Patterns and Relations · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.2.2.LI.4 - Analyse, model, and solve real-life problems involving financial mathematics.

By the end of the lesson, learners can:

Identify whether a financial savings or earnings situation forms an arithmetic progression (AP) or geometric progression (GP) by examining the pattern of change.
Model real-life financial problems by writing the correct AP or GP formula (nth term or sum of n terms) for the given situation.
Solve problems involving regular fixed savings increments using the sum of an AP formula, showing all steps clearly.
Solve problems involving percentage salary increases or compound growth using the sum of a GP formula, showing all steps clearly.
Interpret financial results in real-life terms, such as stating total savings, total earnings, or first-year amounts in GHS, and reflect on honest handling of money.

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Curriculum details

Strand: Algebraic Reasoning (Strand 2)
Sub-strand: Patterns and Relations (2.2)
Content standard: 2.2.2.CS.1 - Demonstrate understanding of patterns and relations involving sequence and series, generate strategies for algebraic formulas, and use them in solving real-life problems. 2.2.2.LO.1 Explore patterns of a sequence using plane figures and find the nth and the sum of the nth term of an arithmetic and geometric progression. Analyse, model, and solve real-life problems involving financial mathematics and exponential growth.
Indicator: 2.2.2.LI.4 - Analyse, model, and solve real-life problems involving financial mathematics.
Suggested placement: Semester 1, Week 18 (Week 18 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.205: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 205

Exemplars (from the NaCCA curriculum)

Put learners in convenient groups and engage them to analyse and model real-life problems of a sequence involving finances. Initiate conversation on the need to be honest in handling money at home and in school.
Example 1: A man saves GHC16500 in ten years. In each year after year, he saved GHC100 more than he did in the previous year. How much did he save in the first year?
Solution: Sequence: a, a+100, a+200, a+300, ... 𝑑 = (𝑎 + 100) − 𝑎 = 100. 𝑛 = 10, 𝑆 10 = 16500 𝑛 𝑆 𝑛 = (2𝑎 + (𝑛 − 1)𝑑 2 𝑛 16500 = (2𝑎 + (10 − 1)100 2 𝑎 = 1200
Hence, he saved GHC1200 in the first year. Example 2: A job pays a salary of GHC25,000 for the first year. For the next 19 years, the salary increases by 5% each year. What is the total amount of money earned over the twenty years?
Solution 100+5 . 𝑟 = = 1.05, 𝑎 = 25000 𝑛 = 20 100 𝑆 20 = 25000 + 25000(1.05) + 25000(1.05) 2 + ⋯ + 25000(1.05) 20−1 .
𝑎(𝑟 𝑛 −1) . S 20 = 𝑟−1 25000(1.05 20 −1) .𝑆 20 = = GHC 826,648.85 1.05−1
Teaching and Learning Resources:
- * Matchsticks * Cardboard
Assessment (2.2.2.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.