Applications of Expressions… · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.2.1.LI.3 - Analyse, model, and solve word problems of simultaneous linear equations involving numbers, age, etc.

By the end of the lesson, learners can:

Read a word problem carefully and identify the two unknown quantities to be represented as variables.
Translate word problems involving numbers and ages into a pair of simultaneous linear equations.
Solve the resulting simultaneous equations using either the elimination method or the substitution method, with correct working shown.
Interpret the solution in the context of the original word problem and verify that it satisfies both conditions given in the problem.
Model and solve at least one real-life word problem involving numbers or ages working in a mixed-ability group.

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Curriculum details

Strand: Algebraic Reasoning (Strand 2)
Sub-strand: Applications of Expressions, Equations and Inequalities (2.1)
Content standard: 2.2.1.CS.1 - Demonstrate knowledge and understanding of the concept of simultaneous equations involving two variables and apply it to solve every day-life problem. 2.2.1.LO.1 Solve linear equations in two variables using the elimination, substitution and graphical methods. 2.2.1.LO.2 Analyse, model, and solve simultaneous linear equations involving real-life problems.
Indicator: 2.2.1.LI.3 - Analyse, model, and solve word problems of simultaneous linear equations involving numbers, age, etc.
Suggested placement: Semester 1, Week 14 (Week 14 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:

content standard text - p.191: this sub-strand prints 2 learning outcomes (2.2.1.LO.1, 2.2.1.LO.2) against one content standard, which is what its scope-and-sequence row also promises, so 2.2.1.LO.2 has no content standard of its own; it is carried on this row with its competencies rather than dropped
Curriculum reference: NaCCA curriculum document, p. 196

Exemplars (from the NaCCA curriculum)

Using Talk for Learning strategy, review with the whole class the concept of linear equations involving word problems.
Collaborative Learning: Using think-pair-share activity, task learners to analyse, model and solve real-life problems involving numbers and age using any of the methods. Appreciate the need to treat each other fairly.
Example: The difference of twice one number and three times a second number is equal to 2, and the sum of these numbers is 11. Find the two numbers.
Solution: Learners in the various groups, through discussion, will come out with the equations.
i.e. let x be the first number, and y be the second number. Twice one number (the first number) is 2𝑥 Three times the second number is 3𝑦 The difference equals 2 gives 2𝑥 − 3𝑥 = 2 ... (1) The sum of these numbers is 𝑥 + 𝑦 = 11 ... (2)
Solving these equations simultaneously, the numbers are 𝑥 = 7 and 𝑦 = 4.
Example: The sum of the ages of Kwaku and Ama is 32. In two years' time, Kwaku will be three times as old as Ama. How old are they now?
Solution: Let Kwaku's age be 𝑥 and Ama's age be 𝑦 The sum of their ages 𝑥 + 𝑦 = 32 This means that 𝑥 = 32 − 𝑦 and 𝑦 = 32 − 𝑥 In two years' time, Kwaku's age will be +2. (I.e., 32 − 𝑦 + 2 = 34 − 𝑦) In two years time, Ama's age will be 𝑦 + 2. (I.e., 32 − 𝑥 + 2 = 34 − 𝑥) In two years time, Kwaku's age will be equal to three times Ama's age i.e., 𝑥 + 2 = 3(34 − 𝑥)
By simplifying 𝑥 = 25 this is Kwaku's age. To find Ama's age, substitute Kwaku's age into any of the equations. Therefore, Ama's age is 7.
Project-based Learning: In small mixed-ability/gender groups, solve direct and indirect real word problems consisting of simultaneous equations in two variables using all three methods.
Teaching and Learning Resources:
- * Geodot * Rubber bands * Computer
- * GeoGebra * Google search * Mobile phone
- * Calculator * YouTube videos, etc. * Geodot,
- * Rubber bands * Cardboards * Measuring instruments
Assessment (2.2.1.AS.3). The document marks no depth-of-knowledge level for this indicator.