Here is what the KICD curriculum design asks for in Trigonometry, with a sample lesson plan, notes and an exit check you can read before you teach. In Fuma, the same lesson comes out of your own scheme of work, starting from the lesson your class has reached and dated to your term.
Aligned to the KICD curriculum designSample — review before you teach
What learners should be able to do
Specific learning outcomes, word for word from the KICD curriculum design.
a)identify angles and sides of right-angled triangles in different situations
b)identify Sine, Cosine, and Tangent ratios from a right-angled triangle in different situations
c)read tables of trigonometric ratios for acute angles
d)determine trigonometric ratios of acute angles using calculators
e)apply trigonometric ratios to calculate lengths and angles of right-angled triangles in different situations
f)appreciate the use of trigonometric ratios in real-life situations
Key inquiry questions
What is the relationship between angles and sides in a right-angled triangle?
A sample lesson plan: Identifying Sides of a Right-Angled Triangle
This is a sample. Read it and change it for your class before you teach it. In Fuma, everything stays a draft until you approve it.
Grade 9 · Mathematics · 40 minutes
identify the hypotenuse, opposite side, and adjacent side in a right-angled triangle relative to a given acute angle
draw and label the sides of right-angled triangles in different orientations
appreciate the need to identify the marked angle before naming the opposite and adjacent sides
A sample lesson plan
Time
Teacher
Learners
Introduction5 min
Teacher:
Display a large right-angled triangle with the right angle clearly marked.
Ask learners to point out the triangle's parts: vertices, sides, angles.
Question: Which side is longest? Why do you think so?
Learners:
Observe the triangle and name its parts.
Identify the right angle and the longest side.
Share ideas about why one side is longest.
Modelling Right-Angled Triangles10 min
Teacher:
Distribute straws of lengths 6 cm, 8 cm, and 10 cm plus clay to each group.
Instruct groups to form a triangle with one corner as a right angle.
Ask groups to check the corner opposite the longest side forms a right angle.
Mark one acute angle with a sticker or paper dot.
Ask learners to touch the side across from the marked angle.
Ask learners to touch the side touching the marked angle but not the longest side.
Learners:
Arrange straws into a triangle; press clay at corners to hold sides.
Use a set square or book corner to verify the right angle.
Point to the side opposite the marked angle.
Point to the side touching the marked angle but not the longest side.
Compare answers with another group.
Rotate the straw triangle and describe how sides change with the marked angle.
Drawing and Labelling Triangles in Different Orientations10 min
Teacher:
Draw three right-angled triangles on the board in different orientations.
Label one acute angle θ in each triangle.
Ask volunteers to colour the hypotenuse, opposite, and adjacent sides.
Give each pair a worksheet with blank right-angled triangles in various orientations.
Instruct pairs to draw and label H, O, A on each triangle.
Learners:
Observe the drawn triangles and the marked angle θ.
Volunteer to come to the board and point to hypotenuse, opposite, adjacent.
In pairs, complete the worksheet by labelling H, O, A.
Check each other's labels and discuss any disagreements.
Think-Pair-Share: Choosing the Correct Side Relationship10 min
Teacher:
Display a triangle with sides a, b, c and angle P on chart or tablet.
Ask learners to write H, O, A next to sides for angle P.
Change the marked angle to Q; ask learners to relabel sides.
Ask learners to write one sentence explaining their rule for side names.
Select pairs to explain their rule to the class.
Learners:
On mini-whiteboards or paper, write H, O, A for the given angle.
Relabel the same triangle when the marked angle changes.
Write a rule for naming each side.
Check rule with partner: adjacent must not be the hypotenuse.
Share one example where changing the angle changed the opposite side.
Shown: the first 35 minutes of the 40-minute lesson.
Sample teaching notes
Teaching notes are for you at the board: the subject knowledge and what to watch for.
Content Mastery for the Teacher
The one correct procedure — make it a routine learners recite:
1. Find the right angle first (the square corner). The side facing it is the hypotenuse — always, in every right-angled triangle, in every orientation. It is also the longest side, but longest is a consequence, not the definition. Never let a learner find the hypotenuse by picking the side that looks longest; on a diagram not drawn to scale, judging by eye can mislead.
2. Find the marked acute angle (the one given, or the one the question names).
3. The opposite side is the side that does not touch the marked angle at all — you can stand at the marked angle and look straight across to it.
4. The adjacent side is the side that touches the marked angle and is not the hypotenuse. It is the other arm of the angle.
Why the hypotenuse is special and cannot be named by the angle: the right angle is fixed at 90°, so the hypotenuse is the side across from it — a property of the triangle. The two acute angles are the ones that get marked, and each acute angle "sees" the triangle differently, so opposite and adjacent swap when you switch angles. This is the whole lesson in one idea: changing the marked acute angle swaps the opposite and adjacent sides. It is the same triangle, the same lengths, the same hypotenuse — only the two labels move.
Misconceptions and Corrective Moves
Watch-for 1: "Any side touching the marked angle is adjacent."
Why it forms: in earlier grades learners learned "adjacent" as a general word for "next to" — adjacent rooms, adjacent desks. They transfer that everyday meaning to geometry and treat the hypotenuse, which also touches the marked angle, as adjacent too.
How to surface it: during 'Modelling Right-Angled Triangles', ask each group to hold up their straw triangle and, without talking, point to the side they call adjacent when the sticker is on the angle between the 8 cm and 10 cm straws. Expect several groups to point to the 10 cm side (the hypotenuse) or wave vaguely at both touching sides.
A quick exit check, with answers
1.Triangle PQR has a right angle at R. Which side is the hypotenuse?
A. PQ
B. RQ
C. PR
D. Cannot be determined
Show answer
A. PQ
2.The hypotenuse can be correctly called the adjacent side because it touches the marked acute angle.
Show answer
False
3.Triangle ABC has a right angle at B, and angle θ is marked at C. Relative to θ, name: (a) the opposite side, (b) the adjacent side, (c) the hypotenuse. (1 mark each)
Show answer
(a) AB (b) BC (c) AC
4.A right-angled triangle XYZ has its right angle at Y. Explain how the labels adjacent and opposite swap when the marked angle changes from X to Z, and name one side that does not change its label.
Show answer
When the marked angle is X, the opposite side is YZ and the adjacent side is XY. When the marked angle changes to Z, the opposite side becomes XY and the adjacent side becomes YZ; the two labels swap. The hypotenuse XZ does not change its label because it is always the side opposite the right angle.
Outcomes and inquiry questions are quoted from the KICD curriculum design. The lesson plan, notes and exit check are Fuma's draft. Fuma is built from the KICD designs; KICD has not endorsed it.