Math 10C Session 08
Alberta Grade 10 Mathematics course-first tutoring portal aligned to the Biology 30 delivery model.
Session 08: Linear Relations, Slope and Intercepts
Unit focus: M10C-D · KCO targets: M10C-D-KCO-01, M10C-D-KCO-02
Lesson material block: MB-OCP-MATH10C-08
1. Essential knowledge definitions
| Term | Definition |
|---|---|
| relation | A set of ordered pairs linking inputs to outputs. |
| function | A relation in which every input has exactly one output. |
| independent variable | The input variable, usually x, that is chosen or controlled. |
| dependent variable | The output variable, usually y, that depends on the input. |
2. Vocabulary / symbols
- relation: A set of ordered pairs linking inputs to outputs
- function: A relation in which every input has exactly one output
- independent variable: The input variable, usually x, that is chosen or controlled
- dependent variable: The output variable, usually y, that depends on the input
3. Prerequisite ladder
- Relation readiness: relation → ordered pair → independent variable → dependent variable
- Representation readiness: table of values → graph → relation → function
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:
- Move each example through all four representations: words, table, graph, equation.
5. Worked examples
Worked example: Slope from two points
Problem: Find the slope through (2, 5) and (6, 13).
- slope = (y2 - y1)/(x2 - x1)
- = (13 - 5)/(6 - 2)
- = 8/4
Answer: 2
Worked example: Read slope and intercept
Problem: State the slope and y-intercept of y = -2x + 7.
- Compare to y = mx + b
- m = -2, b = 7
Answer: slope -2, y-intercept 7
6. Guided practice
| Prompt | Answer |
|---|---|
| In d = 60t, which is the dependent variable? | d (distance) |
| Give the domain of the points at x = 1, 2, 3. | {1, 2, 3} |
| Is y = 3x + 2 a linear relation? | Yes |
7. Misconception contrast
| Misconception | Correct concept |
|---|---|
| Independent and dependent variables can be swapped freely. | The dependent variable depends on the independent one; the roles are fixed by the situation. |
| Domain and range mean the same thing. | Domain is inputs (x); range is outputs (y). |
8. Exit ticket
Items: M10C-D-ASM-01, M10C-D-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.