| Curricular Competency |
Think creatively and with curiosity and wonder when exploring problems |
Statistics 12 |
Reasoning and modelling |
| Keyword: Think creatively |
Elaboration: by:being open to trying different strategiesappreciating that in statistical contexts, there is often no single correct answerproposing a viable research question for investigationdesigning a study to explore a research questionrefers 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 statistics in situational contexts |
Statistics 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 |
Statistics 12 |
Reasoning and modelling |
| Keyword: Estimate reasonably |
Elaboration: be able to justify the use of an estimate in a statistical contextappreciate that statistical estimators exhibit variation across different samplesuse intuition when sampling distributions via simulations to make inferences |
| Keyword: fluent, flexible, and strategic thinking |
Elaboration: includes:appreciating the role of variationchoosing from different ways to investigate a research question (e.g., Which will be the most appropriate?) |
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| Curricular Competency |
Explore, analyze, and apply statistical ideas using reason, technology, and other tools |
Statistics 12 |
Reasoning and modelling |
| Keyword: analyze |
Elaboration: consider a research problem and determine viable investigation approachescritique existing studies, identifying possible flaws and limitationsdraw viable conclusions from a statistical study |
| Keyword: reason |
Elaboration: inductive and deductive reasoningpredictions, generalizations, conclusions drawn from experiences (e.g., with games and simulations) |
| Keyword: technology |
Elaboration: software for recording, exploring, and communicating datasoftware tools for illustrating and providing information on probability modelsweb-based visualisation/simulation tools that give intuition to inferential concepts |
| Keyword: other tools |
Elaboration: manipulatives such as dice, coins, spinners, and other concrete materials |
|
| Curricular Competency |
Develop thinking strategies to solve puzzles and play games |
Statistics 12 |
Reasoning and modelling |
| Keyword: thinking strategies |
Elaboration: using reason to determine winning strategiesgeneralizing and extending |
|
| Big Ideas |
Transformations of shapes extend to functions and relations in all of their representations. |
Pre-calculus 12 |
No CCG |
| Keyword: Transformations |
Elaboration: Sample questions to support inquiry with students:How can we tell whether a transformation will have invariant points?Under what circumstances will different transformations produce the same result?How do graphical transformations affect the tables of values?How does a transformation affect a point found at the origin as compared to a point on an axis or a point in one of the four quadrants?How can a rational function of the form y = (ax+b) / (cx+d) be considered as a transformation of the reciprocal function y = 1/x ? |
|
| Big Ideas |
Understanding the characteristics of families of functions allows us to model and understand relationships and to build connections between classes of functions. |
Pre-calculus 12 |
No CCG |
| Keyword: functions |
Elaboration: Sample questions to support inquiry with students:How do we decide which kind of function to use to model a given problem?What do functions and relations look like beyond the visible axes?A set of data looks like a parabola, but it is not. What function could be used to model this data?What does the number of zeros tell us about a function?What connections do we see within the characteristics of a particular class of function? |
|
| Big Ideas |
Using inverses is the foundation of solving equations and can be extended to relationships between functions. |
Pre-calculus 12 |
No CCG |
| Keyword: inverses |
Elaboration: undo the operations within an expression or function to reduce the expression to an identity (e.g., x = )Sample questions to support inquiry with students:How can the inverse help to solve an equation?How is solving an equation related to identifying the specific input for a function, given a specific output?How are exponential and logarithmic functions related?How are the laws of exponents connected to the laws of logarithms?What are some other examples of inversely related functions?How are inverses related graphically, and why?How is solving an exponential equation similar to solving a trigonometric equation?How are inverse operations related to solving a polynomial equation by factoring?What is the value of using trigonometric identities to find equivalent expressions?Why do some equations have extraneous roots and other equations do not? |
|
| Content |
trigonometry: functions, equations, and identities |
Pre-calculus 12 |
No CCG |
| Keyword: trigonometry |
Elaboration: examining angles in standard position in both radians and degreesexploring unit circle, reference and coterminal angles, special anglesgraphing primary trigonometric functions, including transformations and characteristicssolving first- and second-degree equations (over restricted domains and all real numbers)solving problems in situational contextsusing identities to reduce complexity in expressions and solve equations (e.g., Pythagorean, quotient, double angle, reciprocal, sum and difference) |
|
| Content |
rational functions |
Pre-calculus 12 |
No CCG |
| Keyword: rational |
Elaboration: characteristics of graphs, including asymptotes, intercepts, point discontinuities, domain, end-behaviour |
|
| Content |
polynomial functions and equations |
Pre-calculus 12 |
No CCG |
| Keyword: polynomial |
Elaboration: factoring, including the factor theorem and the remainder theoremgraphing and the characteristics of a graph (e.g., degree, extrema, zeros, end-behaviour)solving equations algebraically and graphically |
|
| Content |
logarithms: operations, functions, and equations |
Pre-calculus 12 |
No CCG |
| Keyword: logarithms |
Elaboration: applying laws of logarithmsevaluating with different basesusing common and natural logarithmsexploring inverse of exponentialgraphing, including transformationssolving equations with same base and with different basessolving problems in situational contexts |
|
| Content |
geometric sequences and series |
Pre-calculus 12 |
No CCG |
| Keyword: geometric |
Elaboration: common ratio, first term, general termgeometric sequences connecting to exponential functionsinfinite geometric seriessigma notation |
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| Content |
exponential functions and equations |
Pre-calculus 12 |
No CCG |
| Keyword: exponential |
Elaboration: graphing, including transformationssolving equations with same base and with different bases, including base esolving problems in situational contexts |
|
| Content |
transformations of functions and relations |
Pre-calculus 12 |
No CCG |
| Keyword: transformations |
Elaboration: of graphs and equations of parent functions and relations (e.g., absolute value, radical, reciprocal, conics, exponential, logarithmic, trigonometric)vertical and horizontal translations, stretches, and reflectionsinverses: graphs and equationsextension:recognizing composed functions (e.g., y =)operations on functions |
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