Making Predictions… · SHS2 Additional Mathematics

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.3 - Create and solve problems using the axioms and the laws of probability.

By the end of the lesson, learners can:

Create original probability problems that correctly apply the addition law, the multiplication law, or the axioms of probability to events involving friends, family, school life, or community situations.
Solve self-created and peer-created problems using the axioms of probability, including the axiom that 0 ≤ P(A) ≤ 1 and P(A) + P(A’) = 1.
Apply the multiplication law for independent events to find probabilities of combined outcomes such as “both happen” or “one happens and the other does not.”
Apply the addition law or the complement rule (P(at least one) = 1 − P(none)) to solve problems involving “at least one” or “either or” situations.
Verify the reasonableness of probability answers by checking that all results lie between 0 and 1 inclusive, and that probabilities of complementary events sum to 1.

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Curriculum details

Strand: Handling Data (Strand 4)
Sub-strand: Making Predictions with Data (4.2)
Content standard: 2.4.2.CS.1 - Apply the addition and multiplication laws and axioms of probability to solve real life problems. 2.4.2.LO.1 Solve problems using the axioms and the laws of probability. 2.4.2.LO.2 Solve real life problems using combination and permutation.
Indicator: 2.4.2.LI.3 - Create and solve problems using the axioms and the laws of probability.
Suggested placement: Semester 2, Week 17 (Week 37 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

indicator text - p.424: the page prints 2.4.2.AS.3 in the learning-indicator column as well as the assessment column. Filed as 2.4.2.LI.3 for the same reason as 2.4.2.LI.2
Curriculum reference: NaCCA curriculum document, p. 424

Exemplars (from the NaCCA curriculum)

Group work, Talk for Learning, and Building on what others say, Project-based Learning.
Learning Experience: Learners in groups create problems using the axioms and laws of probability.
Activity 1: Multiplication and addition laws Learners in groups lead each other groups to discuss and recall the axioms of probability and the multiplication and addition laws, create some probability problems and solve them.
) Example: The probabilities that two friends, Kojo and Yayra will be in school are and " " respectively. Find the probability that on a given day: .
- Kojo is absent from school, but Yayra is present.
- both are absent from school
- at least one of them will be in school.
Solution ) ! 𝑃(Kojo)= " , 𝑃(Kojo Absent)= " " ) 𝑃(Yayra)= , 𝑃(Yayra absent)= . .
! " ! a) 𝑃(Kojo absent, Yayra present)= " × . = . ! ) ) b) 𝑃(both absent)= " × . = !. ) !" c) 𝑃(at least one of them will be in school)= 1 − 𝑃(none in school) = 1 − !. = !.
Activity 2: Axioms and laws of probability Learners in groups discuss alternative ways of solving problems using the axioms and laws of probability and present their findings in class.
Teaching and Learning Resources:
- Real-life data samples from both the school community and/or outside the school community.
- ICT tools
Assessment (2.4.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.