Measurement of Triangles · SHS1 Additional…

Lesson notes

Learning Objectives

Indicator: 1.2.2.LI.3 - Determine radian measure and apply the knowledge to solve practical problems of arc length.

By the end of the lesson, learners can:

Define a radian as the angle subtended at the centre of a circle when the arc length equals the radius of the circle.
Convert angle measures between degrees and radians using the relationships 180° = π radians and 360° = 2π radians.
State the radian measures of the special angles (0°, 30°, 45°, 60°, 90°, 180°, 270°, 360°) and recall their corresponding degree measures.
Use the formula s = rθ (where θ is in radians) to calculate arc length, radius, or central angle when given the other two quantities.
Solve practical word problems involving arc length in real-life situations such as road curves, bicycle wheels, and circular running tracks.

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Curriculum details

Strand: Geometric Reasoning and Measurement (Strand 2)
Sub-strand: Measurement of Triangles (2.2)
Content standard: 1.2.2.CS.1 - Demonstrate understanding of the measurement of triangles and radians. 1.2.2.LO.1 Describe diagrammatically and algebraically ways of representing problems involving angles of elevation and depression and solve related word problems. Identify values of the special angles, explain the radian measure orally and mathematically and find coordinates of the unit circle and their corresponding angles in the quadrants. 1.2.2.LO.2 Identify values of the special angles in degrees and radians and solve problems relating to the coordinates of the unit circle.
Indicator: 1.2.2.LI.3 - Determine radian measure and apply the knowledge to solve practical problems of arc length.
Suggested placement: Semester 2, Week 7 (Week 27 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.175: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
Curriculum reference: NaCCA curriculum document, p. 175

Exemplars (from the NaCCA curriculum)

Collaborative learning, Experiential Learning, and initiate Talk for Learning.
Learning Experience: Use collaborative learning and experiential learning and initiate Talk for Learning to discuss radian measure, unit circle and arc length.
Activity 1: Using Experiential and collaborative learning, learners discuss and share ideas on unit circle, radian measure and arc length.
- Learners in collaborative groups conceptualise 1 radian measure.

A labelled geometric diagram with its points, axes, measurements and construction marks visible.

O 𝜃 = , when 𝑠 = 𝑟, the radian measure is 1 3
- Learners use 𝑠 = 𝜃 to find arc length and solve practical problems.
- Learners in mixed-ability group investigate and brainstorm on how to find the length of the arc Z Z when 𝜃 is in degrees, that is = × 2𝜋 or "/(° × 𝜋 "/(°
Activity 2:
- Using collaborative learning, learners convert degrees to radians and vice versa.
- Learners recollect the relationship between 360° and 2𝜋, as well as 180° and 𝜋.
That is 360° = 2𝜋 and 180° = 𝜋
Through brainstorming and building on what others say, learners convert degrees to radians and vice versa.
\ That is, to convert from degrees to radians, multiply the given degrees by , and to convert from !1(° !1(° radians to degrees, multiply the given radian value by . \
Teaching and Learning Resources:
- Inclinometer Protractor rule tape measure
- SHS mathematics curriculum
- Video clips
Assessment (1.2.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.