SHS2 Additional Mathematics · Semester 2 Week 19: Making Predictions with Data

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.2 - Solve real life problems involving permutations.

By the end of the lesson, learners can:

Define permutation as an arrangement of objects where order matters, and distinguish it from a simple selection.
Apply the formula nPr = n! / (n - r)! to compute the number of ways to arrange r objects chosen from n distinct objects.
Solve problems involving permutations with restrictions, such as numbers divisible by 5 or objects that must occupy fixed positions.
Solve real life problems involving arrangements of people, objects, or digits, presenting their reasoning clearly.
Work collaboratively in groups to explain and justify their solutions to permutation problems using appropriate mathematical vocabulary.

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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.2 - Apply the concepts of permutation and combination 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.2 - Solve real life problems involving permutations.
Suggested placement: Semester 2, Week 19 (Week 39 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:

exemplars - p.427: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
Curriculum reference: NaCCA curriculum document, p. 427

Exemplars (from the NaCCA curriculum)

Group work, Talk for Learning, and Building on what others say.
Learning Experience: Learners in groups solve problems involving permutations.
Activity 1: Permutation Learners in groups recall the concepts of arrangements or permutation as arranging objects where order is very important, i.e. 𝑎 is different from 𝑏 and 𝑎, 𝑎, 𝑏 etc., are all different arrangements.
Example 1: How many numbers can be formed from 2,3,4 and 5, if each number must be divisible by 5?
Solution Think through the problem as follows: For 2,3,4,5:
- The digit is divisible by 5 = 1𝑃 ! = 1
- Two digits ending 5 = 3𝑃 ! = 3
- Three digits ending 5 = 3𝑃 ) = 6
- Four digits ending 5 = 3𝑃 " = 6 ∴Total number of arrangements= 1 + 3 + 6 + 6 = 16
Teaching and Learning Resources:
- Real-life data samples from both the school community and/or outside the school community.
- ICT tools
- YEAR THREE
Assessment (2.4.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.