Position and Transformation · JHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: B8.3.3.1.2 - Draw rotation image in a coordinate plane and determine the angle of rotation.

By the end of the lesson, learners can:

State the coordinates of object points and their corresponding image points under a rotation about the origin through 90°, 180° and 270°.
Draw the image of a given 2D shape on a coordinate plane after a clockwise or anti-clockwise rotation about the origin through a given angle.
Determine the angle of rotation (90°, 180° or 270°) when given the coordinates of an object and its image.
Use the rotation rules (x, y) → (-y, x), (x, y) → (-x, -y) and (x, y) → (y, -x) to find image points without drawing.
Apply rotation rules to solve word problems involving positions on a coordinate grid.

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Curriculum details

Strand: Geometry and Measurement (Strand 3)
Sub-strand: Position and Transformation (3.3)
Content standard: B8.3.3.1 - Perform a single transformation (i.e. rotation) on a 2D shape using graph paper (including technology) and describe the properties of the image under the transformation (i.e. congruence)
Indicator: B8.3.3.1.2 - Draw rotation image in a coordinate plane and determine the angle of rotation.
Suggested placement: Term 3, Week 7 (Week 31 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. 152
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g. 1. Rotate a shape through a given centre of rotation and angle of rotation using rotation rules.

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. Visible labels, values, and notation include: i. State the object points and its corresponding image points under a given rotation.; ii. Draw points of shapes under a clockwise or anti-clockwise rotation through a given angle; about the origin (90°, 180°, 270°).

i. State the object points and its corresponding image points under a given rotation.
ii. Draw points of shapes under a clockwise or anti-clockwise rotation through a given angle about the origin (90º, 180º, 270º).
E.g. 2. Determine the angle of rotation using the points of an object, its images and centre.