Proportional Reasoning · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.1.2.LI.2 - Establish the relevance of ratios, rates and proportions in their day-to-day activities, make generalisations and apply them to solve real-world problems.

By the end of the lesson, learners can:

Explain how ratios, rates and proportions appear in at least three different everyday situations in their own lives, using appropriate mathematical vocabulary
Generalise the process of setting up a proportion from a word problem and solve for the unknown quantity
Apply proportional reasoning to convert between currencies using current exchange rates obtained from banks or forex bureaus
Justify the fairness or otherwise of a given financial decision (such as comparing mobile money charges or utility bills) using proportional comparisons
Present a short report on an exchange rate scenario, showing the mathematical working and the real-world implication of the decision made

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Curriculum details

Strand: Numbers for Everyday Life (Strand 1)
Sub-strand: Proportional Reasoning (1.2)
Content standard: 2.1.2.CS.2 - Demonstrate an understanding of proportional reasoning using mathematical connections among ratios, rates and proportions to solve daily problems, including compound interest, tax (VAT, E- Levy), utilities, depreciation, etc. 2.1.2.LO.2 Analyse the relevance of ratios, rates and proportions in solving date-to-day problems.
Indicator: 2.1.2.LI.2 - Establish the relevance of ratios, rates and proportions in their day-to-day activities, make generalisations and apply them to solve real-world problems.
Suggested placement: Semester 1, Week 11 (Week 11 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. 183

Exemplars (from the NaCCA curriculum)

In a collaborative and gender-responsive group, model strategies for extending the ideas of proportional reasoning to inter-country exchange rates.
Create scenarios to bring out moral lessons where learners come to the realisation that there is a reward in truth and honesty leading to responsible citizenship.
Using Project-based and Experiential Learning, task learners to; i. Visit and collect exchange rates-related data from banks and forex bureaus to solve current financial problems.
ii. One country's currency can be changed to another using exchange rates at banks or forex bureau. Explain that exchange rates are not fixed, and they change almost every day, etc.
Teaching and Learning Resources:
- * Geodot * Rubber bands * Computer
- * GeoGebra * Google search * Mobile phone
- * Calculator * YouTube videos, etc. * Geodot,
- * Rubber bands * Cardboards * Measuring instruments
Assessment (2.1.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.