JHS1 Mathematics · Term 3 Week 7: Position and Transformation

Lesson notes

Learning Objectives

Indicator: B7.3.3.1.2 - Plot points and shapes (i.e. plane figures) on a coordinate plane and draw their images under reflection in given lines

By the end of the lesson, learners can:

Plot given points and plane figures accurately on a coordinate plane, labelling the x-axis and y-axis correctly.
Draw the image of a given shape when reflected in the x-axis (line y = 0), the y-axis (line x = 0), and the line y = x.
State and apply the coordinate rules for reflection: (a, b) maps to (a, -b) in the x-axis, (-a, b) in the y-axis, and (b, a) in the line y = x.
Compare the object and its image under reflection and recognise that reflection preserves shape and size (the image is congruent to the object).
Use graph paper accurately (and, where available, digital tools such as GeoGebra) to perform and verify reflections.

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Curriculum details

Strand: Geometry and Measurement (Strand 3)
Sub-strand: Position and Transformation (3.3)
Content standard: B7.3.3.1 - Perform a single transformation (i.e. reflection and translation) on a 2D shape using graph paper (including technology) and describe the properties of the image under the transformation (i.e. congruence, similarity, etc.)
Indicator: B7.3.3.1.2 - Plot points and shapes (i.e. plane figures) on a coordinate plane and draw their images under reflection in given lines
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. 73
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

Figure from the jhs1 mathematics curriculum, printed page 73

E.g. 1: Plot points and shapes (i.e. plane figures) with given coordinates in the number plane.
i. Plot the points A (3, 1), B (3, 3), C (4, 3), D (4, 2), E (5, 2), F (5, 3), H (6, 3), and I (6, 1).

E.g. 2: Identify points with given coordinates and lines (i.e. constant lines parallel to the x-axis or y-axis) in the number plane. Draw and label the axes of the coordinate plane and label the lines such as Line 1 is y-axis or x=0; Line 2 is x-axis or y=0; Line 3 is y=x; Line 5 is y = -1, etc.
E.g. 3: Plot given points (or shape) the number plane and draw its images under reflection in (i) the x-axis, (ii) y-axis and (iii) y=x
i. (a) Draw point A (-1, 1) as the image of point A (1, 1) under a 2
reflection in the y axis (or line x=0)
(b) Draw point P (1, -1) as the image of point A (1, 1) under a reflection in the x axis (or line y=0) and
(c) Draw point A2 (-1, 1) as the image of point P (1, -1) under a reflection in the line y=x.
ii. Draw triangle A'B'C' as the image of triangle ABC under the reflection x=0, y=0, y=x and any other line.
Compare the images
E.g. 4: Derive the coordinate rules
i. If (a, b) is reflected on the x-axis, its image is the point (a, -b)
ii. If (a, b) is reflected on the y-axis, its image is the point (-a, b)
iii. If (a, b) is reflected on the line y = x, its image is the point (b, a)
iv. If (a, b) is reflected on the line y = -x, its image is the point (-b, - a) NB: Reflection can occur over a line and/ or in a point.