| Curricular Competency |
Explain and justify mathematical ideas and decisions in many ways |
Foundations of Mathematics and Pre-calculus 10 |
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 |
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| 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 and Pre-calculus 10 |
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 |
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| Curricular Competency |
Solve problems with persistence and a positive disposition |
Foundations of Mathematics and Pre-calculus 10 |
Understanding and solving |
| Keyword: persistence and a positive disposition |
Elaboration: not giving up when facing a challengeproblem solving with vigour and determination |
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| Curricular Competency |
Apply flexible and strategic approaches to solve problems |
Foundations of Mathematics and Pre-calculus 10 |
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 |
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| Curricular Competency |
Visualize to explore and illustrate mathematical concepts and relationships |
Foundations of Mathematics and Pre-calculus 10 |
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. |
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| Curricular Competency |
Develop, demonstrate, and apply mathematical understanding through play, story, inquiry, and problem solving |
Foundations of Mathematics and Pre-calculus 10 |
Understanding and solving |
| Keyword: inquiry |
Elaboration: includes structured, guided, and open inquirynoticing and wonderingdetermining what is needed to make sense of and solve problems |
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| Curricular Competency |
Think creatively and with curiosity and wonder when exploring problems |
Foundations of Mathematics and Pre-calculus 10 |
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 |
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| Curricular Competency |
Model with mathematics in situational contexts |
Foundations of Mathematics and Pre-calculus 10 |
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 |
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| Curricular Competency |
Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number |
Foundations of Mathematics and Pre-calculus 10 |
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., estimating the solution for a system of equations from a graph) |
| Keyword: fluent, flexible, and strategic thinking |
Elaboration: includes:using known facts and benchmarks, partitioning, applying whole number strategies to rational numbers and algebraic expressionschoosing from different ways to think of a number or operation (e.g., Which will be the most strategic or efficient?) |
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| Curricular Competency |
Explore, analyze, and apply mathematical ideas using reason, technology, and other tools |
Foundations of Mathematics and Pre-calculus 10 |
Reasoning and modelling |
| Keyword: analyze |
Elaboration: examine the structure of and connections between mathematical ideas (e.g., using an area model to factor a trinomial) |
| Keyword: reason |
Elaboration: inductive and deductivereasoningpredictions, 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 to 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 |
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| Curricular Competency |
Develop thinking strategies to solve puzzles and play games |
Foundations of Mathematics and Pre-calculus 10 |
Reasoning and modelling |
| Keyword: thinking strategies |
Elaboration: using reason to determine winning strategiesgeneralizing and extending |
|
| Big Ideas |
Representing and analyzing data allows us to notice and wonder about relationships. |
Workplace Mathematics 10 |
No CCG |
| Keyword: Representing and analyzing data |
Elaboration: Sample questions to support inquiry with students:How do we choose the most appropriate graph to represent a set of data?How do graphs help summarize and analyze data?How can simulations help us make inferences?How can investigating trends help us make predictions?Why are graphs used to represent data?Why do we graph data? |
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| Big Ideas |
Flexibility with number builds meaning, understanding, and confidence. |
Workplace Mathematics 10 |
No CCG |
| Keyword: Flexibility |
Elaboration: Sample questions to support inquiry with students:How does using a measuring tool increase fluency and flexibility with decimals and fractions?How does solving puzzles and playing games help our understanding of number?Why are fractions important for imperial measurements?How does base 10 make the metric system easier to use?How is the order of operations connected to formula calculations?How do we determine which unit is the most appropriate to use?What level of estimation is considered reasonable when purchasing goods? |
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| Big Ideas |
3D objects can be examined mathematically by measuring directly and indirectly length, surface area, and volume. |
Workplace Mathematics 10 |
No CCG |
| Keyword: measuring |
Elaboration: Sample questions to support inquiry with students:What measurement is the most important for examining 3D objects?Why is it important to understand the components of a formula? |
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| Big Ideas |
Proportional reasoning is used to make sense of multiplicative relationships. |
Workplace Mathematics 10 |
No CCG |
| Keyword: Proportional reasoning |
Elaboration: reasoning about comparisons of relative size or scale instead of numerical difference |
| Keyword: multiplicative |
Elaboration: the multiplicative relationship between two numbers or measures is a relationship of scale rather than an additive difference (e.g., “12 is three times the size of 4” is a multiplicative relationship; “12 is 8 more than 4” is an additive relationship)Sample questions to support inquiry with students:What are the similarities and differences between strategies for solving proportional reasoning problems in different contexts?How does understanding the relationship between multiplication and division help when working with proportions?How are proportions used to describe changes in size? |
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