JHS1 Mathematics · Term 2, Week 7

Variables and Equations

Lesson notes

Learning Objectives

Indicator: B7.2.3.1.2 - Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically.

By the end of the lesson, learners can:

Model linear equations of the form x + a = b and ax + b = cx + d using counters, integer tiles, or objects on a balance.
Solve linear equations by performing the same operation on both sides of the balance or tile model.
Describe, orally, the steps taken to solve a linear equation using concrete materials.
Record the solution process symbolically, showing each step of the operation.
Verify solutions by substituting the value back into the original equation.

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: B7.2.3.1.2 - Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically.
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. 43
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g. 1 Model and solve linear equations set with objects on a balance
i. Solution:

Balance model and worked equation subtract 3 from both sides of x + 3 = 7 to obtain x = 4. The wide colour table is... — A balance model and worked equation subtract 3 from both sides of x + 3 = 7 to obtain x = 4. The wide colour table is arranged with horizontal divisions, vertical divisions, coloured regions.

x + 3 = 7
-3 - 3
x = 4
ii. Solution:

Wide colour mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions,... — A wide colour mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions, coloured regions. The wide colour table is arranged with horizontal divisions, vertical divisions, coloured regions.

3x + 1 = 3x + 5
-3x - 3x 2x + 1 = 5
-1 - 1
2x = 4
x = 2
iii. Solution:

3y + 4 = 2y + 8
-2y - 2y y + 4 = 4 + 4
-4 - 4
y = 4
E.g. 2. Model and solve linear equations set with shapes on a balance
i. In each balance the mass of one shape is given in grams. Find the mass of the other shape.

ii. In each balance the mass of one rhombus is 12 grams. Find the mass of the pentagon.

Nearly square colour labelled teaching diagram uses vertical divisions, coloured regions. The nearly square colour... — A nearly square colour labelled teaching diagram uses vertical divisions, coloured regions. The nearly square colour labelled teaching diagram is arranged with vertical divisions, coloured regions. The nearly square colour labelled teaching diagram is arranged with vertical divisions, coloured regions.

iii. Use the three equations below to find the value of

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