| Curricular Competency |
Use mathematical vocabulary and language to contribute to discussions in the classroom |
Calculus 12 |
Communicating and representing |
| Keyword: discussions |
Elaboration: partner talks, small-group discussions, teacher-student conferences |
|
| Curricular Competency |
Represent mathematical ideas in concrete, pictorial, and symbolic forms |
Calculus 12 |
Communicating and representing |
| Keyword: Represent |
Elaboration: using models, tables, graphs, words, numbers, symbolsconnecting meanings among various representations |
|
| Curricular Competency |
Explain and justify mathematical ideas and decisions in many ways |
Calculus 12 |
Communicating and representing |
| Keyword: Explain and justify |
Elaboration: using mathematical arguments to convinceincludes anticipating consequences |
| Keyword: decisions |
Elaboration: Have students explore which of two scenarios they would choose and then defend their choice. |
| Keyword: many ways |
Elaboration: including oral, written, visual, use of technologycommunicating effectively according to what is being communicated and to whom |
|
| Curricular Competency |
Engage in problem-solving experiences connected with place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures |
Calculus 12 |
Understanding and solving |
| Keyword: connected |
Elaboration: through daily activities, local and traditional practices, popular media and news events, cross-curricular integrationby posing and solving problems or asking questions about place, stories, and cultural practices |
|
| Curricular Competency |
Solve problems with persistence and a positive disposition |
Calculus 12 |
Understanding and solving |
| Keyword: persistence and a positive disposition |
Elaboration: not giving up when facing a challengeproblem solving with vigour and determination |
|
| Curricular Competency |
Apply flexible and strategic approaches to solve problems |
Calculus 12 |
Understanding and solving |
| Keyword: flexible and strategic approaches |
Elaboration: deciding which mathematical tools to use to solve a problemchoosing an effective strategy to solve a problem (e.g., guess and check, model, solve a simpler problem, use a chart, use diagrams, role-play) |
| Keyword: solve problems |
Elaboration: interpret a situation to identify a problemapply mathematics to solve the problemanalyze and evaluate the solution in terms of the initial contextrepeat this cycle until a solution makes sense |
|
| Curricular Competency |
Visualize to explore and illustrate mathematical concepts and relationships |
Calculus 12 |
Understanding and solving |
| Keyword: Visualize |
Elaboration: create and use mental images to support understandingVisualization can be supported using dynamic materials (e.g., graphical relationships and simulations), concrete materials, drawings, and diagrams. |
|
| Curricular Competency |
Develop, demonstrate, and apply conceptual understanding of mathematical ideas through play, story, inquiry, and problem solving |
Calculus 12 |
Understanding and solving |
| Keyword: inquiry |
Elaboration: includes structured, guided, and open inquirynoticing and wonderingdetermining what is needed to make sense of and solve problems |
|
| Curricular Competency |
Think creatively and with curiosity and wonder when exploring problems |
Calculus 12 |
Reasoning and modelling |
| Keyword: Think creatively |
Elaboration: by being open to trying different strategiesrefers to creative and innovative mathematical thinking rather than to representing math in a creative way, such as through art or music |
| Keyword: curiosity and wonder |
Elaboration: asking questions to further understanding or to open other avenues of investigation |
|
| Curricular Competency |
Model with mathematics in situational contexts |
Calculus 12 |
Reasoning and modelling |
| Keyword: Model |
Elaboration: use mathematical concepts and tools to solve problems and make decisions (e.g., in real-life and/or abstract scenarios)take a complex, essentially non-mathematical scenario and figure out what mathematical concepts and tools are needed to make sense of it |
| Keyword: situational contexts |
Elaboration: including real-life scenarios and open-ended challenges that connect mathematics with everyday life |
|
| Curricular Competency |
Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number |
Calculus 12 |
Reasoning and modelling |
| Keyword: Estimate reasonably |
Elaboration: be able to defend the reasonableness of an estimate across mathematical contexts |
| Keyword: fluent, flexible, and strategic thinking |
Elaboration: includes:using known facts and benchmarks, partitioning, applying number strategies to approximate limits, derivatives, and integralschoosing from different ways to think of a number or operation (e.g., Which will be the most strategic or efficient?) |
|
| Curricular Competency |
Explore, analyze, and apply mathematical ideas using reason, technology, and other tools |
Calculus 12 |
Reasoning and modelling |
| Keyword: analyze |
Elaboration: examine the structure of and connections between mathematical ideas (e.g., limits, derivatives, integrals) |
| Keyword: reason |
Elaboration: inductive and deductive reasoningpredictions, generalizations, conclusions drawn from experiences (e.g., in puzzles, games, coding) |
| Keyword: technology |
Elaboration: graphing technology, dynamic geometry, calculators, virtual manipulatives, concept-based appscan be used for a wide variety of purposes, including:exploring and demonstrating mathematical relationshipsorganizing and displaying datagenerating and testing inductive conjecturesmathematical modelling |
| Keyword: other tools |
Elaboration: manipulatives such as algebra tiles and other concrete materials |
|
| Curricular Competency |
Develop thinking strategies to solve puzzles and play games |
Calculus 12 |
Reasoning and modelling |
| Keyword: thinking strategies |
Elaboration: using reason to determine winning strategiesgeneralizing and extending |
|
| Big Ideas |
Trigonometry involves using proportional reasoning to solve indirect measurement problems. |
Pre-calculus 11 |
No CCG |
| Keyword: proportional reasoning |
Elaboration: comparisons of relative size or scale instead of numerical difference |
| Keyword: indirect measurement |
Elaboration: using measurable values to calculate immeasurable values (e.g., calculating the width of a river using the distance between two points on one shore and an angle to a point on the other shore)Sample questions to support inquiry with students:How is the cosine law related to the Pythagorean theorem?How can we use right triangles to find a rule for solving non-right triangles?How do we decide when to use the sine law or cosine law?What would it mean for an angle to have a negative measure? Identify a context for making sense of a negative angle. |
|
| Big Ideas |
Quadratic relationships are prevalent in the world around us. |
Pre-calculus 11 |
No CCG |
| Keyword: relationships |
Elaboration: Sample questions to support inquiry with students:What are some examples of quadratic relationships in the world around us, and what are the similarities and differences between these?Why are quadratic relationships so prevalent in the world around us?How does the predictable pattern of linear functions extend to quadratic functions?Why is the shape of a quadratic function called a parabola?How can we decide which form of a quadratic function to use for a given problem?What effect does each term of a quadratic function have on its graph? |
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