| Curricular Competency |
Take risks when offering ideas in classroom discourse |
Foundations of Mathematics 12 |
Communicating and representing |
| Keyword: discourse |
Elaboration: is valuable for deepening understanding of conceptscan help clarify students’ thinking, even if they are not sure about an idea or have misconceptions |
|
| Curricular Competency |
Use mathematical vocabulary and language to contribute to discussions in the classroom |
Foundations of Mathematics 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 |
Foundations of Mathematics 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 |
Foundations of Mathematics 12 |
Communicating and representing |
| Keyword: Explain and justify |
Elaboration: use 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 |
Foundations of Mathematics 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 |
Foundations of Mathematics 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 |
Foundations of Mathematics 12 |
Understanding and solving |
| Keyword: flexible and strategic approaches |
Elaboration: deciding which mathematical tools to use to solve a problemchoosing an appropriate 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 |
Foundations of Mathematics 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 |
Foundations of Mathematics 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 |
Foundations of Mathematics 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 |
Foundations of Mathematics 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 context |
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 |
Foundations of Mathematics 12 |
Reasoning and modelling |
| Keyword: Estimate reasonably |
Elaboration: be able to defend the reasonableness of an estimated value or a solution to a problem or equation (e.g., regression analysis and combinatorics calculations) |
| Keyword: fluent, flexible, and strategic thinking |
Elaboration: includes using known facts and benchmarks; partitioning; applying whole number strategies to graphing; regression choice; probability |
|
| Curricular Competency |
Explore, analyze, and apply mathematical ideas using reason, technology, and other tools |
Foundations of Mathematics 12 |
Reasoning and modelling |
| Keyword: analyze |
Elaboration: examine the structure of and connections between mathematical ideas (e.g., conic sections, functions, financial planning) |
| Keyword: reason |
Elaboration: inductive and deductive reasoningpredictions, generalizations, conclusions drawn from experiences (e.g., with puzzles, games, and 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 |
Foundations of Mathematics 12 |
Reasoning and modelling |
| Keyword: thinking strategies |
Elaboration: using reason to determine winning strategiesgeneralizing and extending |
|
| Big Ideas |
Data representation allows us to understand and solve problems efficiently. |
Computer Science 12 |
No CCG |
| Keyword: Data representation |
Elaboration: a method of storing and organizing information in a containerSample questions to support inquiry with students:When should we create our own data type?How do computers use electricity to represent data?How can we organize our data types more efficiently?How do we decide which data types to use? |
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