Standards: Connecticut has adopted the Common Core State Standards (CCSS) as the Connecticut State Standards (CSS). The relevant Common Core State/Connecticut State Standard is listed after each content bullet (example: CCSS F-IF 3).
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - functions, sequences, recursive rule, explicit rule, arithmetic sequence, geometric sequence, domain, terms, factors, coefficients
CONTENT
a. Recognize that sequences are functions [CCSS F-IF 3]
b. Identify recursive sequences [CCSS F-IF 3]
c. Determine steps to calculate next terms in a sequence [CCSS F-BF 1]
a. Arithmetic Geometric
b. Recursive sequence s
c. Sequences with an explicit formula
d. Sequences to model situations
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - equation, inequality, expression, terms, factors, coefficients, evaluate, linear, solve, associative, property, commutative property, distributive property, inverse operation, variable, real numbers
CONTENT
a. Students will solve word problems with data [CCSS N-Q 1]
b. Students will choose an appropriate display for data [CCSS N-Q 2]
c. Students will round and determine accuracy [CCSS N-Q 3]
a. Terms
b. Factors
c. Coefficients
a. Commutative
b. Associative
c. Distributive
a. Equations
b. Inequalities
a. Evaluating
b. Solving
a. Students will explain and justify of each step [CCSS A-REI 1]
b. Students will using properties to solve inequalities [CCSS A-REI 1]
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - independent variable, dependent variable, ordered pair, mapping diagram, table, graph, function notation, domain, range, vertical line test, equation for a function, function, interval, increasing, decreasing, positive, negative, intercepts, domain restrictions, coordinate plane, axes, graph scale
CONTENT
a. Students will represent a relation as a mapping diagram, table, and graph [CCSS F-IF 1, CCSS A-CED 2]
b. Students will use an equation in two variables to model a relation and represent graphically [CCSS A-CED 2]
c. Students will use function notation to input a domain and output a range and represent graphically [CCSS F-IF 2]
d. Students will identify a function numerically [CCSS F-IF 1]
e. Students will identify a function graphically using the vertical line test [CCSS F-IF 1]
a. Students will interpret the following elements for the graph of a function: [CCSS F-IF 4, CCSS F-IF 5]
i. Domain
ii. Range
iii. Intercepts
iv. Intervals for increasing and decreasing
b. Students will produce the graph of a function given an expression or table [CCSS F-IF 4]
a. Linear [CCSS A-CED 2]
b. Nonlinear [CCSS F-IF 7b]
i. Square root
ii. Cube root
iii. Piecewise
iv. Step
v. Absolute value
ESSENTIAL QUESTIONS
VOCABULARY - rate of change, constant additive change, slope, x-intercept, y-intercept, slope-intercept form, point-slope form, standard form, velocity
CONTENT
a. Students will calculate and interpret slope as rate of change [CCSS F-IF 6]
b. Students will find slope using a graph [CCSS F-IF 6]
c. Students will find the x and y intercepts of a graph or equation [CCSS F-IF 7]
a. Students will write and recognize components of slope-intercept form
b. Students will write and recognize components of point-slope form
c. Students will write and recognize components of standard form
d. Students will manipulate equations from one form to another
a. Students will determine whether a function is linear or not given an equation [CCSS F-LE 1a]
b. Students will find the slopes of parallel and perpendicular lines
c. Students will graph functions in slope-intercept form [CCSS F-IF 7]
d. Students will graphfunctions in point-slope form [CCSS F-IF 7]
e. Students willgraph functions in standard form [CCSS F-IF 7]
a. From a word problem that describes a linear relationship between two quantities [CCSS F-LE 5]
b. Given a table [CCSS F-LE 2]
c. Given a graph [CCSS F-LE 5]
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - central tendency (mean, median, mode), range, standard deviation, outlier, scatter plot, trend line, line of best fit, correlation, causation, correlation coefficient, interpolation, extrapolation
CONTENT
a. Student will use statistics appropriate to the shape of data distribution [CCSS S-ID 2]
b. Given a data set student will calculate the mean, median, mode, outlier (1.5 x IQR rule), and
standard deviation [CCSS S-ID 2]
c. Students will analyze and interpret differences between multiple representations
[CCSS S-ID 1, CCSS S-ID 3]
a. Students will describe how the variables are related [CCSS S-ID 6]
b. Students will interpret slope, y-intercept of line of best fit, and correlation coefficient in the
context of the data [CCSS S-ID 7, CCSS S-ID 8]
c. Students will perform regressions and compute correlation coefficient using technology
[CCSS S-ID 8]
d. For each data point students will be able to calculate residuals compared to the line of best fit [CCSS S-ID 6a]
e. Students will be able to distinguish between correlation and causation [CCSS S-ID 9]
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - solution, substitution, elimination
CONTENT
a. Using technology students will find exact and approximate solutions using a graph and a table of values [CCSS A-REI 11]
[CCSS A-REI 6]
a. Substitution
b. Elimination
a. Students will interpret solutions in the context of the problem
b. Students will model real-life applications as systems of equations and inequalities (i.e. Find the breaking point or most efficient or economical plan)
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - rational exponent, radical, exponential function, exponential growth, exponential decay, growth factor, half-life, compound interest, asymptote
CONTENT
a. Students will review properties of exponents using multi-step problems [CCSS N-RN 2]
b. Students will expand the properties of exponents to rational exponents [CCSS N-RN 2]
a. Students will model a situation [CCSS F-BF 2]
b. Students will translate between the two forms [CCSS F-BF 2]
a. Students will analyze the differences in growth rates for linear versus exponential functions using tables, graphs, equations and verbal descriptions. [CCSS F-LE 3]
a. Prove that exponential functions grow by equal factors over equal intervals [CCSS F-LE 1a]
b. Initial value (principle in applications), end behavior (i.e. asymptotic behavior), and intercepts [CCSS F-IF 7]
a. Compound interest
b. Half-Life and other decay models (i.e. depreciation)
c. Tables of data
ESSENTIAL QUESTIONS
PREREQUISITE SKILLS AND UNDERSTANDING
VOCABULARY - quadratic equation, quadratic function, quadratic formula, factor, vertex, parabola, standard form, vertex form, factored/intercept form, completing the square, monomial, binomial, trinomial, axis/line of symmetry, zero product property, square root property, discriminant, maximum, minimum, first and second differences
CONTENT
a. Finding the zeros of the function
i. Factored/Intercept form - Identify the x-intercepts [CCSS A-SSE 3]
b. Vertex Form
i. Identify vertex (h,k) and the max or min value of the function [CCSS A-SSE 3]
c. Using Standard Form
i. Identifying the y-intercept (0,c), and the axis of symmetry/x-coordinate of vertex
d. Using the Quadratic Formula [CCSS A-REI 4a]
i. Students will find the value of discriminant and understand the nature of roots
ii. Students will relate the value of discriminant to a graphical representation
e. Taking square roots [CCSS A-REI 4a]
a. Students will interpret key features of the graph and tables [CCSS F-IF 4]
i. Intercepts; intervals where the function is increasing/decreasing, positive or negative; relative maximum or minimums; symmetries
a. Show zeros, extreme values (max/min), and symmetry of the graph [CCSS F-IF 8a]
a. Vertical, horizontal, dilations, reflections
b. Identify the value of k (both positive and negative) when graphically given: f(x) + k, kf(x), f(kx), f(x+k)