Cumulative Progress Indicators

Major Outcome

Strategies/Activities Resources with Text Reference

Assessments

4.3.12-C(1)

4.3.12-D(1)

Students will be able to:

• evaluate an algebraic expression.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Text: Algebra II, Glencoe-McGraw Hill

• Use algebraic expressions as models of real-life situations.

• Emphasize! The order of operations -

  • often provides the easiest way to simplify numerical expressions.

  • is programmed into calculators and computers.

  • explain why certain expressions cannot be simplified further.

• The meaning of the various formulas is not as important as how to use them (at this point). Showing students how to evaluate the quadratic formula here saves time later on and sparks recognition when it is proven.

See “Assessment”

4.1.12-A(1)

Students will be able to:

• use the properties of real numbers.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use Venn Diagrams to classify/categorize real numbers.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve linear equation (single variable).

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use linear equations to answer questions about real-life. Include equations with no solution and all real numbers solutions.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve a literal equation for a given variable and evaluate it for specified values of the other variables.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• See appendix for sample problems.

See “Assessment”

4.5.12-A(3)

Students will be able to:

• use problem-solving strategies to solve real-life problems.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Teach different strategies for solving word problems including but not limited to, look for a pattern, solve a simpler problem, draw a chart, figure or diagram and “guess and check”. Begin with numerous examples where students just need to identify what is being asked (unknown). Extend to – what information is needed to solve and what is given. Students need positive, successful problem solving experiences.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve absolute value equations.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12.D(2)

Students will be able to:

• solve simple inequalities.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use inequalities to solve real-life problems. Emphasize and as intersection or as union.

See “Assessment”

4.1.12-A(1)

Students will be able to:

• use the real number line to graph and order real numbers.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• This chapter should be a review of Algebra I Skills.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve absolute value inequalities.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use value inequalities in real-life settings.

See “Assessment”

4.3.12-B(1)

4.3.12-B(2)

Students will be able to:

• identify a relation and a function.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Identify real-life relations that are functions. Include the vertical line test for graph or a function.

f:x x2 – 5x ÷6

f(x) = x2 – 5x ÷ 6

(should be seen as different notation for the same rule).

f(x) should be understood to be the value of the function at x.

• Include the special case of a vertical line reviewing that division by zero is undefined and the fact that such a graph represents only a relation not a function.

See “Assessment”

4.3.12-B(1)

LINEAR EQUATIONS

Students will be able to:

• sketch a graph using a table of values.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

  • Chapter 1

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12B(1)

Students will be able to:

• use intercepts to sketch a quick graph of a line.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Although all methods are important, note the case in using the intercept method:

3x – 4y = 6

if y = 0 then 3x =6 x =2

if x = 0 then 4y = 6 y = 6/4 = 3/2

See “Assessment”

4.3.12-B(2)

Students will be able to:

• interpret slope as a rate of change.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(1)

Students will be able to:

• identify equations whose graphs are horizontal or vertical lines.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(2)

Students will be able to:

• find the slope of a line and identify parallel and perpendicular lines from their slopes.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(1)

4.3.12-B(2)

Students will be able to:

• use the slope-intercept form of a line to sketch a quick graph.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(1)

Students will be able to:

• write equations of lines.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use equations of lines to solve real-life problems.

See “Assessment”

4.3.12-B(1)

4.4.12-A(1)

Students will be able to:

• fit a line to a set of data and write an equation for the line.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use a graphing calculator.

See “Assessment”

4.3.12-B(2)

4.4.12-A(5)

Students will be able to:

• identify whether a set of data shows positive or negative correlation, or no correlation.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-C(1)

Students will be able to:

• use special functions, such as compound functions and step functions.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use these functions in real-life situations.

See “Assessment”

4.3.12-B(1)

Students will be able to:

• graph a linear inequality in two variables.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use a linear inequality in two variables to model real-life situations.

See “Assessment”

4.3.12-B(1)

4.3.12-C(1)

Students will be able to:

• explore the graphs of absolute value equations using a graphing calculator.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use graphs of absolute value equations to answer questions about real-life situations.

See “Assessments”

4.3.12-B(2)

4.3.12-D(2)

4.5.12-F(3)

SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

Students will be able to:

• graph and solve a system of linear equations.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

  • Chapters 1 and 2

• Text: Algebra II, McDougal-Littell

• Use a system of linear equations to answer questions about real-life situations. Use a graphing calculator.

See “Assessment”

4.3.12-B(2)

4.3.12-D(2)

Students will be able to:

• use algebraic methods to solve a linear system.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use a linear system to answer questions about real-life situations.

See “Assessment”

4.3.12-C(1)

Students will be able to:

• write and use linear systems to model real-life situations.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(2)

4.3.12-D(2)

Students will be able to:

• Graph a system of linear inequalities to find the solution to the system.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use a system of linear inequalities to model a real-life situation.

See “Assessment”

4.3.12-B(2)

4.3.12-D(2)

Students will be able to:

• solve a system of linear equations in three variables.

• Text: Algebra I Review, AGS Publishing

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use a system in three variables to answer questions about real-life situations.

See “Assessment”

4.1.12-A(4)

POWERS, ROOTS AND RADICALS

Students will be able to:

• use properties of exponents to evaluate and simplify exponential expressions.

• Text: Algebra II, AGS Publishing

• Chapter 7

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.1.12-B(2)

Students will be able to:

• evaluate n^th roots of real numbers using radical notation and rational exponent notation.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use n^th roots to solve real-life problems.

• Develop a table of squares, cubes, and 4^th power for 1-10. Point out that finding roots is the inverse of finding positive integer powers.

• Stress the definitions of principal roots for even powers and that this definition is not needed for odd powers.

• A review of the divisibility rules is helpful.

• Also review methods of finding all the factors of an integer.

• Remind students about rationalizing the denominator.

• Review conjugates.

• Motivate the need for rationalizing by comparing the long division of

1 and √2

√2 2

• A “discovery” approach is useful here. Stress that the base cannot be changed when applying the laws of exponents.

See “Assessment”

4.1.12-B(2)

Students will be able to:

• use properties of roots to evaluate and simplify expressions containing radicals and rational exponents.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use properties of roots to solve real-life problems. This concept is similar to “adding like terms” of polynomials.

See “Assessment”

4.1.12-B(2)

Students will be able to:

• use properties of roots to evaluate and simplify expressions containing radicals and rational exponents.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use properties of roots to solve real-life problems. This concept is similar to “adding like terms” of polynomials.

See “Assessment”

4.1.12-B(2)

4.2.12-D(2)

Students will be able to:

• solve equations that have radicals and rational exponents.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use radical equations to solve real-life problems. Stress the need to check and discard false roots since raising an equation to a power creates an equation that may have more roots than the original equation.

See “Assessment”

4.3.12-D(1)

POLYNOMIALS AND POLYNOMIAL FUNCTIONS

Students will be able to:

• add, subtract and multiply polynomials.

• Text: Algebra II, AGS Publishing

• Chapter 5

• Text: Algebra II, McDougal-Littell

• Use polynomial operations to solve real-life problems. Add/subtract only terms that are “like” terms. A non-mathematical example like apples and bananas might help them to remember.

See “Assessment”

4.3.12-D(1)

Students will be able to:

• factor polynomial expressions and equations.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use factoring to solve real-life problems. Factoring is included as a review. The goal is to build speed, accuracy and ability to determine when to factor. The use of factoring should be the major focus in the future. Use examples where the coefficient of the quadratic term is one. Develop the relationships that must be true for the factors in reference to the “signs”, the linear term, and the constant term. Namely,

  • if a sign of constant term is

+: both factor signs are the same

-: factors signs are different.

• • product of factor constants must equal constant term.

  • sum/difference of factors equals linear coefficient.

• Relate factoring of quadratic polynomials to finding the product of binomials and/or trinomials.

See “Assessment”

4.1.12-A(1)

4.1.12-B(1)

QUADRATIC EQUATIONS AND PARABOLAS

Students will be able to:

• identify, add, subtract, and multiply imaginary and complex numbers.

• Text: Algebra II, AGS Publishing

• Chapters 3 and 4

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(1)

4.3.12-B(2)

4.3.12-B(4)

4.5.12-F(3)

Students will be able to:

• graph a quadratic equation.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use the graph of a quadratic equation in a real-life setting.

• Use a graphing calculator.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve a quadratic equation by finding square roots and factoring.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use quadratic equations as models of real-life situations.

• Students should be reminded to take both roots when an even root is introduced to an equation.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve a quadratic equation by completing the square.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use “completing the square” to solve real-life problems.

See “Assessment”

4.3.12-D(2)

Students will be able to:

• use the quadratic formula to solve quadratic equations.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use quadratic models in real-life settings. Sing the quadratic formula to the tune of Pop-Goes the Weasel.

See “Assessment”

4.3.12-D(2)

4.5.12-A(2)

Students will be able to:

• solve equations using quadratic techniques, remainder and factor theorems.

• Text: Algebra II, AGS Publishing

• Chapters 1- 3

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-B(2)

Students will be able to:

• perform operations with functions.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use function operations in real-life situations.

See “Assessment”

4.3.12-B(2)

Students will be able to:

• identify inverse relations and inverse functions and verify that two functions are inverses of each other.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-D(1)

RATIONAL FUNCTIONS

Students will be able to:

• multiply and divide rational expressions, writing the result in simplest form.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use rational expressions as real-life models. Emphasize that dividing terms is incorrect because 1 is not the identity of addition.

• Addends do not “cancel”.

• Dividing opposite expressions such as

a - b yields -1, but students often mistake

b - a (a + b) and (a – b) for opposites.

• Pointing out that both terms must have opposite signs will help.

See “Assessment”

4.3.12-D(1)

Students will be able to:

• add and subtract rational expressions and simplify complex fractions.

• Text: Algebra II, AGS Publishing

• Chapter 6

• Text: Algebra II, McDougal-Littell

• Use rational expressions as models of real-life situations. Show two methods of simplifying complex fractions.

  • Multiply by reciprocal of denominator.

  • Find the LCD of all fractions. Then multiply both the numerator and the denominator by the LCD.

• Emphasize that fraction bars are grouping symbols. Expressions within numerators or denominators must be combined before dividing. Denominators can be “cleared” by multiplying by 1 in the form of LCD

LCD

This should be presented as an alternative to strictly

following the order of operations.

• Emphasize that it is the multiplication property of equality that allows denominators to be “cleared”. Denominators of expressions cannot be “cleared”.

Compare m + 2 2

m - 2 + m + 2

with m + 2 2

m - 2 + m + 2 = 1

See “Assessment”

4.3.12-B(1)

4.3.12-B(2)

Students will be able to:

• graph a rational function.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Graph a rational function using asymptotes. Use these graphs as a way to introduce restricted values.

See “Assessment”

4.3.12-C(1)

Students will be able to:

• use direct, inverse and joint variation in real-life models.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-D(1)

4.3.12-D(2)

Students will be able to:

• solve equations that contain rational expressions.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use rational equations to solve real-life problems.

• Students have trouble solving this type of equation. The following “tips” may help:

• • state restrictions on the variable first

  • distribute “-“ in the numerator in the same step that the denominator is factored.

See “Assessment”

4.3.12-B(1)

4.3.12-B(2)

4.3.12-B(4)

4.3.12-D(1)

EXPONNENTIAL AND LOGARITHMIC FUNNCTIONS

Students will be able to:

• graph exponential functions and evaluate exponential expressions.

• Text: Algebra II, AGS Publishing

• Chapter 8

• Text: Algebra II, McDougal-Littell

• Use exponential functions as models for real-life situations. Note the restrictions on the base and the domain and range of each. Use graphing calculators. Students should be able to differentiate between linear and exponential growth, i.e., y=2x and f(x) = 2^x.

See “Assessment”

4.3.12-B(1)

4.3.12-B(2)

4.3.12-B(4)

4.3.12-C(1)

4.3.12-D(1)

4.5.12-C(4)

Students will be able to:

• evaluate logarithmic expressions , graph logarithmic functions, and use logarithms in real-life situations.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• The meaning of logarithms must be learned.

• Stress the symmetry of the graphs with respect to the line. y = x

See “Assessment”

4.3.12-D(2)

Students will be able to:

• solve exponential and logarithmic equations.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use exponential and logarithmic equations to answer questions about real-life.

See “Assessment”

4.3.12-D(1)

Students will be able to:

• use properties of logarithms.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

• Use logarithmic to solve real-life problems

See “Assessment”

4.3.12-A(1)

SEQUENCES AND SERIES

Students will be able to:

• write and use sequences and series.

• Text: Algebra II, AGS Publishing

• Chapter 11

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-A(1)

4.5.12-C(4)

Students will be able to:

• analyze and describe sequences and series found in the real world.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-A(1)

4.512-C(4)

Students will be able to:

• find the n^th term and the sum of an arithmetic series and use in real-life problems.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-A(1)

4.5.12-C(4)

Students will be able to:

• Find the n^th term and the sum of a finite geometric series and use in real-life problems.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-A(1)

4.5.12-C(4)

Students will be able to:

• find the sum of an infinite geometric series and use in real-life problems.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.3.12-C(3)

4.5.12-A(2)

Students will able to:

• identify, classify, and apply recursive functions to the solutions of problems.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.5.12-A(2)

Students will be able to:

• use and apply the Binomial Theorem to the solution of real world problems.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.4.12-B(1)

Students will be able to:

• use the Fundamental Counting Principle and permutations to find probabilities.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.4.12-B(1)

Students will be able to:

• use combinations to count the number of ways an event can happen and find probabilities.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”

4.4.12-B(1)

4.5.12-C(4)

Students will be able to:

• find and use the probability of an event to answer questions about real-life situations.

• Text: Algebra II, AGS Publishing

• Text: Algebra II, McDougal-Littell

See “Assessment”