SHS2 Additional Mathematics · Semester 2 Week 20: Making Predictions with Data

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.3 - Model and solve real life problems involving combination.

By the end of the lesson, learners can:

Distinguish between situations where order matters (permutation) and where order does not matter (combination), and justify their choice with a clear reason.
State and apply the combination formula nCr = n! / [r!(n - r)!] correctly to compute the number of ways of selecting r objects from n distinct objects.
Solve multi-step combination problems that involve constraints, such as “must include” or “at least” conditions, by breaking the problem into separate cases and adding the results.
Model a real life situation from their own community as a combination problem, translate it into mathematical notation, and solve it correctly.
Present and explain their group’s combination problem and solution to the class 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.3 - Model and solve real life problems involving combination.
Suggested placement: Semester 2, Week 20 (Week 40 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.428: 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. 428

Exemplars (from the NaCCA curriculum)

Group work, initiate Talk for Learning, and building on what others say, Project-based Learning.
Learning Experience: Learners in groups create and solve real life problems involving combination.
Activity 1: Combinations Learners in groups apply the knowledge of combination where order does not matter to solve real life problems.
Example 1: In a certain examination, a candidate is to answer 6 out of 8 questions. How many choices does the candidate have if
- the first 2 questions must be answered
- at least three of the first four questions must be answered.
Solution:
- If the first two questions must are selected, then there are 6𝐶 , ways of selecting the next 4.
6𝐶 , = ,!)! = 15 ways /!
- At least 3 out of the first 4 questions gives 4𝐶 " × 4𝐶 " or 4𝐶 , × 4𝐶 ) 𝑖. 𝑒. ( 4 × 4) + (1 × 6) = 22
Example 2: A committee of 5 teachers is to be formed from 5 males and 4 females. Find the number of ways of forming the committee if
- there must be only 2 females
- one particular man must be included.
Solution
- The committee must comprise of 3 men and 2 women Thus giving us 5𝐶 " × 4𝐶 ) = 60 𝑤
- If we select that particular man, there are 8 persons remaining, and we need any 4 to make up the 5. 1∙7∙/∙. 𝑆 1 × 8𝐶 , = ,∙"∙) = 70 ways
Activity 2 Modelling and solving Combination problems Learners work in groups to create real life problems involving combination and solve them.
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.3). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.