JHS1 Mathematics · Term 2 Week 7: Variables and Equations

Lesson notes

Learning Objectives

Indicator: B7.2.3.1.1 - Translate word problems to linear equations in one variable and vice versa

By the end of the lesson, learners can:

Identify the unknown quantity in a word problem and represent it with a variable such as x.
Translate simple word problems involving addition, subtraction, and multiplication into linear equations in one variable.
Translate given linear equations into meaningful word problems.
Use flag diagrams to show the operations in a word problem and work backwards using inverse operations to find the value of the unknown.
Check their solutions by substituting the value back into the original equation.

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Curriculum details

Strand: Algebra (Strand 2)
Sub-strand: Variables and Equations (2.3)
Content standard: B7.2.3.1 - Demonstrate an understanding of linear equations of the form x + a = b (where a and b are integers) by modelling problems as a linear equation and solving the problems concretely, pictorially, and symbolically.
Indicator: B7.2.3.1.1 - Translate word problems to linear equations in one variable and vice versa
Suggested placement: Term 2, Week 7 (Week 19 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, Common Core Programme (JHS1-JHS3), 2023, p. 41
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1: Use a flag diagram for equations and their inverses to solve equations.
i. Think of a number, double it and subtract 7. The result is 41. What was the original number? The flag diagram is:

Figure from the jhs1 mathematics curriculum, printed page 41

i.e. 2x- 7 = 41 To solve the equation, move in the opposite direction and do the inverse

of the operations. 2x - 7 = 41 +7 +7
2x = 48
÷2 ÷2 x = 24
E.g.2: Translate word problems to linear equations.
i. The sum of the ages of two friends is 25, and the older one is 4 times that of the younger one. Write this as a mathematical sentence?
i.e. let the age of the younger one be x ∴the age of older one = 4x 4x + x = 25
ii. Adaako and Afrakoma shared 40 oranges. Afrakoma had 6 more than Adaako. Write a mathematical sentence for this word problem. i.e. let x represent Adaako's share. ∴ Afrakoma's share is x + 6 and their share put together gives 40. ∴ x + (6 + x) = 40
E.g. 3 Write word problems for given linear equations
i. x + x = 15 i.e. the sum of two equal numbers is 15
ii. 2x - 4 = 12 i.e. when 4 is taken away from 2times a certain number, the result is 12.
iii. 2 x = 4 3
i. e. two-thirds of a certain number is 4.