SHS1 Mathematics · Semester 1 Week 17: Patterns and Relations

Lesson notes

Learning Objectives

Indicator: 1.2.2.LI.1 - Extend the knowledge of the coordinates of two points to find the gradient and equation of a straight line.

By the end of the lesson, learners can:

Calculate the gradient of a straight line given the coordinates of two points on the line, using the formula m = (y₂ - y₁)/(x₂ - x₁).
Determine the equation of a straight line using the point-slope form y - y₁ = m(x - x₁) when given a point and the gradient.
Determine the equation of a straight line when given two points on the line.
Rearrange a linear equation into the form y = mx + c and state the gradient and y-intercept.
Apply the gradient and equation of a straight line to solve problems in real-life situations, such as comparing the steepness of ramps or roads.

Sign in with your phone number to read the full note and download the GES plan - free.

Sign in with phone number

Curriculum details

Strand: Algebraic Reasoning (Strand 2)
Sub-strand: Patterns and Relations (2.2)
Content standard: 1.2.2.CS.2 - Demonstrate understanding of the gradient and equation of a straight line, the magnitude of a line segment, and its applications in real-life situations. 1.2.2.LO.2 Determine the gradient and equation of a straight line and find the distance between two points on a straight line.
Indicator: 1.2.2.LI.1 - Extend the knowledge of the coordinates of two points to find the gradient and equation of a straight line.
Suggested placement: Semester 1, Week 17 (Week 17 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:

exemplars - p.80: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 80

Exemplars (from the NaCCA curriculum)

Using think-pair-share strategies, discuss the midpoint of a line segment using everyday real objects e.g., book lengths, classroom length, etc.
Examples: i. Compute the midpoint of the line segment whose endpoints are P (8, -16) and Q(4,-4). ii. Examine the value of b if the midpoints of P(3,7) and Q(5,b) are (4,-1), etc. Extend to evaluate and discuss the gradient of the specified form of the equation of a straight line and apply them to solve problems. iii. Compute the equation of a line which passes through the points (-2, -3) and (1, -1). iv. Write the equation of the line that passes through the point (3, -1) with a slope of 3. v. Determine the equation of a straight line that passes through the point (−2, 4) with gradient 1 − . 2 Evaluate the gradient of the line with equation 2𝑦 + 3𝒙 = 2, etc. vi.

Figure from the shs1 mathematics curriculum, printed page 80

 4
3
2
1 -3 -2 -1 0 1 2 3 4 5
-1 .
-2
. -3
-4
Teaching and Learning Resources:
- * GeoGebra * Algebraic tiles * Graph boards
- * Patterns * Calculator
- * Technology tools such as * Mobile phone * Computer
- * YouTube videos, etc.
Assessment (1.2.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.