New Colorado P12 Academic Standards
Current Display Filter: Mathematics  All  by Specific Prepared Graduate Competency  (Remove PGC Filter)
Content Area: Mathematics
Grade Level Expectations: High School
Standard: 2. Patterns, Functions, and Algebraic Structures
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
Relevance & Application:
Nature Of:

^{1} If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). (CCSS: FIF.1)
^{2} For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n \(\geq\) 1. (CCSS: FIF.3)
^{3} Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (CCSS: FIF.4)
^{4} For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. (CCSS: FIF.5)
^{5} presented symbolically or as a table. (CCSS: FIF.6)
^{6} For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10,. (CCSS: FIF.8b)
^{7} For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (CCSS: FIF.9)
^{8} For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (CCSS: FBF.1b)
^{9} both positive and negative. (CCSS: FBF.3)
^{10} Include recognizing even and odd functions from their graphs and algebraic expressions for them. (CCSS: FBF.3)
^{11} Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
For example, f(x) =2 \(x^3\) or f(x) = (x+1)/(x–1) for x \(\neq\) 1. (CCSS: FBF.4a)
Content Area: Mathematics
Grade Level Expectations: Fifth Grade
Standard: 2. Patterns, Functions, and Algebraic Structures
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
Relevance & Application:
Nature Of:

^{1} For example, given the rule "add 3" and the starting number 0, and given the rule "add 6" and the starting number 0, generate terms and the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. (CCSS: 5.OA.3)
^{2} such as the pattern created when saving $10 a month
Content Area: Mathematics
Grade Level Expectations: Fourth Grade
Standard: 2. Patterns, Functions, and Algebraic Structures
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
Relevance & Application:
Nature Of:

^{1} For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. (CCSS: 4.OA.5)
Content Area: Mathematics
Grade Level Expectations: Preschool
Standard: 4. Shape, Dimension, and Geometric Relationships
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations)  (Remove PGC Filter) 

Concepts and skills students master:


Evidence Outcomes  21st Century Skill and Readiness Competencies 
Students Can:

Inquiry Questions:
Relevance & Application:
Nature Of:
