| Big Ideas |
The meanings of, and connections between, operations extend to powers, radicals, and polynomials. |
Pre-calculus 11 |
No CCG |
| Keyword: connections |
Elaboration: Sample questions to support inquiry with students:How are the different operations (+, -, x, ÷, exponents, roots) connected?What are the similarities and differences between multiplication of numbers, powers, radicals, polynomials, and rational expressions?How can we verify that we have factored a trinomial correctly?How can visualization support algebraic thinking?How can patterns in numbers lead to algebraic generalizations?When would we choose to represent a number with a radical rather than a rational exponent?How do strategies for factoring x2+bx+c extend to ax2 +bx + c, a≠1How do operations on rational numbers extend to operations with rational expressions? |
|
| Big Ideas |
Algebra allows us to generalize relationships through abstract thinking. |
Pre-calculus 11 |
No CCG |
| Keyword: generalize |
Elaboration: Sample questions to support inquiry with students:After solving a problem, can we extend it? Can we generalize it?How can we take a contextualized problem and turn it into a mathematical problem that can be solved?How do we tell if a mathematical solution is reasonable?Where can errors occur when solving a contextualized problem?What are the similarities and differences between quadratic functions and linear functions? How are they connected?What do we notice about the rate of change in a quadratic function?How do the strategies for solving linear equations extend to solving quadratic, radical, or rational equations?What is the connection between domain and extraneous roots? |
|
| Content |
financial literacy: compound interest, investments, loans |
Pre-calculus 11 |
No CCG |
| Keyword: financial literacy |
Elaboration: compound interestintroduction to investments/loans with regular payments, using technologybuy/lease |
|
| Content |
trigonometry: non-right triangles and angles in standard position |
Pre-calculus 11 |
No CCG |
| Keyword: trigonometry |
Elaboration: use of sine and cosine laws to solve non-right triangles, including ambiguous casescontextual and non-contextual problemsangles in standard position:degreesspecial angles, as connected with the 30-60-90 and 45-45-90 trianglesunit circlereference and coterminal anglesterminal armtrigonometric ratiossimple trigonometric equations |
|
| Content |
linear and quadratic inequalities |
Pre-calculus 11 |
No CCG |
| Keyword: inequalities |
Elaboration: single variable (e.g., 3x - 7 ≤ -4, x2 - 5x + 6 > 0)domain and range restrictions from problems in situational contextssign analysis: identifying intervals where a function is positive, negative, or zerosymbolic notation for inequality statements, including interval notation |
|
| Content |
quadratic functions and equations |
Pre-calculus 11 |
No CCG |
| Keyword: quadratic |
Elaboration: identifying characteristics of graphs (including domain and range, intercepts, vertex, symmetry), multiple forms, function notation, extremaexploring transformationssolving equations (e.g., factoring, quadratic formula, completing the square, graphing, square root method)connecting equation-solving strategiesconnecting equations with functionssolving problems in context |
|
| Content |
rational expressions and equations |
Pre-calculus 11 |
No CCG |
| Keyword: rational |
Elaboration: simplifying and applying operations to rational expressionsidentifying non-permissible valuessolving equations and identifying any extraneous roots |
|
| Content |
polynomial factoring |
Pre-calculus 11 |
No CCG |
| Keyword: factoring |
Elaboration: greatest common factor of a polynomialtrinomials of the form ax2 + bx + cdifference of squares of the form a2x2 - b2y2may extend to a(f(x))2 + b(f(x)) +c, a2(f(x))2 - b2(f(x))2 |
|
| Content |
radical operations and equations |
Pre-calculus 11 |
No CCG |
| Keyword: radical |
Elaboration: simplifying radicalsordering a set of irrational numbersperforming operations with radicalssolving simple (one radical only) equations algebraically and graphicallyidentifying domain restrictions and extraneous roots of radical equations |
|
| Content |
powers with rational exponents |
Pre-calculus 11 |
No CCG |
| Keyword: powers |
Elaboration: positive and negative rational exponentsexponent lawsevaluation using order of operationsnumerical and variable bases |
|
| Content |
real number system |
Pre-calculus 11 |
No CCG |
| Keyword: real number |
Elaboration: classification |
|
| Curricular Competency |
Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concepts |
Pre-calculus 11 |
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 |
Pre-calculus 11 |
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, with other areas, and with personal interests |
Pre-calculus 11 |
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 |
Pre-calculus 11 |
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 |
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