Proportional Reasoning · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.1.2.LI.1 - Apply the concept of ratios, rates and proportions to solve problems in financial mathematics, health, sports, etc.

By the end of the lesson, learners can:

Convert between ratio, fraction, percent and decimal forms of the same proportional relationship with accuracy.
Set up and solve proportions to find unknown quantities in financial mathematics problems, including VAT, E-Levy, discounts and simple interest.
Apply proportional reasoning to calculate Body Mass Index (BMI) and interpret the results for health advice.
Use rates and proportions to analyse sports statistics, such as goal-scoring rates, bowling averages or points per game.
Justify their choice of proportional method (ratio, rate or proportion) when solving a given real-life problem, explaining each step clearly.

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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.1 - Apply the concept of ratios, rates and proportions to solve problems in financial mathematics, health, sports, etc.
Suggested placement: Semester 1, Week 10 (Week 10 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)

Collaborative group activities: Using think-pair-share strategies, apply the understanding of the concepts ratio in fraction, percent, or decimal form to solve daily problems in financial mathematics, health, sports, etc.
As learners collaborate, bring up scenarios that require learners to be sensitive to the inter-relatedness of the various aspects of life.
Example: Using proportions to solve percent problems.
Exponential Percentages Using mini survey groupings, in collaboration with the Science Department, find the body mass indices of humans around us. Weight i.e., Establish the formula for finding the BMI of bodies as BMI = (Height) 2
and use the results to advise on appropriate weight control among community members.
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.1). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.