of
probability makes it possible to
understand everything from
batting averages to the weather
report or your chances of being
struck by lightning. Probability is
an important topic in mathematics
because the probability of certain
events happening-or not
happening- can be important to us
in the real world.

6. c. What else do I know about this idea (that I do not intend learners to know yet)?
Big idea 1 Big idea 2 Big idea 3
 That you can present your given
data using the contingency table
and find all possible
probabilities.
 Probability is used in advertising in
magazines and newspapers.
 Probability definition- fairly
convincing, though not
absolutely conclusive, intrinsic
or extrinsic evidence of support
d. Difficulties/ limitations connected with teaching this idea.
Big idea 1 Big idea 2 Big idea 3
 Most religious learners may find
it against their religious belief if
they find that the probability
idea is also helpful for gambling.
 The demonstration and example doing
part may take long before lesson
consolidation and assessment may not
be observed by teacher in class on time.
 We could have done as many of
examples as we can if we had
enough time to present.
e. Knowledge about learners thinking which influences my teaching of this idea.
Big idea 1 Big idea 2 Big idea 3
We know that learners like money and
they would like to know the easiest way
of getting it without stealing, hence our
introduction focus their attention in that
manner, by asking them “who would
like to be a millionaire” and given lotto
ticket and asked “if they are definitely
sure they are going to get it right” so as
to elicit the desired concept out of their
mouth.
 Some learners are visual learners, thus
their understanding is deepened through
visual arts e.g. when engaging with new
content we use a real deck of 52 cards
and Venn diagram poster to interpret the
example problem at hand.
 Some learners, as they grow up
they tend not think of their
actions and end up not knowing
what the consequences may be,
thus it is important to know how
to use probability when you make
decisions about your future.

7. f. other factors that influence my teaching of this idea
Big idea 1 Big idea 2 Big idea 3
 Some learners may want to
pursue their careers in major
industries which use
probabilities like sports and
climatologists. Thus they may
want to know what they use to
predict scores and the weather
focus.
 Lotto is a worldwide known authorized
money winning game, thus the learners
know how it is played and this helps
them to elicit the concept desired by the
inviting teacher.
 The learners have prior
knowledge from grade 10
probability.
g. Teaching procedure ( and particular reasons for using these to engage with this idea)
Big idea 1 Big idea 2 Big idea 3
 Make lesson to be authentic so
as to deepen understanding and
meet the needs of visual learners.
 Learner centered teaching approach, to
meet the CAPS policy, to make
learners to be self-directed and self-
determined by finding information on
their own. (not spoon feeding)
 Class discussion to allow every
learner to participate and
exchange thoughts.
h. Specific ways of ascertaining learners’ understanding or confusion around this idea (including likely range of responses)
Big idea 1 Big idea 2 Big idea 3
 Bringing the visual material in
class to deepen understanding of
the event at hand e.g. a deck of
52 cards and lotto tickets
 At the beginning of the lesson we do
recap by asking learners to recall
what they have learned in grade 10
regarding probability, to see if
learners know what they have
learned and what they understand
about it.
 At the end of the lesson we do
recap, to see if learners know what
they have learned by asking them “
what have you learned regarding
probability” and what do you
understand about it.
2. RESOURCES (LTSM)(media)

8. What? How?
 Lotto tickets
 A deck of 52 cards
 Posters
 Chalk board
 Class and Homework handouts.
 To invite learner’s attention.
 To demonstrate the problem at hand during the
engagement phase
 To present the probability terminology and
Venn diagram representing the problem at
hand.
 To write the learner’s response during the
engagement phase.
 For learner’s assessment in class and also at
home.
3. Teacher and learning activities
Examples, class and homework
activities are attached at the back of the
lesson plan.
Solutions of examples and problems are
attached at the back of the lesson plan.
Homework exercise attached at the
back of the lesson plan.
4. Consolidation of the lesson
 What questions are you going to ask to elicit it?  What should learners know and the possible
answers expected from the learners?

9.  When do we say events are mutually exclusive?
 When do we say events are inclusive?
 When are event independent and dependent?
 What is the complement of an event? And give
the mathematical notation for each explanation.
 Two or more events are mutually exclusive when they
have no outcomes in common.
Denoted as 𝑃( 𝐴 ∪ 𝐵) = 𝑃( 𝐴) + 𝑃( 𝐵)
 Two or more events are inclusive when they have
outcomes in common.
Denoted as 𝑃( 𝐴 ∪ 𝐵) = 𝑃( 𝐴) + 𝑃( 𝐵) − 𝑃(𝐴 ∩ 𝐵)
 Two events are independent if the occurrence of one
has no effect on the occurrence of the other, thus the
probability of the intersection of the events is equal to
the product of the probability of the first event and the
second event.
Denoted as 𝑃( 𝐴 ∩ 𝐵) = 𝑃( 𝐴). 𝑃(𝐵)
 The complement of an event is the collection of all
outcomes in the sample space that are not in an event.
Denoted as 𝑃( 𝐴′) = 1 − 𝑃(𝐴)
 And they are dependent if the occurrence of one event
has effect on the occurrence of the other, thus the
probability of the intersection of the events is not equal
to the product of the probability of the first event and the
second event.
Denoted as 𝑃( 𝐴 ∩ 𝐵) ≠ 𝑃( 𝐴). 𝑃(𝐵)
THE POST-INTERACTIVE LESSON PHASE ( SUMMARY ADN INTERGRATION PHASE)
1. Assessment
 Assessment form
 Classwork and Homework
attached at the back.
 Assessment tool
 Memorandum attached at
the back.
 Assessment method
 Educator assessment.

10. 2. Expanded opportunities
 How has the
learner diversity
been addressed
 Gifted learners will have to
provide reasons where
asked to and slow learners
are ask not to if they see
they can’t provide with a
reason
 Enrichment
activities
Same activity but slow
learners do not provide
with reasons
 Remedial activities provided at the
back of the lessonplan.
Self -reflection on lesson
(Pap-eRs)
Strength Weaknesses What implications
will it have for
future lessons?