Shape and Space · JHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: B7.3.1.2.6 - Construct angles whose measures are 15˚ and 75˚.

By the end of the lesson, learners can:

Construct an angle of 75˚ at a given point on a line segment using a pair of compasses and a ruler only.
Construct an angle of 15˚ by bisecting a 30˚ angle that has been constructed first.
State the relationship between 75˚ and the angles 90˚, 60˚, and 30˚ in terms of construction steps.
Bisect a constructed angle of 75˚ to verify the accuracy of the construction.
Use correct geometric language (bisect, arc, vertex, arm) when describing and explaining construction steps.

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Curriculum details

Strand: Geometry and Measurement (Strand 3)
Sub-strand: Shape and Space (3.1)
Content standard: B7.3.1.2 - Demonstrate how to construct a perpendicular to a line from a given point, bisect a line, bisect angles, and construct angles of the following sizes: 30˚, 45˚, 60˚, 75˚
Indicator: B7.3.1.2.6 - Construct angles whose measures are15˚ and 75˚.
Suggested placement: Term 3, Week 1 (Week 25 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:

indicator text - p.57: the code is printed '7.3.1.2.6:' with no grade token
Curriculum reference: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 57
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1: Construct an angle of 15˚ by bisecting an angle of30˚ (i.e. bisect ∠AOD = 60˚ to obtain ∠AOC = 30˚ and then bisect ∠AOC = 30˚ to obtain ∠AOB = 15˚)

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: D; 15°; 170; 16o; 150; 10; BO; 120 110 100; 90; 100; 80; C; 140; o5!

E.g..2 Construct the following:
(i) ∠PQR = 7 1 ˚ 2
(ii) ∠ABC = 60˚
(iii) ∠KLM = 30˚
(iv) ∠RST = 15˚
E.g.3: Use a pair of compasses and a ruler to construct an angle of 75˚ at a point on a given line segment [i.e. construct a right angle ∠AOB = 90˚); bisect the arc MN and join O through Pto obtain ∠AOP 75˚]

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: 80; 60; Ojr; 10 160 150 140 130 120; 70; 100; O2I; 90; 120; 50; 140; 10.

E.g.4: Construct and bisect ∠PQR = 75˚