SHS1 Additional Mathematics · Semester 2 Week 19: Making Predictions with Data

Lesson notes

Learning Objectives

Indicator: 1.4.2.LI.4 - Simplify permutation and combination expressions and solve related problems.

By the end of the lesson, learners can:

State the formulae for nPr and nCr from memory and explain the relationship nCr = nPr / r! in their own words.
Simplify expressions involving permutation and combination notation, such as (n-1)P3 / nP4, by applying factorial identities correctly.
Solve equations involving permutation and combination expressions to find the unknown value of n or r, showing all steps clearly.
Use the relationship between permutations and combinations to convert between the two forms when solving problems.
Verify solutions to permutation and combination equations by substituting the answer back into the original expression.

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Curriculum details

Strand: Handling Data (Strand 4)
Sub-strand: Making Predictions with Data (4.2)
Content standard: 1.4.2.CS.1 - Demonstrate knowledge of basic principles of permutation and combination and interpret probability in everyday life. 1.4.2.LO.1 Explain combination and permutation, state their difference and solve basic problems related to permutation and combination. 1.4.2.LO.2 Explain the terminologies in probability orally and find the relative frequency in a given experiment.
Indicator: 1.4.2.LI.4 - Simplify permutation and combination expressions and solve related problems.
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.
Curriculum reference: NaCCA curriculum document, p. 249

Exemplars (from the NaCCA curriculum)

Collaborative learning, Initiate Talk for Learning and Talk for Learning Approaches, Experiential Learning.
Learning Experience: Learners discuss the relationship between Combinations and Permutations.
Activity: Permutation and combinations theorems and formulae
- Initiate Talk for Learning, Experiential and Collaborative learning Approaches to support learners to use the relationship between permutation and combinations theorems and formulae to solve related problems
- Learners work in their groups to revise combinations and permutation theorems and formulae and use them to solve related problems
Example 1: Solve for n if (n-1) P 3 / n P 4 =1/9
Solution (n-1) P 3 = (n-1)!/(n-4)! and n P 4 = n!/(n-4)! (n-1) P 3 / n P 4 = (n-1)!/(n-4)! /(n!/(n-4)!) =1/n ∴n=9 1/n =1/9
Teaching and Learning Resources:
- Ludo dice, coins, playing cards, objects in a sac or bowl.
- YEAR TWO
Assessment (1.4.2.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding.