Algebra II Instructional Unit Basic Statistics -Displaying data with dotplots and The students will be -Use scientific or graphing -Classroom discussion 2.1.11.A stemplots. able to evaluate calculator to calculate numeric -Homework 2.2.11.A -Calculating measures of center expressions and expressions containing -Problems completed 2.2.11.F (mean, median, and mode). formulas fractions,powers,square roots, during class 2.8.11.D -Graphing scatter plots. parenthesis, and long division -Completion of quiz 2.8.11.N -Finding the line of best fit for bars. -Completion of Unit Test paired data. -Evaluate algebraic -Calculating quartiles and outliers. expressions by using the -Drawing boxplots. substitution principle and order -Calculating measures of spread (IQR and standard deviation) of operations. -Solve application problems that require analyzing a formula, substituting numeric data in the proper place, and calculating. -Evaluate expressions containing absolute value bars. Tuesday, September 09, 2003 Page 1 of 17
Instructional Unit Basic Statistics -Displaying data with dotplots and The students will be -Graph a single set of data by -Classroom discussion 2.4.11.C stemplots. able to construct visual making a dotplot. -Homework 2.5.11.D -Calculating measures of center displays of data. -Organize a single set of data -Participation in a group 2.6.11.B (mean, median, and mode). in a stemplot. activity -Graphing scatter plots. -Compare two sets of data by -Problems completed -Finding the line of best fit for making a back-to-back during class paired data. stemplot. -Completion of quiz -Calculating quartiles and outliers. -Graph the five number -Completion of Unit Test -Drawing boxplots. summary of a set of data by -Calculating measures of spread (IQR and standard deviation) making a boxplot. -Graph two variable data in a scatterplot. Tuesday, September 09, 2003 Page 2 of 17
Instructional Unit Basic Statistics -Displaying data with dotplots and The students will be -Calculate the mean of a set of -Classroom discussion 2.6.11.B stemplots. able to do basic data. -Homework 2.6.11.C -Calculating measures of center statistical analysis on -Find the median of a set of -Participation in a group 2.6.11.D (mean, median, and mode). one variable and two data. activity -Graphing scatter plots. variable data sets. -Identify the mode of a set of -Problems completed -Finding the line of best fit for data. during class paired data. -Calculate the range of a set of -Completion of quiz -Calculating quartiles and outliers. data. -Completion of Unit Test -Drawing boxplots. -Find the five number summary -Calculating measures of spread (IQR and standard deviation) for a set of data. -Calculate the interquartile range for a set of data. -Determine if extreme values can be classified as outliers. -Calculate the standard deviation of a set of data. -Identify which measure of center is the best "average" in different situations. -Determine which set of data has a bigger "spread". -Find the line of best fit for a two variable data situation. -Use the line of best fit to make future predictions. Tuesday, September 09, 2003 Page 3 of 17
Instructional Unit Exponents, Monomials, Polynomials, and Rationals -Using exponent laws to multiply The students will be -Identify rational numbers and -Classroom discussion 2.8.11.N monomial expressions. able to simplify rational expressions. -Homework 2.8.11.P -Using exponent laws to divide expressions and solve -Multiply and divide rational -Participation in a group 2.8.11.S monomial expressions. rational equations. expressions by factoring and activity -Using distributive property to add, canceling. -Problems completed subtract, and multiply polynomials. -Add and subtract rational during class expressions by finding a least -Completion of quiz -Factoring polynomials using common denominator. -Completion of Unit Test multiple methods. -Simplify complex fractions. a. common term -Solve rational equations by b. grouping clearing fractions. c. difference of squares -Solve direct, inverse, and joint d. and sum/difference of variation problems. cubes -Using long division and sythetic division to divide polynomials. -Solving variation problems. -Multiplying and dividing rational expressions. -Adding and subtracting rational expressions. -Solving rational equations. Tuesday, September 09, 2003 Page 4 of 17
Instructional Unit Exponents, Monomials, Polynomials, and Rationals -Using exponent laws to multiply The students will be -Identify like terms and use -Classroom discussion 2.8.11.S monomial expressions. able to add,subtract, distributive property when -Homework -Using exponent laws to divide and multiply monomials asked to add or subtract -Problems completed monomial expressions. and polynomials. monomials. during class -Using distributive property to add, -Use the six basic exponent -Completion of quiz subtract, and multiply polynomials. properties to simplify -Completion of Unit Test expressions containing -Factoring polynomials using multiplication and/or division multiple methods. with monomials. a. common term -Express very large numbers b. grouping and very small numbers in c. difference of squares scientific notation. d. and sum/difference of -Convert numbers that are cubes expressed in scientific notation -Using long division and sythetic to regular decimal form. division to divide polynomials. -Add polynomials by combining -Solving variation problems. like terms. -Multiplying and dividing rational -Subtract polynomials by expressions. distributing the negative sign to -Adding and subtracting rational the second polynomial and then expressions. combining like terms. -Solving rational equations. -Multiply a monomial by a polynomial. -Use the FOIL method to multiplytwo binomials together. -Use the distributive property to multiply polynomials with three terms or higher. -Solve area problems by using monomial and polynomial operations. Tuesday, September 09, 2003 Page 5 of 17
Instructional Unit Exponents, Monomials, Polynomials, and Rationals -Using exponent laws to multiply The students will be -Divide a polynomial by a -Classroom discussion 2.8.11.S monomial expressions. able to divide and monomial. -Homework -Using exponent laws to divide factor polynomials. -Divide polynomials using the -Problems completed monomial expressions. long division method. during class -Using distributive property to add, -In special cases, divide -Completion of quiz subtract, and multiply polynomials. polynomiald using the synthetic -Completion of Unit Test division shortcut. -Factoring polynomials using -Factor polynomials by dividing multiple methods. out a common monomial. a. common term -Factor polynomials by using b. grouping the grouping method. c. difference of squares -Factor trinomials into two d. and sum/difference of binomials. cubes -Factor a difference of squares -Using long division and sythetic into a sum and difference. division to divide polynomials. -Factor sums and differences -Solving variation problems. of cubes by using the -Multiplying and dividing rational appropriate factoring pattern. expressions. -Determine if one polynomial is -Adding and subtracting rational a factor of another polynomial expressions. using division. -Solving rational equations. Tuesday, September 09, 2003 Page 6 of 17
Instructional Unit Linear Equations and Inequalities -Basic scientific and graphing The students will be -Determine if two lines are -Classroom discussion 2.8.11.E calculator functions able to write the parallel or perpendicular by -Homework 2.8.11.L (fractions,powers,parenthesis,divi equation of a line. looking at their slopes. -Participation in a group sion bars). -Write an equation for a line in activity -Evaluating algebraic expressions. slope-intercept form given the -Problems completed -Using algebraic properties to slope and the y-intercept of the during class simplify expressions. line. -Completion of quiz -Solving one variable linear -Write the equation of a line -Completion of Unit Test equations. given the slope and a point -Solving first power absolute value other than the y-intercept. equations. -Write the equation of a line -Solving and graphing one variable given two points on the line. linear inequalities. -Solve problems where a linear -Solving first power absolute value relationship exists between inequalities. two variable by writing an -Graphing points and data in a equation that describes this coordinate plane. relationship and using the -Graphing two-variable linear equation to make predictions. equations. -Solve two variable linear -Finding the slope of a line. inequalities by graphing the -Writing the equation for a linear boundary line and shading the relationship. appropriate solution region. -Graphing equations that are closely related to linear equations. -Solving and graphing two variable linear inequalities. Tuesday, September 09, 2003 Page 7 of 17
Instructional Unit Linear Equations and Inequalities -Basic scientific and graphing The students will be -Simplify algebraic expressions -Classroom discussion 2.1.11.A calculator functions able to solve one using the commutative, -Homework 2.2.11.F (fractions,powers,parenthesis,divi variable linear associative, distributive, -Participation in a group 2.4.11.E sion bars). equations and inverse, and identity properties. activity 2.8.11.D -Evaluating algebraic expressions. inequalities. -Problems completed 2.8.11.N -Using algebraic properties to -Solve one variable linear during class simplify expressions. equations using the properties -Completion of quiz -Solving one variable linear of equality. -Completion of Unit Test equations. -Solve applications problems by -Solving first power absolute value writing and solving equations. equations. -Solving and graphing one variable -Solve equations that contain linear inequalities. more than one variable for a -Solving first power absolute value specific variable using the inequalities. properties of equality. -Graphing points and data in a -Solve absolute value coordinate plane. equations containing a single -Graphing two-variable linear first power variable. equations. -Solve one variable inequalities -Finding the slope of a line. and write the solutions as an -Writing the equation for a linear inequality. relationship. -Graph solution sets for an -Graphing equations that are inequality on a number line. closely related to linear equations. -Solve and graph solution sets for first power absolute value -Solving and graphing two variable inequalities. linear inequalities. Tuesday, September 09, 2003 Page 8 of 17
Instructional Unit Linear Equations and Inequalities -Basic scientific and graphing The students will be -Plot points on a cartesian -Classroom discussion 2.2.11.F calculator functions able to graph linear plane. -Homework 2.5.11.B (fractions,powers,parenthesis,divi equations and -Graph two variable data by -Participation in a group 2.8.11.A sion bars). inequalities. constructing an appropriately activity 2.8.11.J -Evaluating algebraic expressions. labeled cartesian plane and -Problems completed 2.8.11.K -Using algebraic properties to plotting the points. during class simplify expressions. -Identify a linear relation by just -Completion of quiz -Solving one variable linear looking at the equation. -Completion of Unit Test equations. -Graph linear relations by -Solving first power absolute value making a table and plotting equations. points. -Solving and graphing one variable -Calculate the slope of a line by linear inequalities. applying the slope formula to -Solving first power absolute value two points. inequalities. -Find the slope of a line by -Graphing points and data in a counting rise and run on the coordinate plane. graph. -Graphing two-variable linear -Graph a line given only a point equations. on the line and it's slope. -Finding the slope of a line. -Graph special equations -Writing the equation for a linear including the constant equation relationship. and the identity equation -Graphing equations that are (which are both linear), and the closely related to linear equations. absolute value equation and the step equations (which are -Solving and graphing two variable both closely related to linear linear inequalities. equations) Tuesday, September 09, 2003 Page 9 of 17
Instructional Unit Matrices -Storing data in a matrix. The students will be -Find the determinant of a 3x3 -Classroom discussion 2.8.11.G -Adding matrices. able to solve systems matrix using expansion or -Homework -Subtracting Matrices. using matrices diagonals. -Problems completed -Scalar multiplication and matrix -Use determinants to find the during class multiplication. area of a triangle. -Completion of quiz -Determinants. -Recognize the identity matrix -Completion of Unit Test -Using a graphing calculator work and it's properties. with matrices. -Understand the properties of -Properties of the identity matrix. an inverse matrix. -Finding the inverse of a matrix. -Find the inverse of a 2x2 -Using matrices to solve systems of equations. matrix. -Write a system of equations in matrix form. -Use an inverse matrix to solve a system. Tuesday, September 09, 2003 Page 10 of 17
Instructional Unit Matrices -Storing data in a matrix. The students will be -Identify the dimensions of a -Classroom discussion 2.8.11.I -Adding matrices. able to perform basic matrix. -Homework -Subtracting Matrices. operations on matrices -Store data in a matrix. -Participation in a group -Scalar multiplication and matrix -Identify the positions that activity multiplication. different elements of a matrix -Problems completed -Determinants. occupy. during class -Using a graphing calculator work -Describe a geometric figure -Completion of quiz with matrices. using a 2xn matrix -Completion of Unit Test -Properties of the identity matrix. -Add two or more matrices -Finding the inverse of a matrix. together. -Using matrices to solve systems of equations. -Subtract one matrix from another. -Multiply a matrix by a scalar. -Identify the situations where matrix multiplication is possible. -Multiply matrices. -Translate and transform geometric shapes using matrix addition, subtraction, and multiplication. Tuesday, September 09, 2003 Page 11 of 17
Instructional Unit Quadratic Equations and Inequalities -Solving quadratic equations by The students will be -Identify the quadratic term, the -Classroom discussion 2.8.11.N factoring. able to solve quadratic linear term, and the constant -Homework -Solving quadratic equations by equations and term in a quadratic equation. -Participation in a group completing the square. inequalities. -Solve quadratic equations by activity -Solving quadratic equations using factoring the polynomial and -Problems completed the quadratic formula. using the zero product during class -Solving quadratic equations property. -Completion of quiz graphically. -Solve quadratic equations by -Completion of Unit Test -Identifying real and nonreal completing the square and solutions. taking square roots. -Converting quadratic equations -Understand the development from standard form to vertex form of the quadratic formula. and vice versa. -Solve any quadratic equation, -Graphing parabolas. getting both exact and -Solving quadratic inequalities approximate solutions, using using true-false tests. the quadratic formula. -Use the discriminant of a quadratic equation to identify how many solutions and what type of numbers they will be. -Solve quadratic equations by graphing on a graphing calculator. -Solve quadratic inequalities by factoring, dividing the number line into regions, and doing true-false tests. -Solve application problems by writing an appropriate quadratic equation and solving it.
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Instructional Unit Quadratic Equations and Inequalities -Solving quadratic equations by The students will be -Graph quadratic equations by -Classroom discussion 2.8.11.E factoring. able to graph making a table and plotting -Homework 2.8.11.J -Solving quadratic equations by parabolas. points. -Participation in a group 2.8.11.Q completing the square. -Identify properties of a activity 2.8.11.T -Solving quadratic equations using parabola including which way it -Problems completed the quadratic formula. opens,its width, its vertex,it's during class -Solving quadratic equations x-intercepts and its axis of -Completion of quiz graphically. symmetry by analyzing it's -Completion of Unit Test -Identifying real and nonreal equation both in standard form solutions. and vertex form. -Converting quadratic equations -Convert from standard form of from standard form to vertex form a quadratic equation to vertex and vice versa. form. -Graphing parabolas. -Convert from vertex form to -Solving quadratic inequalities using true-false tests. standard form. -Graph a parabola showing vertex, x-intercepts, and axis of symmetry. Tuesday, September 09, 2003 Page 13 of 17
Instructional Unit Roots and Radicals -Calculating roots of real numbers. The students will be -Rewrite the square root of -1 -Classroom discussion able to perform using the imaginary unit I. -Homework -Simplifying radical expressions operations on complex -Simplify square roots of -Problems completed containing numbers, variables, or numbers. negative numbers by writing during class both. them in I form. -Completion of quiz -Expressing roots with rational -Add, subtract, multiply, and -Completion of Unit Test exponents and vice versa. divide pure imaginary numbers. -Solving radical equations and inequalities. -Solve basic equations with -Operations with pure imaginary imaginary solutions. numbers and complex numbers. -Identify the real part and the imaginary part of a complex number. -Add, subtract, multiply, and divide complex numbers. -Use the shortcut for multiplying complex conjugates. -Graph complex numbers in the complex plane. Tuesday, September 09, 2003 Page 14 of 17
Instructional Unit Roots and Radicals -Calculating roots of real numbers. The students will be -Calculate roots of perfect -Classroom discussion 2.8.11.N able to simplify radical powers. -Homework 2.8.11.S -Simplifying radical expressions expressions and solve -Simplify radical expressions -Problems completed containing numbers, variables, or radical equations. using the product and quotient during class both. properties of radicals. -Completion of quiz -Expressing roots with rational -Rationalize the denominator of -Completion of Unit Test exponents and vice versa. a radical expression. -Solving radical equations and -Use the shortcut for multiplying inequalities. radical conjugates. -Operations with pure imaginary numbers and complex numbers. -Rewriting radical expressions using rational exponents and vice versa. -Solve radical equations where the variable is not under the radical sign. -Solve radical equations where the variable is under the radical sign. -Solve application problems where the equations have radicals in them. Tuesday, September 09, 2003 Page 15 of 17
Instructional Unit Systems of Equations and Inequalities -Solving 2x2 systems of equations The students will be -Solve a 2x2 linear system by -Classroom discussion 2.5.11.A graphically. able to solve systems graphing and looking for the -Homework 2.5.11.C -Solving 2x2 systems algebraically.of equations. intersection of the lines. -Participation in a group 2.8.11.D -Solve a 2x2 linear system activity 2.8.11.F -Solving 2x2 systems using using the substitution method. -Problems completed 2.8.11.G determinants. -Solve a 2x2 linear system during class 2.8.11.H -Solving two variable systems of using the multiplication/addition -Completion of quiz inequalities graphically. method (elimination method). -Completion of Unit Test -Solving linear programming -Calculate a 2x2 determinant. problems using systems. -Solving 3x3 systems algebraically. -Solve a 2x2 linear system using determinants. -Solve a 3x3 system using substitution and elimination together. -Identify when a system has no solutions or an infinite amount of solutions. -Solve application problems by writing equations that represent relationships between the variables and solving those equations simultaneously. Tuesday, September 09, 2003 Page 16 of 17
Instructional Unit Systems of Equations and Inequalities -Solving 2x2 systems of equations The students will be -Graph more than one -Classroom discussion 2.5.11.A graphically. able to solve systems two-variable inequality on the -Homework 2.5.11.C -Solving 2x2 systems algebraically.of two variable same coordinate plane and -Participation in a group 2.8.11.D inequalities. shade the solution region for activity 2.8.11.F -Solving 2x2 systems using each inequality. -Problems completed 2.8.11.G determinants. -Shade the region of overlap during class 2.8.11.H -Solving two variable systems of for all of the inequalities. -Completion of quiz 2.11.11.B inequalities graphically. -Point out where the vertices of -Completion of Unit Test -Solving linear programming the solution region are. problems using systems. -Solving 3x3 systems algebraically. -Solve the appropriate system of equations to find the exact location of these vertices. -In a linear programming situation, translate the constraints of the problems into inequality notation. -Solve the system of inequalities that results from all of the constraints and locate all vertices. -Use the Linear Programming Theorem to determine which vertex maximizes or minimizes the equation. -Interpret the results in the context of the problem. Tuesday, September 09, 2003 Page 17 of 17