Ratios and Proportion · B6 Mathematics

Lesson notes

Learning Objectives

Indicator: B6.1.4.1.1 - Use concrete models and pictorial representations to explain a ratio as a concept that shows the number of times one quantity can be obtained in another and write this symbolically and in its simplest form.

By the end of the lesson, learners can:

Use concrete objects (such as counters, bottle tops, or cut-out shapes) to demonstrate how many times one quantity fits into another and state the ratio symbolically.
Draw pictorial representations (shapes, groups of dots, or bar models) to show a given ratio and explain what the ratio means in words.
Simplify a ratio to its simplest form by dividing both terms by the highest common factor (HCF).
Write a ratio in the forms 1 : n and n : 1 when required.
Solve simple word problems involving ratios, expressing answers in simplest form.

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Curriculum details

Strand: Number (Strand 1)
Sub-strand: Ratios and Proportion (1.4)
Content standard: B6.1.4.1 - Demonstrate understanding of the concept of ratios and its relationship to fractions and to the multiplication and division of whole numbers
Indicator: B6.1.4.1.1 - Use concrete models and pictorial representations to explain a ratio as a concept that shows the number of times one quantity can be obtained in another and write this symbolically and in its simplest form
Suggested placement: Term 2, Week 6 (Week 18 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: Mathematics Curriculum for Primary Schools (Basic 4-6), 2019, p. 134
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g. 1. Use concrete objects and/or pictorial representations to explain ratio as a number which tells the number of times a quantity can be obtained in another. In the figures, the area of the shape A is 1 of the area of the 4 shape B; so they are in the ratio 1:4. Shape C is three times the size of A so the ratio of C to A is 3:1.
E.g. 2. Use concrete objects and/or pictorial representations to explain simplest form of a ratio. Shape C is made up of 6 squares and shape A is made up of 2 squares, the areas of the shapes C and A are in the ratio 6:2; and since C is three times A, the ratio 3:1 is the simplest form of 6:2. The simplest form of a ratio is obtained by dividing through by the highest common factor. The ratio of C to B is 6:8 and its simplest form is 3:4. E.g. Simplify (i) 10m : 1000km (ii) Write 4 : 12 in the form 1 : n (iii) Express 15 : 20 in the form n : 1.
E.g. 3. Solve simple problems that involve ratios and finding total ratios. E.g. (i) Out of 24 students in a class, 10 are girls. Find its simplest form the ratio of boys to girls. (ii) A boy's mass is 50kgs, and his sister's is 45kg. Find the ratio of their masses. (iii) If an orange drink is made from concentrate and water in the ratio 3:8, what fraction of the mixture is concentrate?