| Curricular Competency |
Use mistakes as opportunities to advance learning |
Apprenticeship Mathematics 12 |
Connecting and reflecting |
| Keyword: mistakes |
Elaboration: range from calculation errors to misconceptions |
| Keyword: opportunities to advance learning |
Elaboration: by:analyzing errors to discover misunderstandingsmaking adjustments in further attemptsidentifying not only mistakes but also parts of a solution that are correct |
|
| Curricular Competency |
Connect mathematical concepts with each other, other areas, and personal interests |
Apprenticeship Mathematics 12 |
Connecting and reflecting |
| Keyword: Connect mathematical concepts |
Elaboration: to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, popular media and news events, social justice, cross-curricular integration) |
|
| Curricular Competency |
Reflect on mathematical thinking |
Apprenticeship Mathematics 12 |
Connecting and reflecting |
| Keyword: Reflect |
Elaboration: share the mathematical thinking of self and others, including evaluating strategies and solutions, extending, posing new problems and questions |
|
| Curricular Competency |
Take risks when offering ideas in classroom discourse |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship Mathematics 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 |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship 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 |
Apprenticeship 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 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 |
Apprenticeship 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., reasonableness of measurements) |
| Keyword: fluent, flexible, and strategic thinking |
Elaboration: including:using known facts and benchmarks, partitioning, applying whole number strategies to expressions involving proportional reasoning, financial analysis, and logicchoosing from different ways to think of a number or operation (e.g., Which will be the most strategic or efficient?) |
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