Algebra 2
Quadratics POWER STANDARD MA-11-4.2.2 Assessed Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. DOK – 3 SUPPORTING CORE CONTENT MA-11-5.3.4 Assessed Students will solve quadratic equations from real world or mathematical situations. DOK – 2 MA-11-1.2.1a Supporting Students will estimate solutions to problems with real numbers (including very large and very small quantities) in both real world and mathematical situations, and use the estimations to check for reasonable computational results. MA-11-2.2.1a Supporting Students will continue to apply to both real world and mathematical situations U.S. customary and metric systems of measurement. Understandings/ Big Ideas quadratics occur in real life quadratics have a pattern graphically and algebraic representation there is a purpose for minimums and maximums which effect every day life. there is a purpose and value for finding zeros of the function connections can be made between factoring and quadratics complex and imaginary numbers have a role in quadratic equations and inequalities. the quadratic formula is useful for finding zeros Students will be able to. . . identify quadratic functions from graphs and equations recognize and use different forms of quadratic functions (vertex, standard and intercept) model and graph equations and inequalities of quadratics using t-charts, pencil/paper, and calculator locate maximum, minimum, & zeros of a quadratic function presented in algebraic or graphic form derive quadratic functions solve a quadratic by factoring, completing a square, and using the quadratic formula use complex numbers in solving quadratics Essential Questions What patterns occur when objects are thrown or projected? How do you determine the most or the least of a given situation? What are examples of problems with one or more solutions? What relationships exist between a parabola and its equation? Knowledge and Skills/ Learning Targets Students will know. . . how changes in parameters affect graphs of functions (transformations) that quadratics model real life change how the discriminate of the quadratic formula applies to real-life problems
Polynomial and Rational Expressions POWER STANDARD MA-11-5.2.3 Assessed
Students will add, subtract, multiply, and divide simple rational expressions with monomial first-degree denominators and integer numerators (e.g.,
3 4 9 7 3 4 ; ; ; 5x 3y 2a 4b 5x 7y
DOK – 1
5 9 ), and will express the results in simplified form. 2c 11d
SUPPORTING CORE CONTENT MA-11-5.2.1a ADP Benchmark Students will evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables. MA-11-2.2.1a Supporting Students will continue to apply to both real world and mathematical situations U.S. customary and metric systems of measurement. Understandings/ Big Ideas Polynomials and rational expressions operate the same why as fractional whole numbers. Essential Questions How do the basic operations (add, subtract, multiply, and divide) with fractions and whole numbers compare to the basic operations with polynomials and rational expressions? Knowledge and Skills/ Learning Targets Students will know. . . the definition of a rational function
Students will be able to . . . add, subtract, multiply, and divide simple rational expressions with monomial first-degree denominators and integer numerators and will express the results in simplified form evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables.
Polynomial Functions POWER STANDARD MA-11-5.2.2 Assessed Students will: add, subtract, and multiply polynomial expressions; factor polynomial expressions using the greatest common monomial factor; and factor quadratic polynomials of the form ax2+bx+c, when a=1 and b and c are integers. DOK - 2 SUPPORTING CORE CONTENT MA-11-5.2.2a Supporting
Students will factor quadratic polynomials, such as perfect square trinomials and quadratic polynomials of the form
ax2 bx c when a≠1 and b and c are integers.
MA-11-5.2.1a ADP Benchmark Students will evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables. MA-11-2.2.1a Supporting Students will continue to apply to both real world and mathematical situations U.S. customary and metric systems of measurement. Understandings/ Big Ideas Polynomials can represent area and perimeter Functions can be categorized by an equation or graph Essential Questions What is the relationship between polynomials and area? How do you know? How can a function have more than one maximum or minimum? Knowledge and Skills/ Learning Targets Students will know … Definitions of monomial, polynomial, greatest common monomial factor, grouping, difference of squares, perfect square trinomials, rational expressions, radical expressions, integer exponents, rational exponents, perfect square FOIL method Perfect Squares Students will be able to … add, subtract, multiply, divide, and factor monomials and polynomials graph a polynomial function find the zeros, maximums, and minimums of a polynomial function
Exponential and Logarithmic Functions POWER STANDARD MA-11-4.2.2 Assessed Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. DOK – 3 SUPPORTING CORE CONTENT MA-11-5.1.1 Assessed Students will identify and apply multiple representations (tables, graphs, equations) of functions (linear, quadratic, absolute value, exponential) to solve real-world or mathematical problems. DOK – 2 MA-11-1.3.2b ADP Benchmark Students will recognize and solve problems that can be modeled using a finite geometric series, such as home mortgage problems and other compound interest problems. MA-11-5.1.1c ADP Benchmark Students will recognize and solve problems that can be modeled using an exponential function, such as compound interest problems. MA-11-2.2.1a Supporting Students will continue to apply to both real world and mathematical situations U.S. customary and metric systems of measurement. Understandings/ Big Ideas Many real-life relationships are exponential or logarithmic Exponential relationships grow quickly over time and logarithmic relationships grow slowly over time Exponential functions and logarithmic functions are inverses Essential Questions How do scientists use the Richter Scale to calculate the strength of an earthquake? If population growth is exponential, why do we not run out of room on Earth? Students will be able to. . . Solve problems that can be modeled using exponential or logarithmic functions Solve problems that can be modeled using a finite geometric series Knowledge and Skills/ Learning Targets Students will know. . . Definitions of exponential and logarithmic functions
Conics This is a ADP Benchmark concept only.