Variables and Equations · JHS3 Mathematics

Lesson notes

Learning Objectives

Indicator: B9.2.3.1.2

By the end of the lesson, learners can:

State the meaning of solution sets for linear inequalities in one variable.
Draw open and closed circles on a number line to correctly represent strict and inclusive inequalities.
Graph the solution set of a given linear inequality on a number line, with the correct arrow direction.
Solve a linear inequality and then illustrate its solution set on a number line.
Interpret a number-line graph to write the corresponding inequality.

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Curriculum details

Strand: Algebra (Strand 2)
Sub-strand: Variables and Equations (2.3)
Content standard: B9.2.3.1 - Demonstrate understanding of single variable linear inequalities with rational coefficients including: • solving inequalities • verifying • comparing • graphing
Indicator: B9.2.3.1.2 - Illustrate solution sets of linear inequalities on the number line
Suggested placement: Term 2, Week 9 (Week 21 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. 190
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1 Illustrate and explain the inequality signs

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. Visible labels, values, and notation include: Less Than; #Ф); 5.5; 5; 4.5; 4; 3.5; open circle; arrow points to the left; Greater Than; 3; >; H; arrow points to the right; Less Than or Equal To; ≤; closed circle; Greater Than or Equal To.

E.g.2 Graph linear inequalities in one variable on a number line.

Wide colour mathematical teaching visual is organised as a number line with horizontal divisions, vertical... — A wide colour mathematical teaching visual is organised as a number line with horizontal divisions, vertical divisions, coloured regions. Visible labels, values, and notation include: Word Phrase; Inequality; x is less than 5; x<5; a is greater than 0; a is more than 0; y is less than or equal to 2; y is at most 2; m is greater than or equal to 3; m is at least 3; a > 0; Solution Set; +; 0; 12 34561; 3-2-1; Ф; 1; 2;.

E.g.3 Solve and graph linear inequalities on a number line.
i. -3x - 8 > -26 ii. 2x - 3 ≤ 19

Wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical... — A wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions, open white space around the main marks. Visible labels, values, and notation include: 3x - 8>-26; +8; 3x >-18; 3; x< 6; 4; 5; 6 7; 8; 2x ≤ 22; 2x; 22; 2; x ≤ 11; 10; x≤11; 14; *.

2x ≤ 22 2x 22 ≤
2 2 x ≤ 11
E.g.4 Solve and graph linear inequalities on a cartesian plane.
i. 2x ≥ 8 ii. 5y + 3 < 6 + iii. 7x <7 → 3× 7x < 2y 3 3
2x 8 7×3 ≥
2 2 5y - 2y < 6 - 3 7x 21 <
x ≥ 4 3y < 3 7 7 x < 3

∴ y < 1