| Curricular Competency |
Engage in spatial reasoning in a dynamic environment |
Geometry 12 |
Reasoning and modelling |
| Keyword: spatial reasoning |
Elaboration: being able to think about shapes (real or imagined) and mentally transform them to notice relationships |
|
| Curricular Competency |
Develop thinking strategies to solve puzzles and play games |
Geometry 12 |
Reasoning and modelling |
| Keyword: thinking strategies |
Elaboration: using reason to determine winning strategiesgeneralizing and extending |
|
| Big Ideas |
Derivatives and integrals are inversely related. |
Calculus 12 |
No CCG |
| Keyword: inversely related |
Elaboration: The fundamental theorem of calculus describes the relationship between integrals and antiderivatives.Sample questions to support inquiry with students:How are derivatives and integrals related?Why are antiderivatives important?What is the difference between an antiderivative and an integral? |
|
| Big Ideas |
Integral calculus develops the concept of determining a product involving a continuously changing quantity over an interval. |
Calculus 12 |
No CCG |
| Keyword: continuously changing |
Elaboration: area (height x width) under a curve where the height of the region is changing; volume of a solid (area x length) where cross-sectional area is changing; work (force x distance) where force is changingFinding these products requires finding an infinite sum.Sample questions to support inquiry with students:What is the value of using rectangles to approximate the area under a curve?Why is the fundamental theorem of calculus so fundamental? |
|
| Big Ideas |
Differential calculus develops the concept of instantaneous rate of change. |
Calculus 12 |
No CCG |
| Keyword: instantaneous rate of change |
Elaboration: developing rate of change from average to instantaneousSample questions to support inquiry with students:How can a rate of change be instantaneous?When do we use rate of change? |
|
| Big Ideas |
The concept of a limit is foundational to calculus. |
Calculus 12 |
No CCG |
| Keyword: concept of a limit |
Elaboration: Differentiation and integration are defined using limits.Sample questions to support inquiry with students:Why is a limit useful?How can we use historical examples (e.g., Achilles and the tortoise) to describe a limit? |
|
| Content |
integration:- approximations
- fundamental theorem of calculus
- methods of integration
- applications (integration)
|
Calculus 12 |
No CCG |
| Keyword: integration |
Elaboration: definition of an integralnotationdefinite and indefinite |
| Keyword: approximations |
Elaboration: Riemann sum, rectangle approximation method, trapezoidal method |
| Keyword: methods of integration |
Elaboration: antiderivatives of functionssubstitutionby parts |
| Keyword: applications (integration) |
Elaboration: area under a curve, volume of solids, average value of functions differential equationsinitial value problemsslope fields |
|
| Content |
differentiation:- rate of change
- differentiation rules
- higher order, implicit
- applications (differentiation)
|
Calculus 12 |
No CCG |
| Keyword: differentiation |
Elaboration: historydefinition of derivativenotation |
| Keyword: rate of change |
Elaboration: average versus instantaneousslope of secant and tangent lines |
| Keyword: differentiation rules |
Elaboration: power, product; quotient and chaintranscendental functions: logarithmic, exponential, trigonometric |
| Keyword: applications (differentiation) |
Elaboration: relating graph of f(x) to f'(x) and f''(x)increasing/decreasing, concavitydifferentiability, mean value theoremNewton’s methodproblems in contextual situations, including related rates and optimization problems |
|
| Content |
limits:- left and right limits
- limits to infinity
- continuity
|
Calculus 12 |
No CCG |
| Keyword: limits |
Elaboration: from table of values, graphically, and algebraicallyone-sided versus two-sidedend behaviourintermediate value theorem |
|
| Content |
functions and graphs |
Calculus 12 |
No CCG |
| Keyword: functions |
Elaboration: parent functions from Pre-Calculus 12piecewise functionsinverse trigonometric functions |
|
| Curricular Competency |
Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concepts |
Calculus 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/) |
|
| Curricular Competency |
Use mistakes as opportunities to advance learning |
Calculus 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 |
Calculus 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 |
Calculus 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 |
Calculus 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 |
|