SHS1 Mathematics · Semester 1 Week 9: Proportional Reasoning

Lesson notes

Learning Objectives

Indicator: 1.1.2.LI.2 - Analyse daily activities/issues/businesses involving percentage change, including simple problems involving personal or household finance (such as utility bills, exchange rates, project budgeting, school fees, shopping, etc.)

By the end of the lesson, learners can:

Calculate percentage increase and percentage decrease of given quantities using the correct formula and interpret the result in a real-life context.
Analyse a utility bill or price change scenario to determine the percentage change and explain what it means for a household budget.
Apply percentage change concepts to solve problems involving exchange rates, discounts, and project budgeting.
Justify their choice of strategy when solving a percentage change problem and present their reasoning clearly to peers.
Work collaboratively in mixed-ability groups to analyse a personal or household finance scenario and present findings with accuracy and clarity.

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Curriculum details

Strand: Numbers for Everyday Life (Strand 1)
Sub-strand: Proportional Reasoning (1.2)
Content standard: 1.1.2.CS.2 - Demonstrate a conceptual understanding of proportional reasoning on percentages and use it to solve everyday life problems, including simple interest, discount, profit, loss, commission, etc. 1.1.2.LO.2 Create strategies for solving problems involving percentages of personal or household finances.
Indicator: 1.1.2.LI.2 - Analyse daily activities/issues/businesses involving percentage change, including simple problems involving personal or household finance (such as utility bills, exchange rates, project budgeting, school sees, shopping, etc.)
Suggested placement: Semester 1, Week 9 (Week 9 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.49: 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. 48

Exemplars (from the NaCCA curriculum)

Using think-pair-share activities, engage learners to undertake a project or group activities on proportional reasoning involving percent, simple/compound interests, discount, profit, loss, and tax, through problem-solving techniques. Employ differentiated assessment and ensure values such as tolerance, truth, honesty, respect for others' views, etc., among learners.
Examples: 1. Calculate the percentage increase and decrease of a quantity, i.e., if the Public Utility and Regulatory Authority announced an increment in the price of diesel per litre from GHC9.50.00 to GHC13.20, which later declined to GHC12.50. Find the percentage increase and as percentage decrease.
Solution: 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 3.7 Percentage increase = ∗ 100% = ∗ 100% 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 9.50 = 38.95%.
𝑑𝑒𝑐𝑟𝑒𝑚𝑒𝑛𝑡 0.7 Percentage decrease = ∗ 100% = ∗ 100% 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 13.20 = 5.30%
2. Gladys deposited GHC4,000.00 into a bank account, and the annual interest rate is 8%. How much is the interest after 4 years?
Teaching and Learning Resources:
- * Boards * Square or grid paper * Multi-base blocks
- * Algebraic tiles * Video clips
- * Cardboards * Fractional boards
- Models
- SHS Mathematics curriculum, etc.
Assessment (1.1.2.AS.2). The document marks no depth-of-knowledge level for this indicator.