| Curricular Competency |
Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number |
Pre-calculus 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., the zeros of a graphed polynomial function) |
| 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?) |
|
| Curricular Competency |
Explore, analyze, and apply mathematical ideas using reason, technology, and other tools |
Pre-calculus 12 |
Reasoning and modelling |
| Keyword: analyze |
Elaboration: examine the structure of and connections between mathematical ideas (e.g., exponential functions to geometric sequences) |
| 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 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 |
|
| Curricular Competency |
Develop thinking strategies to solve puzzles and play games |
Pre-calculus 12 |
Reasoning and modelling |
| Keyword: thinking strategies |
Elaboration: using reason to determine winning strategiesgeneralizing and extending |
|
| Big Ideas |
Choosing a tool based on required precision and accuracy is important when measuring. |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: measuring |
Elaboration: Sample questions to support inquiry with students:What skills are required for measuring with accuracy?What is the importance of choosing appropriate tools and units when measuring?What are the implications of inaccurate measurements? |
|
| Big Ideas |
Proportional reasoning is used to make sense of multiplicative relationships. |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: Proportional reasoning |
Elaboration: reasoning about comparisons of relative size or scale instead of numerical differenceways of showing proportional comparison when analyzing problems in situational contextsscale diagramsrates of changeSample questions to support inquiry with students:How are proportions used to solve problems?What is the importance of proportional reasoning when making sense of the relationship between two things? |
|
| Big Ideas |
Transferring mathematical skills between problems requires conceptual understanding and flexible thinking. |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: Transferring mathematical skills |
Elaboration: Sample questions to support inquiry with students:How does awareness and knowledge of mathematics in the workplace make learning more meaningful?What is the mathematics required for a particular trade of interest? |
|
| Big Ideas |
Constructing 3D objects often requires a 2D plan. |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: 3D objects |
Elaboration: Sample questions to support inquiry with students:What are some limitations that result when 3D objects are represented in 2D?Which type of 2D representation would be the most appropriate for a 3D object?How does visualization help when solving problems?How does visualization help break down a larger problem? |
|
| Big Ideas |
Design involves investigating, planning, creating, and evaluating. |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: Design |
Elaboration: Sample questions to support inquiry with students:How is a product designed?How can the design process be applied to meet a need or solve a problem? |
|
| Content |
financial literacy: business investments and loans |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: financial literacy |
Elaboration: business investments, loans (lease versus buy), graphical representations of financial growth, projections, expensesextension: project or presentation to share mathematical concepts and skills used in a field/career of interest |
|
| Content |
mathematics in the workplace |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: mathematics in the workplace |
Elaboration: compare and contrast mathematics used in different workplace contextsinterview someone working in a field of interestextension: project that includes an element of design and mathematical thinking |
|
| Content |
3D objects and their views (isometric drawing, orthographic projection) |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: 3D objects |
Elaboration: creating and reading various types of technical drawingsextension: project or presentation to share geometry concepts and skills used in a field/career of interest |
|
| Content |
2D and 3D shapes: including area, surface area, volume, and nets |
Apprenticeship Mathematics 12 |
No CCG |
|
| Content |
similar triangles: including right-angle trigonometry |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: triangles |
Elaboration: situational examples such as stairs and roofsapplication of Pythagorean theoremsituations involving multiple right-angle triangles |
|
| Content |
measuring: using tools with graduated scales; conversions using metric and imperial |
Apprenticeship Mathematics 12 |
No CCG |
| Keyword: measuring |
Elaboration: unit analysisprecision and accuracybreaking of units into smaller divisions to get more precise measurementsextension: project or presentation to share measurement concepts and skills used in a field/career of interest |
|
| Curricular Competency |
Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concepts |
Apprenticeship Mathematics 12 |
Connecting and reflecting |
| Keyword: Incorporate |
Elaboration: by:collaborating with Elders and knowledge keepers among local First Peoplesexploring the First Peoples Principles of Learning (http://www.fnesc.ca/wp/wp-content/uploads/2015/09/PUB-LFP-POSTER-Princi…; e.g., Learning is holistic, reflexive, reflective, experiential, and relational [focused on connectedness, on reciprocal relationships, and a sense of place]; Learning involves patience and time)making explicit connections with learning mathematicsexploring cultural practices and knowledge of local First Peoples and identifying mathematical connections |
| Keyword: knowledge |
Elaboration: local knowledge and cultural practices that are appropriate to share and that are non-appropriated |
| Keyword: practices |
Elaboration: Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining (http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)Aboriginal Education Resources (www.aboriginaleducation.ca)Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/resources/math-first-peoples/) |
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