|Secondary Math 2 Curriculum Map (Quarter 1)|
|Time Frame||Utah State Core Standard||Expected Student Outcome (Objective)||Essential Academic Vocabulary||Assessments (Formative & Summative)||Instructional Learning Activities|
|2 days||A.APR.1||I can add, subtract, and multiply polynomials.|
I can explain why the result of adding, subtracting or multiplying polynomials is always a polynomial.
I can factor trinomials.
|like terms, binomial, trinomial, polynomial, closure, degree, leading coefficient||Polynomials & Radicals #1, 2, 3, 4|
ACT Elem. Algebra: operations involving functions, factoring quadratic expressions.
|Use algebra tiles or other manipulatives for addition, subtraction, and multiplication of polynomials.|
Try to find two polynomials whose sum/product is not a polynomial.
Polynomial Puzzler: http://illuminations.nctm.org/Lessons.aspx
Algebra Tiles, Polyominoes: http://nlvm.usu.edu/
|F.BF.1b||I can combine standard function types by adding, subtracting, and multiplying.|
I can combine functions to model real world situations.
|explicit expression, function||Polynomials & Radicals #5|
ACT Elem. Algebra: operations involving functions
|The total revenue for a company is found by multiplying the price per unit by the number of units sold minus the production cost. The price per unit is modeled by p(n)=-0.5n^2+6. The number of units sold is n. Production cost is modeled by c(n)=3n+7. Write the revenue function.|
|4 days||I can factor quadratic functions to determine the zeros.||binomial, trinomial, perfect square trinomial|
|5 days||N.RN.1, N.RN.2||I can extend the properties of integer exponents to rational exponents.|
I can define rational exponents.
I can simplify expressions involving radicals and rational exponents.
|rational exponent, radical, radicand, index, nth root||Polynomials & Radicals #6, 7, 9, 10|
ACT Elem. Algebra: properties of exponents and square roots
|Relate rational exponents to integer and whole number exponents.|
Compare contexts where radical form is preferable to rational exponents and vice versa.
|N.RN.3||I can explain why sums and products of rational numbers are rational. |
I can explain why the sum of a rational and an irrational number is irrational.
I can explain why the product of a nonzero rational number and an irrational number is irrational.
I can calculate the sums and products of rational and irrational numbers from real world applications.
|rational, irrational||Polynomials & Radicals #8||Teach computation by using formal definitions.|
Explore sums and products of rational and irrational numbers to discover patterns where the results are either rational or irrational.
|7 days||F.IF.4, F.IF.5, F.IF.7a,b||I can interpret key features (intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior) of a quadratic function.|
I can graph key features of a quadratic function from a verbal description of the relationship.
I can determine the appropriate domain of a relationship in the context of a problem. (i.e. I can determine if the domain is restricted given the context.)
I can graph linear and quadratic functions (with or without technology) given an equation, and show key features such as intercepts, maxima and minima.
I can graph absolute value and piecewise-defined functions.
I can compare and contrast key features of various functions including differences in domain and range, intercepts, and rates of change.
|increasing, decreasing, interval, intercept, maximum, minimum, symmetry, end behavior, quadratic, vertex|
domain, function, independent variable, dependent variable, discrete, continuous
piecewise, step function, axis of symmetry, absolute value, |x|
|Graphing #1, 2, 4, 5, 6||Given key features of a quadratic function, sketch the function by hand.|
Use graphing technology to explore and identify key features of a quadratic function.
Compare key features of linear, exponential, and quadratic functions.
Use interval notation or symbols of inequality to communicate key features of graphs.
Discuss contexts where the domain of a function should be limited to a subset of integers, positive or negative values, or some other restriction to the real numbers.
Find real-world contexts that motivate the use of step functions.
Compare the absolute value function to its piecewise definition.
|A.CED.2||I can graph quadratic functions and inequalities in two variables, using appropriate labels and scales.||dependent variable, independent variable, rate of change||ACT Coordinate Geometry: Graphs and equations of polynomials||Connect other representations, tabular, contextual, and algebraic to the graph of a quadratic.|
Graph a quadratic equation in multiple ways by making a table of values; doing transformations; using the vertex, a point, and line of symmetry.
|F.BF.3||I can identify and explain the effect of a constant “k” on the parent graph of f(x) (i.e: f(x) + k, kf(x), f(kx), and f(x + k)) using various representations.|
I can use technology to illustrate and then explain the effects of “k” on a graph.
I can find the value of “k” given the parent graph and a graph of the transformed function.
I can recognize even and odd functions from their graphs and algebraic expressions.
|even function, odd function, rigid transformation, dilation, symmetry||Graphing #8||Use graphing technology to explore transformations of functions.|
Explore transformations that preserve characteristics of graphs of functions and which do not.
TI Transform App
|F.IF.8a||I can write a quadratic function in an equivalent appropriate form (i.e. standard form, vertex form, and intercept form) to highlight items of interest (zeros, extreme values, and symmetry).|
I can explain the relationship between the roots and the coefficients of a quadratic function.
I can explain the relationship between the roots and the factors of a quadratic function.
|binomial, trinomial, perfect square trinomial, completing the square, zero, extreme values (maximum and minimum), vertex, axis of symmetry||Graphing #7||Use manipulatives for multiplying, factoring, and completing the square.|
|F.IF.6||I can calculate the average rate of change of a function over a specified interval using an equation or a table. |
I can interpret the average rate of change of a function.
I can estimate the average rate of change from a graph.
|average rate of change, interval, Δ , secant line||Graphing #3||Compare the graphs of a linear, exponential, and quadratic function over several of the same intervals and discuss average rates of change.|
In honors courses, discuss the relationship of the slope secant lines as they approximate a tangent line.
* If pressed for time, skip this standard.
|An Essential Standard|