Math 10C Session 04
Alberta Grade 10 Mathematics course-first tutoring portal aligned to the Biology 30 delivery model.
Session 04: Trigonometry Applied Modelling
Unit focus: M10C-B · KCO targets: M10C-B-KCO-01, M10C-B-KCO-02
Lesson material block: MB-OCP-MATH10C-04
1. Essential knowledge definitions
| Term | Definition |
|---|---|
| right triangle | A triangle containing one 90-degree angle. |
| hypotenuse | The side opposite the right angle; the longest side of a right triangle. |
| opposite side | The side directly across from the reference angle. |
| adjacent side | The side next to the reference angle that is not the hypotenuse. |
2. Vocabulary / symbols
- right triangle: A triangle containing one 90-degree angle
- hypotenuse: The side opposite the right angle; the longest side of a right triangle
- opposite side: The side directly across from the reference angle
- adjacent side: The side next to the reference angle that is not the hypotenuse
3. Prerequisite ladder
- Ratio readiness: right triangle → hypotenuse → opposite side → sine
- Solve a side: sine → diagram construction from word problem → reasonableness of trig answers
4. Mini-lesson explanation
- Concept launch linked to the session KCO targets.
- Worked model delivered with explicit think-aloud reasoning.
- Error analysis using this unit's common misconceptions.
Teacher explanation prompts:
- Require a labelled diagram before any calculation in a word problem.
5. Worked examples
Worked example: Write a sine ratio
Problem: opposite = 7, hypotenuse = 12. Write sin(t).
- sin = opposite/hypotenuse
- = 7/12
Answer: 7/12
Worked example: Find an angle
Problem: cos(t) = 0.5. Find t.
- Use the inverse cosine
- t = cos^-1(0.5)
Answer: 60 degrees
6. Guided practice
| Prompt | Answer |
|---|---|
| opposite = 5, adjacent = 12. Write tan(t). | 5/12 |
| Evaluate sin 30 degrees. | 0.5 |
| If tan(t) = 1, find t. | 45 degrees |
7. Misconception contrast
| Misconception | Correct concept |
|---|---|
| Opposite and adjacent are interchangeable. | Opposite is across from the angle; adjacent is beside it (not the hypotenuse). |
| Use sine for every triangle problem. | Choose the ratio from the sides you have (SOH-CAH-TOA). |
8. Exit ticket
Items: M10C-B-ASM-01, M10C-B-ASM-02
2/2 concept targets met with no high-risk misconception tags.
9. Semantic marking targets
accepted_concept_match, equivalent_wording, calculation_or_reasoning_evidence, unit_symbol_formula_accuracy, diagram_table_data_interpretation, misconception_identification, next_step_recommendation, human_review_flag
Scored against the accepted concept registry; equivalent wording accepted only when it preserves the concept.
10. Learner-report update
Fields updated: session_evidence, kco_mastery_delta, misconception_recurrence, next_lesson_recommendation, human_review_required
High-impact assessment/reporting decisions require human review.