High School

MATHEMATICS CURRICULUM GUIDE

Advanced Topics in Mathematics Course Number 129830 A/IYA

HS Advanced Topics in Math.doc

Vision Statement of Volusia County Schools Through the individual commitment of all, our students will graduate with the knowledge, skills, and values necessary to be successful contributors to our democratic society.

The School District of Volusia County

The School Board of Volusia County

Ms. Judy Andersen, Chairman Mrs. Vicki Bumpus, Vice Chairman

Ms. Judith G. Conte Mr. Earl C. McCrary

Dr. Jeff Timko

Superintendent of Schools Mr. William E. Hall

Assistant Superintendent for Curriculum and School Improvement Services

Dr. Chris J. Colwell

Director of Program Accountability and Student Achievement Dr. Nicolene R. Junkins

Coordinator of High School Services

Mrs. Allene Dupont

Mathematics Specialist, K-12 Mrs. Margaret Bambrick

July 2002

PREFACE

This guide is one of many that have been developed to correlate the SUNSHINE STATE STANDARDS for mathematics with specific courses taught in Volusia County Schools. The Advanced Topics In Mathematics guide is designed to meet the needs of teachers, students, and the community. The purpose of this course is to extend an in-depth understanding of math topics for students who have completed Algebra I, II, and Geometry. This will provide a college level foundation to students not aspiring to a math, science, or technical major. FOR THE TEACHER: This guide provides direction and assistance in the planning and delivery of instruction for Advanced Topics In Mathematics in accordance with the NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS STANDARDS. Planning and delivering instruction based on Content Statements ensures coverage of all appropriate Sunshine State Standards. Basic assumptions include: (1) all students have access to calculators and computers; (2) classroom activities are student-centered, emphasizing concrete experiences and active/experiential learning; (3) all courses have increased emphasis on problem-solving, estimation, and real-world applications; (4) evaluation includes alternative methods of assessment; and (5) all strands addressed in the Sunshine State Standards are developed across the PreK-12 curriculum. FOR THE STUDENT: This guide helps to ensure those students completing Advanced Topics In Mathematics will have met all appropriate district and state standards established for that course. Advanced Topics In Mathematics, taken in sequence with other designated mathematics courses, will enable students to meet or exceed state standards in the area of mathematics education. FOR OUR INVOLVED COMMUNITY: This guide demonstrates the district’s commitment to implement and maintain high educational standards in all subject areas at every grade level.

USER'S GUIDE FOR ALL USERS: A coding system is used in all curriculum guides to identify Sunshine State Standard Benchmarks and course Content Statements. Benchmarks: For easy reference, each strand, standard, and benchmark has been assigned a unique identification code. For example:

LA.A.1.1.1

Subject Area Benchmark

Strand Standard Level LA.A.1.1.1. Benchmark

Subject Area Level Strand Standard

The first two letters of the code identify the subject area (e.g., LA for language arts). The third letter identifies the strand. The number in the fourth position identifies the general standard under the strand. The number in the fifth position identifies the development level: (1 = PreK-2, 2 = grades 3-5, 3 = grades 6-8, 4 = grades 9-12). The last number identifies the benchmark under the grade cluster within the standard. Content Statements:

A. The first letters from left to right will be the course's Volusia County three-letter code group. The fourth letter will be an "X" as a default. B. The first three numbers from left to right will uniquely identify the content statement within the course. The last place will be an "X" as a

default. Example for Eastern and Western Heritage -- NNF N N F X 0 0 5 X

Volusia County's

Course Code

For future use, default is X.

Content Statement #

For future use, default is X.

WRITERS AND CONTRIBUTORS Margaret Bambrick Educational Development Center Lisa Beard Pine Ridge High School Deborah Beavers DeLand High School Margaret Borden Seabreeze High School Beverly Brant Seabreeze High School Gail Burton Title I Middle School Resource Teacher Johnnie Ebbert DeLand High School Suzanne Gibson Mainland High School Diane Greenstreet Atlantic High School

OTHER RESOURCES

FCAT: Florida Comprehensive Assessment Test, Mathematics Test Items and Performance Task Specifications for Grade 10

1997

FCAT: Florida Comprehensive Assessment Test, Mathematics Orientation Book for Grade 10

1997 Field Test

Florida Curriculum Framework: PreK-12 Sunshine State Standards and Instructional Practices, 1996.

National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics, 1989.

Volusia County Mathematics Curriculum

Mona Lilavois Atlantic High School Joel Manning Title I Middle School Resource Teacher Anne Patterson Educational Development Center Vicky Ridder Atlantic High School Mary Ann Straube Deltona High School Renee Trueman New Smyrna Beach High School Betsy Turner Title I Middle School Resource Teacher Emma Ward Title I Middle School Resource Teacher

SUNSHINE STATE STANDARDS ALIGNMENT

Advanced Topics in Mathematics 120830A/IYA 1 Credit Sunshine State

Standard (Benchmark)

Content Statement

The Student

Sample Performance Descriptions

The Student

Assessment

Goal 3 Standards

1. The student demonstrates and understands the use of the real and complex number systems.

MA.A.1.4.1

IYAX001X: Associates verbal names, written words, and standard numerals with integers, rational numbers, irrational numbers, real numbers, and complex numbers.

Identifies real world uses of integers, rational numbers, irrational numbers, real numbers, and complex numbers.

FCAT-M 2, 3, 4

2. The student uses graphs, tables and equations to represent functions. The student operates on expressions and matrices and solves exponential and logarithmic functions.

MA.A.1.4.3 MA.A.1.4.2

IYAX002X: Finds the domain, range and equation of a linear function to model a real-life situation.

Explores local jobs for high school students. Assuming the pay is an hourly rate, explains the possible weekly earnings based on a legal student work schedule.

FCAT-M 6

MA.A.1.4.3 MA.A.2.4.2

IYAX003X: Uses the general form, f(x)=ax2+ bx + c for quadratic functions as well the quadratic formula and graphs to solve real-world problems.

Graphs and explains the path of a shot put as a function of time and distance. 1,3

MA.A.2.4.2 IYAX004X: Identifies a function as discrete or continuous. Identifies the differences between cellular phone plans charging for any portion of a minute or those who charge by the actual seconds of use.

2,3,6

MA.A.1.4.4 MA.D.1.4.1

IYAX005X: Identifies domain and range for absolute value functions and other piecewise functions. Applies and solves problems.

Uses a salary-plus-commission pay schedule for determining possible monthly earnings. Writes the plan as a piecewise function.

FCAT - M 1,3

MA.A.1.4.4

IYAX006X: Explores functions that involve radicals, identifies domain and range. Solves problems and identifies any extraneous roots.

Uses Heron's formula to find the area of a triangle given the three side lengths. Answers the question: ”What are some possible triangles with the same area but different side lengths?”

1,3

MA.A.1.4.4 IYAX007X: Identifies domain and range for rational functions.

Explores the relationship between an astronaut's weight at sea level and in orbit.

FCAT - M 3

MA.D.1.4.2

IYAX008X: Explores and applies the relationship of the graph of a parent function and a translation.

Using graphing calculator technology, discovers how to manipulate the equation of a parent function to translate graphs horizontally, vertically, and stretches and shrinks.

MA.A.1.4.4 IYAX009X: Explores composite functions. Given the area of a circle, finds the radius. Then finds the circumference. Writes the function for finding the circumference given radius r.

FCAT - M 2,3

MA.D.1.4.1 IYAX010X: Understands the functions which model exponential growth and decay.

Plutonium-239 has a half-life of 24,000 yrs. If it becomes harmless after 10 half-lives, how much will remain of a 1 gram sample when it is considered harmless?

2,3

MA.D.1.4.1 IYAX011X: Solves problems modeled by exponential equations.

Finds the number of bacteria present in a culture after t hours. 2,3

Sunshine State Standard

(Benchmark)

Content Statement

The Student

Sample Performance Descriptions

The Student

Assessment

Goal 3 Standards

2. The student uses graphs, tables and equations to represent functions. The student operates on expressions and matrices and solves exponential and logarithmic functions. MA.D.1.4.2 IYAX012X: Uses exponential functions with negative x-

values. Explains the relationship between y=abx and y=ab-x 2,3

MA.A.1.4.4 IYAX013X: Understands the meaning of fractional exponents.

Finds cube roots by using the function x3=b and then rewrites using 1/3 as an exponent.

MA.A.2.4.2 IYAX014X: Works with the number e and models situations using those exponential functions.

Uses the formula A = Pert to find the amount of an investment of P dollars for t years at a continually compounded annual rate of r.

2,3,6

MA.D.1.4.1 IYAX015X: Identifies if an inverse of a function exists and if it does then writes that inverse.

Converts from Celsius to Fahrenheit by using the function y =(9/5)x + 32. Writes the inverse for this function.

FCAT - M 2,3

MA.A.1.4.4 IYAX016X: Learns the properties of logarithms and uses them to solve equations.

The amount of money in an account at the end of a 5 year period can be modeled by A = ln 50 + 5r where r is the annual rate. Find the amount for an account with 6% interest.

2,3,6

3. The student demonstrates an understanding of the geometry associated with relations and functions.

MA.C.2.4.1 MA.C.3.4.2

IYAX017X: Uses the rectangular coordinate system to apply the distance formula, midpoint formula, and properties of perpendicularity, parallelism, tangency, congruency, similarity, reflections, symmetry, flips, slides, turns, enlargements, rotations, and fractals.

Students work in groups of three, one student draws a figure (function or other geometric shape) on graph paper, second student performs one of the properties listed, then third student describes in writing the property used and specifics regarding the translation or illustration.

FCAT - M 2,3

MA.C.2.4.2 MA.B.1.4.2

IYAX018X: Understands the properties of polygons, circles, and relationships of arcs and angles.

Solves practice problems on SAT practice tests involving circles. FCAT - M 2,3

4. The student applies trigonometry and the properties of similarity and congruence of triangles in problem solving.

MA.B.1.4.3

IYAX019X: Identifies the relationships of sine, cosine, and tangent for right triangles.

Describes how to use right triangle relationships to determine the height of a model rocket.

2,3

MA.B.1.4.3 MA.B.2.4.1 MA.A.4.4.1

IYAX020X: Uses the Law of Sines to solve real-world problems involving sides and angles of triangles. Uses estimation strategies to check reasonableness of results.

Uses the Law of Sines to determine the distance across a water trap on a local golf course.

2,3,6

MA.B.1.4.3 MA.B.2.4.1 MA.A.4.4.1

IYAX021X: Uses the Law of Cosines to solve real-world problems involving sides and angles of triangles.

Uses the Law of Cosines to determine the distance across a water trap on a local golf course. Determines the angle to hit away from the pin in order to minimize the distance across water.

2,3,6

IYAX022X: Converts rectangular coordinates to polar coordinates and polar coordinates to rectangular coordinates.

Obtains a map of a local camping park. Finds a central location for your campsite and shows interesting places in the campground on a coordinate grid. Redisplays with polar coordinates.

2,3,6

Sunshine State Standard

(Benchmark)

Content Statement

The Student

Sample Performance Descriptions

The Student

Assessment

Goal 3 Standards

5. The student demonstrates an understanding of fundamental trigonometric identities.

IYAX023X: Understands and recognizes equivalent trigonometric functions.

Compares the graphs of each side of the identity to determine if the expressions are equivalent.

6. The student demonstrates an understanding and applies appropriate measures of central tendency and variability.

MA.E.1.4.2 IYAX024X: Describes the effect of adding a constant to a data set on the mean and standard deviation.

Writes a function giving the mean of 10 test scores. Answers the following questions: “If 5 points are added to each score, what is the new mean? Given the standard deviation of the original set, what will be the new standard deviation?

FCAT - M 2,3,4

MA.E.1.4.3 IYAX025X: Organizes and displays data using line graphs, scatter plots, histograms, and box-and-whisker plots.

Consults an almanac to find the annual median income for the residents of 40 U.S. cities, 10 from each of the NE, NW, SE, SW quadrants. Displays in a box-and-whisker plot and also a histogram. What does each show about the data?

FCAT - M 2,3,4

IYAX026X: Identifies the frequency of a result and displays it with a histogram. Explores the skew by identifying mean and median and their relationship.

Develops a histogram, which displays the distance from school to home for the members of your class. Identifies the mean and median and discusses the skew of the data set.

FCAT - M 2,3,4

MA.E.3.4.1 IYAX027X: Organizes using relative frequencies and displays the data.

Develops a histogram which displays the distance from school to home for the members of your class. Organizes the data into a relative frequency histogram so that you identify what percent live in each half-mile increment.

2,3,4

IYAX028X: Finds the standard deviation for a data set. Examines the annual rainfall over the last 20 years in your area. Finds the deviations from the mean and the standard deviation.

FCAT - M 2,3,4

6. The student demonstrates an understanding and applies appropriate measures of central tendency and variability.

MA.E.2.4.2

IYAX029X: Determines the probability of either or both of two independent events occurring.

On the last turn of a game, you need to toss a coin and it be "heads" and to roll a six-sided number cube and it be "even" in order to win. What is the probability that you would win?

FCAT - M 2,3,4

Sunshine State Standard

(Benchmark)

Content Statement

The Student

Sample Performance Descriptions

The Student

Assessment

Goal 3 Standards

7. The student demonstrates understanding and applies permutations and combinations.

IYAX030X: Identifies that two events are independent or dependent and finds conditional probabilities.

When playing with a standard deck of cards, you need to get two cards of the same suit in order to score. Explains why the probability is different when each drawn card is then replaced than from a scenario where you draw without replacement until scoring.

2,3,4

IYAX031X: Determines the average gain or loss for repeated situations to get an expected value.

Devises a raffle example for a local charity, which needs to raise $5000. If the prizes distributed are one first prize, two second prizes and three third prizes, determines the cost of each ticket, the expected number of tickets sold, and the value of the prizes so that the charity can meet its goal.

2,3,4

IYAX032X: Explores geometric models for probabilities. Two teams of two play a game where each team member is allowed one roll of a number from one to six. A team wins if they have the highest sum without going over nine. Determines the probability of rolling nine or less and shows with a coordinate plane and a coordinate pair for each possibility.

IYAX033X: Writes and applies a formula for an arithmetic sequence.

Suppose a "bowling" game was devised so that the pins were in the same pattern but were set up 20 rows deep. How many pins would have to be knocked down for a strike?

FCAT - M 2,3,4

IYAX034X: Writes and applies a formula for a geometric sequence.

A set of dominoes is set up so that the first knocks down two, those two knock down two each and this continues so that each one knocks down two. how many dominoes will have fallen after 100 sets of knockdowns?

FCAT - M 2,3,4

IYAX035X: Explores recursive formulas. Finds the nth term of a sequence.

Finds the interest on a single interest period. Assumes the interest is retained as additional principal and computes the interest for the next period. Continues this for five periods. Writes a formula to help you find the accumulated money after 20 periods.

FCAT - M 2,3,4

IYAX036X: Finds the sum of a finite series.

You are given $1 on the first of the month, $2 the next day and $4 the third day. If this trend continues, how much will you have received after 30 days?

FCAT - M 2,3,4

MA.A.2.4.1 IYAX037X: Finds the limit, if it exists of an infinite series and identifies the sum.

Examines a Sierpinski triangle of original area 1 and then follows the pattern by removing the center triangle created by the midpoints of the sides. If you continue, will the area eventually be 0? What will it be after 10 removals?

2,3,4

Addendum

Bloom’s Taxonomy

Assessment Alignment Key

Goal 3 Standards

FCAT Glossary; Grades 8, 10

FCAT Mathematics Reference Sheet; Grade 8, 10

FCAT Science Reference Sheet; Grade 8, 10

1USING BLOOM’S TAXONOMY TO INCREASE STUDENT ACHIEVEMENT

Research indicates that students who are exposed, consistently, to oral and written higher level questions demonstrate greater academic success than students who are limited to lower order questions. Bloom’s Taxonomy provides a hierarchy of cognitive skills that teachers can use to frame questions and activities that promote higher order thinking opportunities for students. The Florida Comprehensive Assessment Test (FCAT) uses two classifications of cognitive skills. Level I includes the knowledge, comprehension, and application (in familiar situation) categories, and Level II includes the application (in unique situations), analysis, synthesis, and evaluation categories. The chart below provides action verbs and question stems that are associated with each level of Bloom’s Taxonomy. CATEGORY ACTIONS QUESTION STEMS Knowledge (recalling-eliciting factual answers)

Ask, cite, count, define, indicate, inquire, know, list, locate, name, recite, state, tabulate, tell

Who, What, Why, When, Where, How, How much, What does it mean, Which one, Match, Choose

Comprehension (grasping meaning, translating, interpreting, extrapolating)

Associate, classify, compare, convert, describe, explain, extrapolate, give examples, identify, interpret, match, measure, put in order, recognize, report, restate, specify, stipulate, summarize, translate

State in your own words, Give an example, Condense the paragraph, What part doesn’t fit, What seems to be, What exceptions are there, Which are facts, Which are opinions, Translate, Outline, Explain what is meant, This represents

Application (using knowledge in situations that are new, unfamiliar, or have a new slant)

Apply, calculate, compute, demonstrate, do , estimate, find, illustrate, manipulate, relate, simulate, solve, use, utilize

What would result, Choose the best statements that apply, Estimate a solution, Apply a formula to, Select the best solution, Use new information to determine

Analysis (taking it apart) Analyze, categorize, classify, chart, code, compare, contrast, diagram, derive, determine, differentiate, dissect, draw conclusions, examine, experiment, investigate, make inferences, organize, question, separate, sequence, sort, survey, test

What is the function, What is the main idea or underlying theme, What statement is irrelevant or extraneous to, What does the author believe or assume, What ideas justify the conclusion, What is the premise, What persuasive technique, What is the relationship between

Synthesis (creating, combining elements into a pattern not clearly apparent before)

Arrange, assemble, change, combine, construct, design, develop, formulate, generalize, integrate, modify, plan, predict, produce, represent, set up, write

How would you test, Propose an alternative, Develop a plan, Design a model, Compose a song or play, Formulate a theory or hypothesis

Evaluation (judging, evaluating according to some set criteria)

Appraise, argue, assess, choose, conclude, critique, deduce, evaluate, grade, justify, prioritize, rate, rank, recommend, select, value

What fallacies, consistencies or inconsistencies appear, Find the errors in, Which is more important, more logical, more appropriate

1 6-8-00

ASSESSMENT ALIGNMENT KEY FCAT MATHEMATICS Grades K-12

CODE APPLICATION FCAT-M

Student uses science skills in a content application. Applications require problem solving beyond computation. These skills are found in the following Sunshine State Mathematics Strands:

Number Sense, Concepts, and Operations Measurement Geometry and Spatial Sense Algebraic Thinking Data Analysis and Probability

FCAT READING Grades K-12

CODE APPLICATION FCAT-R

Student uses reading skills in a content application. Applications require thinking not recall. These skills are found in the following Sunshine State Reading and Literature Standards:

The student uses the reading process effectively. The student constructs meaning from a wide range of texts. The student understands the common features of a variety of literary forms. The student responds critically to fiction, nonfiction, poetry, and drama.

FLORIDA WRITES! Grades K-12

CODE APPLICATION

FW-N Narrative - Student is writing to tell a story (GRADES K-4 ONLY).

FW-E Expository- Student is writing to explain.

FW-P Persuasive- Student is writing to convince (GRADES 5-10 ONLY).

HSCT-MATHEMATICS Grades 4-12

CODE SKILL

HSCT-M 1 Solve real-world problems using a variety of problem-solving strategies.

HSCT-M 2 Solve problems involving consumer application and percents.

HSCT-M 3 Apply geometric relationships to solve problems, using models when appropriate.

HSCT-M 4 Solve problems involving measurements in real-world situations, given formulas when appropriate.

HSCT-M 5 Analyze and apply the concepts of simple probability to real-world situations.

HSCT-M 6 Determine the appropriateness of statements or predict outcomes from data represented in charts, tables, or graphs.

HSCT-M 7 Translate phrases or sentences into algebraic expressions or equations and vice-versa.

HSCT-M 8 Plot and locate ordered pairs to represent real-world data. (x horizontal, y vertical).

HSCT-M 9 Solve one-step equations.

HSCT-M 10 Use ratios and proportions in problem-solving situations.

HSCT COMMUNICATIONS Grades 4-12

CODE APPLICATION

HSCT-C 1 Determine the main idea stated in a paragraph.

HSCT-C 2 Answer who, what, where, when, which, and how questions about sentences or paragraphs.

HSCT-C 3 Identify the cause or effect in a paragraph.

HSCT-C 4 Follow written directions

HSCT-C 5 Identify the main idea implied in a paragraph.

HSCT-C 6 Identify an appropriate conclusion or generalization for a paragraph.

HSCT-C 7 Distinguish between facts and opinions in a paragraph.

HSCT-C 8 Obtain appropriate information from pictures, maps, or signs.

HSCT-C 9 Obtain appropriate information from diagrams, tables, graphs, or schedules.

HSCT-C 10 Obtain appropriate information from indexes, tables or contents, or dictionary entries.

HSCT-C 11 Identify the appropriate source to obtain information using materials such as dictionaries, encyclopedias, atlases, directories, and newspapers.

FLORIDA COMPREHENSIVE ASSESSMENT TEST ALIGNMENT

Reading Content Tested / Grade 10 FCAT Reading is an assessment of the Sunshine StateStandards in reading. The Literature content area containspassages such as fictional stories, poems and folk tales. Theinformation content area contains passages such as magazineand newspaper articles about science, history or other topics.FCAT Reading assesses the following areas: R1 interpreting the meaning of text based on context clues R2 determining stated or implied main idea and identifying

relevant details R3 determining author’s purpose and point of view and

their effects on text R4 making and confirming inferences from what is read,

including interpreting diagrams, graphs, and statisticalillustrations.

R5 identifying devices of persuasion and methods of

appeal and their effectiveness R6 recognizing cause and effect R7 recognizing the use of comparison and contrast in a

text R8 analyzing the effectiveness of complex elements of

plot, such as setting, major events, problems, conflicts,and resolutions

R9 locating, gathering, analyzing, and evaluating written

information for a variety of purposes R10 selecting and using appropriate study and research

skills and tools according to the type of informationbeing gathered or organized

R11 analyzing the validity and reliability of primary source

information and using the information appropriately R12 synthesizing information from multiple sources to draw

conclusions

Mathematics Content Tested FCAT Mathematics is an assessment of the SunshineState Standards in mathematics. FCAT mathematicsassesses content from the following areas: Number Sense, Concepts, and Operations M1 identifying operations (+, -, x, ÷) and effects of

operations M2 determining estimates M3 knowing how numbers are represented and

used

Measurement M4 recognizing measurements and units of

measurement M5 comparing, contrasting, and converting

measurements

Geometry and Spatial Sense M6 describing, drawing, identifying, and analyzing

two- and three-dimensional shapes M7 visualizing and illustrating changes in shapes M8 using coordinate geometry

Algebraic Thinking M9 describing, analyzing, and generalizing

patterns, relations, and functions M10 writing and using expressions, equations,

inequalities, graphs, and formulas M11 analyzing, organizing, and interpreting data M12 identifying patterns and making predictions,

inferences, and valid conclusions M13 using probability and statistics

Writing Content Tested FCAT Writing is an assessment of the Sunshine StateStandards in writing. For this assessment, the studentproduces, in a 45-minute time period, a focused,organized, supported draft in response to a given prompt.FCAT writing assesses content from the following areas: W1 maintains clear focus of main ideas, theme, or

unifies point in one or more paragraphs W2 demonstrates organization and development of

topic (beginning, middle, end) in one or moreparagraphs

W3 uses quality details (examples, illustrations) to

support appropriate depth and thoroughness oftopic

W4 utilizes correct writing conventions (punctuation,

capitalization, spelling) and sentence structure W5 reflects a variety of question response

methods/types: Persuasive – the purpose of this type of writingis to convince the reader to accept a particularpoint of view or to take a specific action

Expository – the purpose of this type of writing isto inform, clarify, explain, define, or instruct bygiving information, explaining why or how,clarifying a process, or defining a concept

GOAL 3 STANDARDS

Standard 1

Florida students locate, comprehend, interpret, evaluate, maintain, and apply information, concepts, and ideas found in literature, the arts, symbols, recordings, video and other graphic displays, and computer files in order to perform tasks and/or for enjoyment.

Standard 2

Florida students communicate in English and other languages using information, concepts, prose, symbols, reports, audio and video recordings, speeches, graphic displays, and computer-based programs.

Standard 3

Florida students use numeric operations and concepts to describe, analyze, disaggregrate, communicate, and synthesize numeric data, and to identify and solve problems.

Standard 4

Florida students use creative thinking skills to generate new ideas, make the best decision, recognize and solve problems through reasoning, interpret symbolic data, and develop efficient techniques for lifelong learning.

Standard 5

Florida students display responsibility, self-esteem, sociability, self-management, integrity, and honesty.

Standard 6

Florida students will appropriately allocate time, money, materials, and other resources.

Standard 7

Florida students integrate their knowledge and understanding of how social, organizational, informational, and technological systems work with their abilities to analyze trends, design and improve systems, and use and maintain appropriate technology.

Standard 8

Florida students work cooperatively to successfully complete a project or activity.

Standard 9

Florida students establish credibility with their colleagues through competence and integrity, and help their peers achieve their goals by communicating their feelings and ideas to justify or successfully negotiate a position that advances goal attainment.

Standard 10

Florida students appreciate their own culture and the cultures of others, understand the concerns and perspectives of members of other ethnic and gender groups, reject the stereotyping of themselves and others, and seek out and utilize the views of persons from diverse ethnic, social, and educational backgrounds while completing individual and group projects.

Standard 11

Families will share the responsibility of accomplishing the standards set in Goal 3 throughout a student’s education from preschool through 12th grade.

Grade 8

In addition to the terms defined in the FCAT Grade 5 glossary, these terms pertain to the Sunshine State Standards in mathematics for Grades 6-8 and the content assessed on the Florida Comprehensive Assessment Test (FCAT) in mathematics at Grade 8. Absolute value a number's distance from zero (0) on a number line. The absolute value of both 4, written |4|, and

negative 4, written | –4|, equals 4.

Algebraic equation a mathematical sentence in which two expressions are connected by an equality symbol

Algebraic expression an expression containing numbers and variables (e.g., 7x), and operations that involve numbers and variables (e.g., 2x + y or 3a – 4). Algebraic expressions do not contain equality or inequity symbols

Algebraic order of operations

the order of performing computations is parentheses first, then exponents, followed by multiplication and division, then addition and subtraction. For example, 5+ (12–) ÷ 2 – 3 x 2 = 5 + 10 ÷ 2 – 3 x 2 = 5 + 5 – 6 = 10 – 6 = 4.

Break a zigzag on the line of the x- or y-axis in a line or bar graph indicating that the data being displayed does not include all of the values that exist on the number line used. Also called a Squiggle

Circumference the perimeter of a circle is called its circumference

Complementary Angles two angles, the sum of which is exactly 90º.

Coordinates numbers that correspond to points on a graph in the form (x, y)

Data displays different ways of displaying data in tables, charts, or graphs, including pictographs, circle graphs, single, double, or triple bar and line graphs, histograms, stem-and-leaf plots, and scatterplots

Diameter a line segment from any point on the circle passing through the center to another point of the circle

Enlargement an increase in size in all directions by a uniform amount

Exponent the number of times the base occurs as a factor. For example, 23 is the exponential (exponential form) form of 2 x 2 x 2. The numeral two (2) is called the base, and the numeral three (3) is called the exponent

Face one of the plane surfaces bounding a three-dimensional figure (a side)

Function a relation in which each value of x is paired with a unique

Function table a table of x-values and y-values (ordered pairs) that represents the function, pattern, relationship or sequence between the two variables

Height (h) a line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or basal plane.

Hypothesis a proposition or supposition developed to provide a basis for further investigation or research

Integers the numbers in the set {…, –4, –3, –2, –1, 0, 1, 2, 3, 4, …}

Intersection the point at which two lines meet

Inverse operation an action that cancels a previously applied action. For example, subtraction is the inverse operation of addition

Irrational number a real number that cannot be expressed as ratio of two numbers (e.g., 2 )

Linear equation an algebraic equation in which the variable quantity or quantities are in the first power only and the graph is a straight line (e.g., 20 = 2 (w + 4) + 2w and y = 3x +4)

Midpoint of a line segment

that point on a line segment that divides it into two equal parts

Negative exponent used in scientific notation to designate a number smaller than one (1) (e.g., 3.45 x 10 –2 equals 0.0345).

Odds the ratio of one event occurring to it not occurring

Ordered pair the location of a single point on a rectangular coordinate system where the digits represent the position relative to the x-axis and y-axis [e.g., (x, y) or (3, 4)].

Organize data to arrange data in a display that is meaningful and that assists in the interpretation of the data. See Data displays

Perpendicular forming a right angle

Pi (π) the symbol designating the ratio of the circumference of a circle to its diameter, represented as either 3.14 or 722

Prism a three-dimensional figure (polyhedron) with congruent, polygonal bases and lateral faces that are all parallelograms.

Probability, empirical the likelihood of an event happening that is based on experience and observation rather than on theory

Probability, theoretical the likelihood of an event happening that is based on theory rather than on experience and observation

Proportion a mathematical sentence stating that two ratios are equal

Pythagorean theorem the square of the hypotenuse (c) of a right triangle is equal to the sum of the square of the legs (a and b), as shown in the equation a2 + b2 = c2

Quadrant any of the four regions formed by the axes in a rectangular coordinate system

Radical an expression that has a root (square root, cube root, etc.) (e.g. 25 is a radical). Any root can be specified by an index number, b, in the form b a (e.g., 3 8 . A radical without an index number is understood to be a square root

Radical sign the symbol ( ) used before a number to show that the number is radicand

Radicand a number that appears with a radical sign (e.g., in 25 , 25 is the radicand)

Radius a line segment extending from the center of a circular sphere to a point on the circle or sphere

Rate/distance calculations involving rates, distances and time intervals, based on the distance, rate, time formula (D = rt)

Ratio the comparison of two quantities (e.g., the ratio of a and b is ba

, where b ≠ 0)

Rational number a real number that can be expressed as a ratio of two integers

Real numbers All rational and irrational numbers

Regular polygon a polygon that is both equilateral and equiangular

Right circular cylinder a cylinder in which the bases are parallel circles perpendicular to the side of the cylinder

Scatter plot a graph of data points, usually from an experiment, that is used to observe the relationship between two variables

Scientific notation a shorthand method of writing very large or very small numbers using exponents in which a number is expressed as the product of a power of 10 and a number that is greater than or equal to (1) and less than 10 (e.g., 7.59 x 105 = 759, 0000. It is based on the ideas that it is easier to read exponents than it is to count zeros. If a number is already a power of 10, it is simply written 1027 instead of 1 x 1027

Sequence an ordered list with either a constant difference (arithmetic) or a constant ration (geometric)

Similar figures two figures that are the same shape have corresponding, congruent angles, and have corresponding sides that are proportional in length

Solid figures three-dimensional figures that completely enclose a portion of space

Squiggle see Break

Supplementary angles two angles, the sum of which is exactly 180º

Surface area of a geometric solid

The sum of the areas of the faces of the figure that create the geometric solid

Tessellation a covering of a plane with congruent copies of the same patter with no holes and no overlaps, like floor tiles

x-intercept the value of x on a graph when y is zero (0). The x-axis is the horizontal number line on a rectangular coordinate system.

y-intercept the value of y on a graph when x is zero (0). The y-axis is the vertical number line on a rectangular coordinate system.

Grade 10 In addition to the terms defined in the FCAT Grades 5 and 8 glossaries, these terms pertain to the Sunshine State Standards in mathematics for Grades 9-12 and the content assessed on the Florida Comprehensive Assessment Test (FCAT) in mathematics at Grade 10.

Additive identity the number zero, (0) that is, adding 0 does not change a number's value (e.g., 5 + 0 = 5)

Additive inverse a number and its additive inverse have a sum of zero (0) (e.g., in the equation 3 + -3 = 0, 3 property and -3 are additive inverses of each other)

Associative property the way in which three or more numbers are grouped for addition or multiplication does not change their sum or product [e.g., (5 = 6) + 9 = 5 + ( 6 + 9) or ( 2 x 3) x 8 = 2 x (3 x 8)]

Commutative property the order in which two numbers are added or multiplied does not change their sum product (e.g., 2 + 3 = 3 + 2 or 4 x 7 = 7 x 4)

Distributive property for any real numbers a, b, and x, x (a + b) = ax + bx

Equivalent expressions expressions that have the same value but are presented in a different format using the properties of numbers [e.g., ax + bx = (a + b) x]

Finite graph a graph having definable limits

Intercept the value of a variable when all other variables in the equation equal zero (0) - - [on a graph, the values where a function crosses the axes]

Multiplicative identity the number one (1), that is, multiplying by 1 does not change the number one (1), that is, multiplying by 1 does not change a number’s value (e.g., 5 x 1 = 5)

Multiplicative inverse (reciprocal) any two numbers with a product of 1 (e.g., 4 and

41

)

Natural numbers (counting numbers)

the numbers in the set (1, 2, 3, 4, 5, ….)

Operational shortcut a method having fewer arithmetic calculations

Planar cross section the intersection of a plane and a three-dimensional figure

Proof a set of steps that demonstrate the truth of a given statement. Each step can be justified with a reason, such as a given statement. Each step can be justified with a reason, such as a given, a definition, an axiom, or a previously proven property.

Reciprocal See Multiplicative inverse.

Reflexive axiom of equality

a number or expression is equal to itself (e.g., ab = ab)

Right triangle geometry finding the measures of missing sides or angles of a right triangle when given the measures of other sides or angles. See Pythagorean theorem in the Grade 8 Glossary.

Rise the change in y going from one point of x to another (the vertical change on the graph)

Run the change in x going from one point of y to another (the horizontal change on the graph)

Slope the constant, m, in the linear equation for the slope-intercept form y = mx + b. The ratio of change in the vertical axis (y-axis) to each unit change in the horizontal axis (x-axis) in the form rise/run

Solid figures three-dimensional figures that completely enclose a portion of space (e.g., a rectangular solid, cube, sphere, right circular cylinder, right circular cone, and regular square pyramid)

Systems of equations a group of two or more equations that share variables. The solution to a system of equations is an ordered number set that makes all of the equations true.

Transitive property when the first element has a particular relationship to a second element that in turn has the same relationship to a third element, the first has this same relationship to the third element (e.g., if a = b and b = c, then a = c). Identity and equality are transitive relationships.

Grade 8 Reference Sheet excludes AU