SHS1 Mathematics · Semester 1 Week 8: Proportional Reasoning

Lesson notes

Learning Objectives

Indicator: 1.1.2.LI.1

By the end of the lesson, learners can:

Construct visual models (including 10 by 10 grids and number lines) that show the equivalence between a given fraction, its decimal representation, and its percentage.
Convert any given fraction to a decimal and then to a percentage, and reverse the process from percentage to decimal to fraction.
State the general rule for converting between fractions, decimals, and percentages and justify it using a diagram.
Use mental mathematics vocabulary (plus, minus, times, divide, product, sum, difference) to perform quick conversions between fractions, decimals, and percentages.
Apply fraction, decimal, and percentage conversions to estimate and compare quantities in everyday household and personal finance situations.

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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.1 - Develop models to examine connections between and among fractions, percentages and decimal numbers and make generalisations.
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.
Curriculum reference: NaCCA curriculum document, p. 48

Exemplars (from the NaCCA curriculum)

Through Think-pair-share, explore properties of rational numbers from diagrams (such as Figure 6 above) to establish strategies for reviewing the connection between fractions and decimal numbers and solve real-life problems involving them.
Employ differentiated assessment and ensure values such as tolerance, truth, honesty, respect for others' views, etc., among learners.
Examples: i. Convert fractions to decimals and percentages and use these representations in estimations, computations, and applications. ii. Play mental mathematics games: Learners use simple mental strategies to perform the following.
a) Addition using words and phrases like plus, add, calculate the sum, increase a number by, and find the total.
b) Subtraction using words and phrases like minus, from a number take, find the difference, and what must be added to make.
c) Multiplication using words and phrases like 'times', 'multiply', 'find the product', 'square', and 'what must be divided by ... to give ....'
d) Division using words and phrases like 'divide', 'share', 'how many times does it go into?', and 'what must be multiplied by ... to give ...'
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.1). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.