Proportional Reasoning · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.1.2.LI.1

By the end of the lesson, learners can:

Explain the concept of a ratio as a comparison of two quantities of the same unit or dimension, and express it in the forms a:b or a/b, read as “a to b”.
Explain the concept of a rate as a comparison of two quantities of different units or dimensions, and express it as a quotient with a denominator of 1 unit where appropriate.
Distinguish clearly between ratios and rates by identifying the units (or lack of units) in each comparison.
Write ratios and rates from real-life situations involving quantities in Ghanaian settings, using correct mathematical vocabulary.
Work cooperatively in mixed-ability pairs and groups, respecting and appreciating the contributions of all members regardless of gender or background.

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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.1 - Demonstrate knowledge and understanding ratios, rates and proportions and use it to solve real-world problems. 2.1.2.LO.1 Establish the similarities among ratios, rates and proportions and use these to solve problems.
Indicator: 2.1.2.LI.1 - Explain the concepts ratios and rate as a comparison of quantities.
Suggested placement: Semester 1, Week 8 (Week 8 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.180: 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.180: 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. 180

Exemplars (from the NaCCA curriculum)

Using think-pair-share activities, explain the concepts ratio and rate as a comparison of measures of quantities with similar and/or different dimensions using related mathematical statements and real-life understanding situations.
Encourage the use of appropriate mathematics vocabulary for ratio and rate whiles respecting and appreciating how much contributions each individual can make to the lesson, leading to developing the value of tolerance and appreciation for diversity.
Using a blend of whole-class and group activities, review and model the concepts of ratio, rates and proportional reasoning to establish among their parallels by engaging all learners to work with partners to discover the following:
Ratio versus Rate i. Establish a ratio by comparing two quantities of the same unit of measure. This ratio can be 𝒂 expressed as a: b or and read as '𝒂 to 𝒃'. E.g., Write a ratio for the number of males to females 𝒃 in a country. ii. Establish the rate by comparing two quantities of the different units of measure. E.g., If Ananga earns GHȻ5000.00 for working 24 hours, then his average rate of pay per hour is worked as iii. GHs5000.00 GHs 308.33 = = GHs 308.33 24 hours 1 hour iv. Proportion: A proportion is a statement that compares two ratios or rates to be equal.
Application of ratio, rate and proportions a) Reflections: If a function reflects in the line 𝑥 = 𝑦 , then the function is 1:1 b) Rate of currency exchange between US dollars ($) and Ghana cedis (GHȻ) is GHȻ 10.04 per US dollar. How many GHȻ are equivalent to 5,275$? GHs 10.04 x = = $ 1 5,275 
⇒= x 10.04 × 5,375 = GHs 53,965.00
In the course of leading these activities, model the behaviour of gender responsiveness and have the ability to tackle injustice among learners, which learners emulate, leading to self/social awareness and responsible decisions.
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 4 Extended critical thinking and reasoning.
Skills of conceptual