Basic Algebra Competencies

7/23/2001 9:19:15 AM

Goals | Course Competencies

Goals

Core Abilities

Demonstrate critical thinking
 learner identifies a problem to be solved, task to be performed, or decision to be made
 learner evaluates information
 learner makes inferences and connections
 learner identifies criteria to evaluate the solution, process, or decision
 learner selects an appropriate solution, process, or decision
Use mathematics effectively
 learner performs computations using appropriate methods
 learner demonstrates knowledge and application of measurement
 learner reads, interprets, and generates graphical information
 learner demonstrates knowledge and application of formulas
 learner uses critical thinking skills in a mathematical context

Course Competencies

1. Use Venn Diagrams to represent Operations of Sets.

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : Low

Criteria - Performance will be satisfactory when:
 learner shows the intersection of two or more sets
 learner shows the union of two or more sets.
 learner constructs the subset of a given set.
 learner uses the terminology of set theory correctly.
 learner uses set notation correctly.
 you list the elements of a set.
 you determine whether a given set is finite or infinite.

Competence will be demonstrated:
 in the use of venn diagrams to represent operations of sets.
 in an objective classroom exam, quiz, or challenge problem session.

Learning Objectives
a. Show the intersection of two or more sets.
b. Show the Union of two or more sets.
c. Construct the subset of a given set.
d. Use the terminology of set theory correctly.
e. Use set notation correctly.
f. List the elements of a set.
g. Determine whether a given set is finite or infinite.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
There are no Standards linked to this Competency.

2. Perform basic operations with real numbers.

Properties
Domain : Cognitive
Level : Knowledge
Importance : Essential
Difficulty : Low

Criteria - Performance will be satisfactory when:
 learner performs addition calculations and obtain results in compliance with rules of real numbers.
 learner performs subtraction calculations and obtain results in compliance with rules of real numbers.
 learner performs multiplication calculations and obtain results in compliance with rules of real numbers.
 learner perform division calculations and obtain results in compliance with rules of real numbers.

Competence will be demonstrated:
 in the performance of basic operations with real numbers.
 on an objective classroom exam, quiz, or challenge problem.
 on a homework exercise or an assigned learning center activity.
 on an on-line website lesson and quiz at: http://www.madison.tec.wi.us/ald/learningcenter/signednumbersindex.html 

Learning Objectives
a. Write the subsets of real numbers.
b. Add real numbers.
c. Subtract real numbers.
d. Write the product of two real numbers.
e. Write the quotient of two real numbers.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Compare real numbers
Perform and explain operations on real numbers

3. Perform computations involving rational expressions.

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner performs computations involving rational expressions.
 learner performs correct computations
 learner demonstrates that a reduced ratio has a greatest common factor of one
 learner produces an answer which makes a given proportion a true statement

Competence will be demonstrated:
 in the performance of computations involving rational expressions.
 in an objective classroom exam, quiz, or group problem-solving session

Learning Objectives
a. Find the sum of two or more rational numbers
b. Find the difference of two rational numbers
c. Find the product of two or more rational numbers
d. Find the quotient of two rational numbers
e. Classify a number or variable as an element of a set
f. Estimate a plausible answer
g. Change improper fractions to mixed numbers and vice versa
h. Write a fraction that shows the ratio comparison of two measurements
i. Solve a proportion
j. Find the absolute value of a rational number
k. Perform a combination of operations on rational numbers using the Order of Operation concept
l.
m.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Perform and explain operations on real numbers

4. Factor algebraic expressions.

Properties
Domain : Cognitive
Level : Application
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner writes whole numbers as a series of prime factors in ascending order
 learner demonstrates that fractions are written with a greatest common factor of one for numerator and denominator
 learner demonstrates that rational expressions have a greatest common factor of one
 learner shows that polynomials are written as a series of reduced polynomials with a greatest common factor of one


Competence will be demonstrated:
 in the factoring of algebraic expressions.
 in an objective classroom exam, quiz, or problem-solving group session

Learning Objectives
a. Write the greatest common factor of two or more numbers
b. Perform prime factorization on a whole number
c. State at least two reasons for factoring expressions
d. Write the factors of two or more terms using the grouping method
e. Write the factors of the difference of two perfect squares
f. Write the factors of a perfect square trinomial
g. Write the factors of a trinomial using guess and check
h. Write the quotient of a polynomial and a monomial
i. Outline an approach to factoring a polynomial

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways

5. Solve first degree equations and inequalities.

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner identifies a given equation containing a variable as a single term with a coefficient of one
 learner selects appropriate inverse operations to solve equations
 learner obtains a solution which makes the original equation or inequality a true statement

Competence will be demonstrated:
 in the solving of first degree equations and inequalities.
 in an objective classroom exam, quiz, or challenge problem session

Learning Objectives
a. Combine like terms.
b. Evaluate an algebraic expression.
c. Determine whether an equation is true or false.
d. Evaluate a formula.
e. Solve equations of the form x+a = c or x-a = c.
f. Solve equations of the form ax = c or x/a = c.
g. Solve equations of the form ax+b = c or ax-b = c.
h. Solve equations of the form ax/b+c = d.
i. Solve equations of the form ax+b = cx+d.
j. Develop a strategy for solving algebraic equations.
k. Explain why using a sequence of steps is important in solving equations.
l. Determine whether an inequality is true or false.
m. Solve a first degree inequality of the form ax+b>c
n. Solve a first degree inequality of the form ax+b<c
o. Solve equations explicitly for indicated variable
p. Critique equation solving strategies presented in class

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities

6. Solve second degree equations.

Properties
Domain : Cognitive
Level : Synthesis
Importance : Essential
Difficulty : High

Criteria - Performance will be satisfactory when:
 learner writes an equation which has factors set equal to zero or the perfect square is set equal to a constant.
 learner identifies coefficients of a quadratic equation in standard form.
 learner selects appropriate method for solving second degree equations
 learner generates the equation which satisfies the conditions of the problem.
 learner solves second degree equations using the selected method.
 you select relevant solution(s).
 you apply skill to an applied technical problem.
 you apply the process for solving problems according to the problem solving criteria.

Competence will be demonstrated:
 in the solving of second degree equations.
 on an objective classroom exam, quiz, or challenge problem.

Learning Objectives
a. Combine like terms
b. Develop a procedure for solving quadratic equations.
c. Demonstrate solving a quadratic equation using the quadratic formula.
d. Demonstrate solving a quadratic equation with a leading coefficient of one by using the factoring method.
e. Explain why the Zero Factor Theorem is essential for solving quadratic equations.
f. Identify a quadratic equation which has no solution.
g. Identify solutions having a positive and negative square root.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities

7. Solve word problems.

Properties
Domain : Cognitive
Level : Analysis
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner demonstrates an understanding of the problem by drawing a sketch with labels, when applicable.
 learner translates each English phrase into an algebraic expression and fit these expressions together into in equation or inequality.
 learner solves for all the unknowns asked for in the problem.
 learner checks the solution(s) in the word statement.
 learner states results clearly.

Competence will be demonstrated:
 in the solving of word problems.
 on an objective classroom exam, quiz, or challenge problem.

Learning Objectives
a. Read the problem through quickly, then read it through again vary carefully and completely and make a sketch if it helps to understand the problem.
b. Identify the unknown quantities that are to be determined.
c. Name these quantities, using variables.
d. Express all known relationships in terms of the variable names.
e. Read the problem again, checking the relationships you have written down.
f. Solve the resulting equations.
g. Interpret your results in terms of the original problem.
h. Compare your solutions with the conditions of the problem.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies when solving mathematical real-world and non- routine problems.
Use reason and logic
Communicate logical arguments and clearly show why a result does or does not make sense, why the reasoning is or is not valid, and an understanding of the difference between examples that support a conjecture and a proof of the conjecture
Use geometric models to solve mathematical and real-world problems

8. Simplify expressions involving exponents.

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner demonstrate an understanding of the laws of exponents
 learner applies the laws of exponents.
 learner demonstrates how like terms are combined.
 learner applies order of operation to simplifying expressions.

Competence will be demonstrated:
 in the simplification of expressions involving exponents.
 on an objective classroom exam, quiz, or challenge problem.

Learning Objectives
a. Combine like terms.
b. Apply the laws of exponents.
c. Write each product using exponents.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways

9. Simplify expressions using scientific notation.

Properties
Domain : Cognitive
Level : Application
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner calculates the product of two numbers in powers of ten form.
 learner calculates the quotient of two numbers in powers of ten form.
 learner calculates the sum of two numbers in powers of ten form.
 learner calculates the difference of two numbers in powers of ten form.
 learner converts numbers from decimal notation to scientific notation.
 you apply the process for solving problems according to the problem solving criteria.

Competence will be demonstrated:
 in the simplification of expressions using scientific notation.
 on an objective classroom exam, quiz, or challenge problem.

Learning Objectives
a. Use scientific notation to represent extremely large and small numbers.
b. Write a number as a decimal that is greater than or equal to 1 and less than 10 multiplied by a power of 10.
c. Write the correct equivalent of a number, if the exponent is negative.
d. Convert a number from standard notation to scientific notation.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways

10. Determine the Absolute Value of a Number

Properties
Domain : Cognitive
Level : Analysis
Importance : Important
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner determines the absolute value of a number.
 learner recognizes the absolute value of a number.
 learner evaluates the absolute value of a number.
 learner determines the opposite or additive inverse of a number.
 learner distinguishes between finding the absolute value of a number and removing parentheses.

Competence will be demonstrated:
 in the determination of the absolute value of a number.
 on an objective classroom examination

Learning Objectives
a. Recognize the absolute value of a number.
b. Evaluate the absolute value of a number.
c. Determine the opposite or additive inverse of a number.
d. Distinguish between finding the absolute value and removing parentheses.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
There are no Standards linked to this Competency.

11. Perform computations using scientific notation.

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : Medium

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Write the product of numbers expressed in scientific notation by adding the exponents.
b. Write the quotient of numbers expressed in scientific notation by subtracting the exponents.
c. Convert all numbers to the same power of ten (exponent) and add or find the difference of the digit terms.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways

12. Perform basic operations using polynomials.

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : High

Criteria - Performance will be satisfactory when:
 learner adds polynomials.
 learner subtracts polynomials by first, forming the additive inverse of the minuend.
 learner multiplies polynomials.
 learner divides polynomials.
 learner applies the process for solving problems according to the problem solving criteria.

Competence will be demonstrated:
 in performing basic operations using polynomials.
 on an objective classroom exam, quiz, or challenge problem.

Learning Objectives
a. Recognize polynomials.
b. Add polynomials.
c. Subtract polynomials.
d. Manipulate polynomials using the multiplication operation.
e. Manipulate binomials using the FOIL method.
f. Write common monomial factors of polynomials.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies when solving mathematical real-world and non- routine problems.
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways

13. Perform division by monomials only.

Properties
Domain : Cognitive
Level : Application
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner factors using the greatest common factor
 learnaer expresses both the numerator and the denominator as products of prime factors.
 learner uses the Properties of Real Numbers and the Laws of Exponents to simplify or reduce the fraction.
 learner converts mixed numbers to improper fractions.

Competence will be demonstrated:
 in the performance of division by monomials only.
 on an objective classroom exam, quiz, or challenge problem.

Learning Objectives
a. Write the reciprocal of the divisor.
b. Write the product of the first term and the reciprocal of the divisor.
c. Write the product in lowest terms.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways

14. Apply study strategies

Properties
Domain : Cognitive
Level : Application
Importance : Essential
Difficulty : Low

Criteria - Performance will be satisfactory when:
 learner solves problems using the standard problem solving criteria.
 learner completes computer aided skills development activities.
 learner shows your work in a clear and logical order.
 learner verifies solution.
 learner labels solution with appropriate unit(s).

Competence will be demonstrated:
 in the application of study strategies.
 on an objective classroom exam, quiz, challenge problem.
 on a homework exercise.
 on an assigned learning center activity.

Learning Objectives
a. Develop the view that mathematics is a growing discipline, interrelated with human culture.
b. Develop an understanding of the connections of mathematics to other disciplines.
c. Practice interactive learning through collaborative activities.
d. Acquire the ability to read, write, listen to, and speak mathematics.
e. Use appropriate technology to enhance mathematical thinking and understanding.
f. Use appropriate technology to solve mathematical problems and judge the reasonableness of results.
g. Apply mathematics through modeling real-world situations.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly

15. Convert units of measurements

Properties
Domain : Cognitive
Level : Comprehension
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner converts within the Metric system.
 learner converts within the English system.
 learner converts between the English and Metric systems.
 learner applies skill to an applied (technical) problem.
 learner applies the process for solving (technical) problems according to the problem solving criteria.

Competence will be demonstrated:
 in the conversion of units of measurements.
 on an objective classroom exam, quiz, or challenge problem.
 in an assigned learning center activity.

Learning Objectives
a. Write down the given or known quantity.
b. Write down the unit needed in the answer.
c. Develop a plan of conversions leading to the needed or desired units.
d. Use conversion factors as needed.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Number Operations and Relationships--Students will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem solving.

16. Graph a linear equation

Properties
Domain : Cognitive
Level : Application
Importance : Important
Difficulty : High

Criteria - Performance will be satisfactory when:
 learner plots 3 points of a given linear equation.
 learner identifies a horizontal or vertical line when given its equation.
 learner graphs a line on a rectangular coordinate plane given 1 point on on the line and its slope.
 learner graphs a line on a rectangular coordinate plane given its equation in standard form: Ax + B = C.
 learner graphs a line on a rectangular coordinate plane given its formula in point-slope form.

Competence will be demonstrated:
 in the graphying of linear equations.
 on an objective classroom exam, quiz, or challenge problem.
 in an assigned learning center activity.

Learning Objectives
a. Plot points on the rectangular coordinate plane.
b. Identify the coordinates of specific points on the coordinate plane.
c. Identify the quadrants that contain specific points.
d. Solve the equation for y in terms of x.
e. Specify any three real numbers as replacement values for x.
f. Calculate the corresponding replacement values for y.
g. Construct a table of these x and y values.
h. Graph these ordered pairs (x, y) on a coordinate plane.
i. Draw a line through two of the points.
j. Verify that the third point lies on the line.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity

17. Calculate dimensions of geometric figures

Properties
Domain : Cognitive
Level : Application
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner calculates the perimeter of various polygons and circles.
 learner calculates the area of various triangles, rectangles, circles, and composite figures.
 learner calculates the volume of various rectangular prisms; right circular cylinders and cones; spheres; and composite solids.
 learner labels your answers appropriately in units, square units, or cubic units as associated with perimeter, area, or volume.
 learner measures the classroom and estimate how much paint is required to paint the walls and ceiling.

Competence will be demonstrated:
 in calculating dimensions of geometric figures.
 on an objective classroom exam, quiz, or challenge problem.
 in an assigned learning center activity.

Learning Objectives
a. Apply the Pythagorean Theorem.
b. Calculate the perimeters of polygons.
c. Calculate the circumference of a circle.
d. Calculate the areas of selected plane figures.
e. Calculate the areas of certain irregular plane figures.
f. Calculate the volumes of selected three-dimensional solids.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Use geometric models to solve mathematical and real-world problems

18. Evaluate algebraic expressions, given variable values

Properties
Domain : Cognitive
Level : Comprehension
Importance : Essential
Difficulty : Low

Criteria - Performance will be satisfactory when:
 learner utilizes the order of operations hierarchy.
 learner evaluates some common formulae such as A = ½BH for various given values of B, H, and A.
 learner analyzes the behavior of some common functions such as D = RT for various given values of independent variables R, and T.

Competence will be demonstrated:
 in the evaluation of algebraic expressions given variable values.
 on an objective classroom exam, quiz, or challenge problem.
 in an assigned learning center activity.

Learning Objectives
a. Apply the rules for the order of operations.
b. Evaluate exponents of algebraic expressions.
c. Evaluate expression using addition.
d. Evaluate expression using subtraction.
e. Evaluate expression using multiplication.
f. Evaluate expression using division.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Select and use appropriate procedures in problem solving situations involving the application of different number systems (natural, integers, rational, and real)

19. Apply math problem solving skills

Properties
Domain : Cognitive
Level : Application
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner composes a sequence of steps that *you* follow to solve a given problem.
 learner analyzes your problem-solving process during the solution of a word problem.
 learner determines the known and unknown values in a given word problem.
 learner names the known and unknown values in a given word problem. (E.g., L = 3, W = 7, A = ?)
 learner identifies the key words and phrases that translate directly into algebraic notation. (E.g., "is" translates as "=")
 you write algebraic expressions or equations which represent the given problematic situation.
 you solve algebraic equations obtained during the translation phase of the problem-solving process.
 you answer the question with appropriate units if necessary.
 you ask yourself if your answer is reasonable.

Competence will be demonstrated:
 in the application of math problem solving skills.
 on an objective classroom exam, quiz, or challenge problem.
 in an assigned learning center activity.

Learning Objectives
a. Assess information from reading the problem.
b. Formulate a plan for solving the problem..
c. Articulate the plan.
d. Complete the plan.
e. Evaluate the plan.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data
Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities

20. Perform Operations with Algebraic Fractions

Properties
Domain :
Level :
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:
 learner performs addition operations and obtain results in accordance with the rules of operations of Algebraic Fractions.
 learner performs subtraction operations and obtain results in accordance with the rules of operations of Algebraic Fractions.
 learner performs multiplication operations and obtain results in accordance with the rules of operations of Algebraic Fractions.
 learner performs division operations and obtain results in accordance with the rules of operations of Algebraic Fractions

Competence will be demonstrated:
 in the performance of operations with algebraic fractions.
 on an objective classroom exam, quiz, challenge problem.
 in an assigned Learning Center/Lab via computer-interactive activities.

Learning Objectives
a. Add algebraic fractions.
b. Subtract algebraic fractions.
c. Write the product of two algebraic fractions..
d. Write the quotient of two algebraic fractions

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
There are no Standards linked to this Competency.

21. Apply significant figure rules

Properties
Domain : Cognitive
Level : Comprehension
Importance : Essential
Difficulty : Medium

Criteria - Performance will be satisfactory when:
 learner performs addition calculations and obtains results in compliance with rules of significant figures.
 learner performs subtraction calculations and obtain results in compliance with rules of significant figures.
 learner performs multiplication calculations and obtain results in compliance with rules of significant figures.
 learner performs division calculations and obtain results in compliance with rules of significant figures.
 learner measures an object and record it with the correct number of significant figures.
 you write asentence explaining why significant figures are necessary in the applied sciences.
 you calculate the margin of error in a computation involving numbers written with significant figures (use the symbol ± to express your answer).

Competence will be demonstrated:
 in the application of significant figure rules.
 on an objective classroom exam, quiz, or challenge problem.
 in an assigned learning center activity.

Learning Objectives
a. Apply the rules for addition and subtraction.
b. Apply the rules for multiplication and division.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
Routinely assess the acceptable limits of error
Work with data in the context of real-world situations

22. Apply knowledge of tables and graphs.

Properties
Domain : Cognitive
Level : Application
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Analyze and represent situations involving variable quantities with tables, graphs and verbal descriptions.
b. Convert between different representations such as tables, graphs and verbal descriptions.
c. Analyze tables and graphs to identify and generalize patterns and relationships.

Linked Core Abilities
Demonstrate critical thinking
Use mathematics effectively

Linked Standards
There are no Standards linked to this Competency.

23. Solve problems involving formulas and functions.

Properties
Domain : Affective
Level : Internalizing
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Recognize that a variety of problem situations may be modeled by the same function (e.g. y=mx+b, y=ax^2, y=a^x, y=1/x)
b. Evaluate formulas and functions accurately.
c. Analyze and use functional relationships to explain how a change in one quantity results in a change in the other quantity when dealing with linear, quadratic or exponential equations.

Linked Core Abilities
There are no Core Abilities linked to this Competency.

Linked Standards
There are no Standards linked to this Competency.

24. Solve higher level equations including quadratic, exponential, and trigonometric.

Properties
Domain : Affective
Level : Internalizing
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Analyze and represent situations involving variable quantities with equations.
b. Create and use algebraic expressions and equations to model situations and solve problems.
c. Solve linear equations.
d. Solve quadratic equations.
e. Solve exponential equations.
f. Solve trigonometric equations.
g. Solve systems of linear equations in two and/or three variables.
h. Recognize and use direct and indirect varation.

Linked Core Abilities
There are no Core Abilities linked to this Competency.

Linked Standards
There are no Standards linked to this Competency.

25. Apply knowledge of basic data analysis.

Properties
Domain : Psychomotor
Level :
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Construct, interpret and draw inferences from tables, charts and graphs.
b. Make inferences and convincing arguments that are based on data analysis.
c. Evaluate arguments that are based on data analysis, including distinguishing between correlation and causation.
d. Represent data graphically in ways that make sense and are appropriate to the context.

Linked Core Abilities
There are no Core Abilities linked to this Competency.

Linked Standards
There are no Standards linked to this Competency.

26. Apply knowledge of basic statistics.

Properties
Domain : Psychomotor
Level :
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Apply measures of central tendency (mean, median, mode) and analyze the effect of changes in data on these measures.
b. Use an informal line of best fit to predict from data.
c. Apply and recognize the role of sampling and the impact and the impact of bias on statistical claims.
d. Use and interpret a frequency distribution of outcomes.
e. Compare and contrast different sets of data on the basis of measures of central tendency and dispersion (range and standard deviation).

Linked Core Abilities
There are no Core Abilities linked to this Competency.

Linked Standards
There are no Standards linked to this Competency.

27. Apply knowledge of basic probability.

Properties
Domain : Psychomotor
Level :
Importance :
Difficulty :

Criteria - Performance will be satisfactory when:

Competence will be demonstrated:

Learning Objectives
a. Recognize the difference between experimental and theoretical probabilities.
b. List possible outcomes of experimental probabilities.
c. Make accurate predictions that are based on experimental or theoretical probabilities.
d. Calculate problems based on given experimental data.

Linked Core Abilities
There are no Core Abilities linked to this Competency.

Linked Standards
There are no Standards linked to this Competency.