SHS2 Mathematics · Semester 1 Week 19: Patterns and Relations

Lesson notes

Learning Objectives

Indicator: 2.2.2.LI.5 - Analyse, model, and solve real-life problems involving exponential growth.

By the end of the lesson, learners can:

Identify real-life situations that exhibit exponential growth and distinguish them from linear growth situations.
Model exponential growth problems using the formula Un = ar^(n-1), where a is the initial value and r is the growth factor.
Solve multi-step problems involving population growth, bacterial growth, and other exponential phenomena.
Justify their solutions by interpreting the meaning of the result in the context of the original problem.
Critically evaluate peer solutions, giving fair and constructive feedback during group presentations.

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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.5 - Analyse, model, and solve real-life problems involving exponential growth.
Suggested placement: Semester 1, Week 19 (Week 19 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.206: the equation text on this page is set in a CambriaMath subset whose /ToUnicode map doubles every letter and gets many of them wrong, and the glyph ids could not be lined up with the extraction to repair it, so any italic variable here may be doubled or be the wrong letter; read the page
exemplars - p.206: 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. 206

Exemplars (from the NaCCA curriculum)

Put learners into convenient groups and engage them in pairs to analyse and model real-life problems of sequence involving growth and discuss your findings.
Encourage learners to give fair criticisms to their colleagues' presentations. And in doing so, creating a sustainable discourse for learners to question norms, practices, and opinions; and to reflect on one's own values, perceptions and actions for decision-making as they engage in group and whole class activities on exponential growth.
Example: An island has a population of 1500 and is growing at a rate of 3% per year. What will the population be after 7 years?
Solution 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 → 𝑈𝑈 1 . 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌 1 → 𝑈𝑈 2 . 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌 2 → 𝑈𝑈 3 . ↓. 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌 7 → 𝑈𝑈 8 .𝑈𝑈 𝑛𝑛 = 𝑎𝑎𝑟𝑟 𝑛𝑛−1 𝑟𝑟 = 1.03, 𝑛𝑛 = 7 𝑎𝑎 = 1500. 𝑈𝑈 8 = 1500(1.03) 7 𝑈𝑈 8 = 1844.81
Teaching and Learning Resources:
- * Matchsticks * Cardboard
Assessment (2.2.2.AS.5). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.