Measurement of Triangles

Lesson notes

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.2 - Use special triangles and the unit circle to determine the geometrical and functional values of trigonometric ratios, including special angles.

Suggested placement

Semester 2, Week 6 (Week 26 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.171: 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
• exemplars - p.173: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 171

Exemplars (from the NaCCA curriculum)

Collaborative learning, experiential learning, and initiate Talk for Learning, Project-Based Learning.
Learning Experience: Use collaborative learning and experiential learning to conceptualise the functional values of trigonometric ratios, including special angles.
Activity 1:
- With the use of experiential learning, learners investigate the trigonometric functional values of angles.
- In collaborative groups, construct circles, assume that the radius is one (1) and label the coordinates of the terminal sides angle as (𝑥, 𝑦) 

From the unit circle, learners discover that the trigonometric ratios of the unit circle are 𝑠 = 𝑦, A ! ! 0 𝑐 = 𝑥, 𝑡 = 0 , 𝑐 = A , 𝑠 = 0 , and 𝑐 = A
- Learners, in collaborative groups, state the functional values of trigonometric ratios using the unit circle. 

Activity 2:
- Through collaborative learning, experiential learning, and brainstorming, learners identify the values of other trigonometric ratios.
- Learners in groups explore values trigonometric ratios using a circular model (Unit circle).

Activity 3: Learners work in groups to establish the trigonometric function values for 45° using a 45 − 45 − 90 triangle.

𝑐45° = 2 √2 𝑠45° = 2 𝑠45° = 2 √2 𝑐45° = 2 𝑡45° = 1 𝑐45° = 1
Activity 4: Learners work in groups to establish the trigonometric values for 30° and 60° using a 30 − 60 − 90 triangle.

𝜃 30° 60° 1 𝑠 √3 2 2 1 𝑐 √3 2 2 𝑡 √3 √3 3 𝑐 2 2√3 3 𝑠 2√3 2
3 𝑐 √3 √3 2
Activity 4: Research and group work: Learners to find alternative ways to deduce the functional values of the trigonometric ratios and share them with the class.
Teaching and Learning Resources:
- Inclinometer Protractor rule tape measure
- SHS mathematics curriculum
- Video clips
Assessment (1.2.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.