Overview
This course develops a flexible, reflective approach to solving problems in middle-school mathematics. Topics include number, ratio, algebra, geometry, measurement, probability, and data, with emphasis on interpreting conditions, identifying constraints, selecting effective strategies, and communicating mathematical reasoning.
Students apply diagrams, tables, graphs, equations, estimation, pattern recognition, working backward, simpler cases, and systematic testing to unfamiliar problems. The course addresses integers, fractions, decimals, ratios, rates, percentages, proportional reasoning, equations, expressions, coordinate graphs, measurement, angle relationships, charts, summary statistics, and introductory probability. Emphasis is placed on multiple solution methods, mathematical modeling, appropriate tool use, validation of results, and distinguishing exact from approximate answers.
Learning Outcomes
- Analyze mathematical problems by identifying relevant information, constraints, assumptions, and required quantities.
- Represent mathematical situations using diagrams, tables, graphs, equations, and other appropriate models.
- Select and apply efficient strategies involving patterns, estimation, proportional reasoning, algebraic methods, and systematic case analysis.
- Solve problems involving numbers, ratios, rates, percentages, equations, geometry, measurement, data, and introductory probability.
- Evaluate the validity, precision, and reasonableness of mathematical solutions, including the distinction between exact and approximate results.
- Diagnose errors in mathematical reasoning and formulate constructive corrections.
- Synthesize multiple solution methods and defend the suitability of a selected approach.
- Communicate mathematical reasoning in clear, organized language using accurate notation and supporting representations.
- Reflect on unsuccessful approaches and revise strategies to persevere through unfamiliar problems.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Tutorial | 2 hours | Weekly | All semester |
| Workshop | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Problem-solving portfolio with written strategies and reflections | 20.00% |
| Assignment | Mathematical modeling assignment using representations and justified assumptions | 15.00% |
| Quiz | Quizzes (4 × 5%) | 20.00% |
| Test | Practical problem-solving test | 20.00% |
| Exam | Final examination | 25.00% |
Prerequisites
- Requirement 4 NCEA Level 2 Mathematics credits, externally assessed
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.