High School

MATHEMATICS CURRICULUM GUIDE

Intensive Mathematics Course Number 1204000 /IRS 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.

HS Intensive Math.doc

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 Intensive Mathematics guide is designed to meet the needs of teachers, students, and the community. FOR THE TEACHER: The guide provides direction and assistance in the planning and delivery of instruction for Intensive Mathematics. Planning and delivering instruction based on Content Statements ensures coverage of all appropriate Sunshine State Standards as indicated in the student’s academic improvement plan. Intensive Mathematics, taken in addition to other designated mathematics courses, will provide remedial instruction and practice in mathematics skills and concepts to enable students to meet state standards in the five strands of mathematics. FOR THE STUDENT: The guide helps to ensure that students completing Intensive Mathematics will have met all appropriate district and state standards identified in the student’s academic improvement plan. Intensive Mathematics, taken in addition to other designated mathematics courses, will provide remedial instruction and practice in mathematics skills and concepts to enable students to meet state standards in the area of mathematics education. (Students may repeat this course if, on subsequent offerings, the required level of proficiency increases.) FOR THE INVOLVED COMMUNITY: The guide demonstrates the district’s commitment to implement and maintain high educational standards (and to provide remedial instruction) in mathematics 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.

SUNSHINE STATE STANDARDS ALIGNMENT INTENSIVE MATHEMATICS Sunshine State Standard (Benchmark)

The Student

Content Statement

1204000/IRS The Student

Sample Performance Descriptions

Assessment

Goal 3 Standards

M3

3,4

M3

3,4

M3

3,4

M3

3,4

1. The student understands the different ways numbers are represented and used in the real world. MA.A.1.4.2 MA.A.1.4.2 MA.A.1.4.4

MA.A.1.4.4

IRSX001X: (9) Students will compare, order, and determine the relative size of real numbers. IRSX002X: (10) Students will compute, identify, and/or compare the relative size of real numbers. IRSX003X: (9) Students will use numbers expressed in equivalent forms, including integers, fractions, decimals, percents, scientific notation and other exponential forms, radicals, and absolute value. IRSX004X: (10) Students will identify and/or represent numbers in equivalent forms.

Creates “piles” of pennies, paper, etc, showing the physical size of 10, 100, 1000, etc. Matches (different forms) numerals from index cards to correct position on a number line. Compares NFL, NBA, MLB or NHL salaries in scientific notation. Creates card sets – various fractions, percents, decimals, radicals, and play a matching game.

2. The student understands the effects of operations on numbers and the relationships among these operations, selects appropriate operations, and computes for problem solving. MA.A.3.4.1

MA.A.3.4.1 MA.A.3.4.2 MA.A.3.4.2 MA.A.3.4.3 MA.A.3.4.3

IRSX005X: (9) Students will determine, analyze, and/or identify the effects or results of mathematical operations (including appropriate inverse operations) on real numbers. IRSX006X: (10) Students will analyze and identify the effects or results of mathematical operations. IRSX007X: (9) Students will use an alternative strategy that permits an operational shortcut and/or use the correct order of operations to solve a problem. IRSX008X: (10) Students will identify an alternative strategy that permits an operational shortcut and/or use the correct order of operations to solve a problem. IRSX009X: (9) Students will solve real-world problems using appropriate computation with real numbers. IRSX010X: (10) Students will solve real-world problems using appropriate computation.

Analyzes the formulas on the FCAT Mathematics Reference Sheet and write real world problems that apply those formulas.

M1

3,4

Plans a class party, for 30 students from a pizza menu, with different pizzas, toppings and drinks (Glencoe Skills, Exercises, and Applications Workbook – Skills 16 –20 Unit 7 Activity 4). Finds the numbers 1 – 100 using any one digit 4 times.

M1

3,4,8

M1

3,4

Completes AIM Higher – FCAT Math Level H - Challenge on Performing Operations pages 87 – 90.

M1

3,4

Reads stories from “Math Stories for Problem Solving Success” and answer related questions from Problem Set A. Reads stories from “Math Stories for Problem Solving Success” and answer related questions from Problem Set B.

M1 R9 M1 R9

2,3,4 2,3,4

Sunshine State Standard (Benchmark)

The Student

Content Statement

Assessment

Goal 3 Standards

Draws their hand on grid paper and estimates the area by upper and lower bounds.

M2

3,4

Completes AIM Higher – FCAT Math Level H – Challenge on Forming Estimates on pages 93 – 94.

M2

3,4

Uses pattern blocks or 1” x 1” tiles to show various shapes with a specific area to find the maximum perimeter.

M4

3,4,8

Uses pattern blocks or 1” x 1” tiles to show various shapes with a specific perimeter to find the maximum area.

M4

3,4,8

Investigates dividing the face of the clock into angles.

M4

3,4

Create a spinner given a specific number of sections. (Glencoe Skills, Exercises, and Applications Workbook – Skill 52 Unit 10 Activity 3). Creates a scale drawing of their “dream” house with at least 1 bathroom, a kitchen, 2 bedrooms, etc.

M4

3,4

M4

3,4

The Student

Sample Performance Descriptions

3. The student uses estimation in problem solving and computation. MA.A.4.4.1 MA.A.4.4.1

IRSX011X: (9) Students will use an appropriate estimation strategy or determine the reasonableness of results. IRSX012X: (10) Students will demonstrate or explain the strategies used to estimate a solution or determine and explain the reasonableness of results.

4. The student measures quantities in the real world and uses the measures to solve problems. MA.B.1.4.1 MA.B.1.4.1 MA.B.1.4.2 MA.B.1.4.2 MA.B.1.4.3

IRSX013X: (9) Students will use and derive formulas to solve problems involving perimeter, area, surface area, circumference, or volume. IRSX014X: (10) Students will solve a problem by using and/or deriving formulas for perimeter, circumference, area, surface area, or volume. IRSX015X: (9) Students will solve problems by using formulas (derived or standard) for rate, distance, time, or angle measures. IRSX016X: (10) Students will solve problems by using and/or deriving formulas for rate, distance, time, angle measures, or are lengths. IRSX017X: (9) Students will use an appropriate proportion to solve real world measurement problems, which may include similar figures or scale drawings.

5. The student compares, contrasts, and converts within systems of measurement (both standard/nonstandard and metric/customary). MA.B.2.4.1

IRSX018X: (9) Students will use indirect methods of measurement to solve problems within systems of measurement.

MA.B.2.4.1

IRSX019X: (10) Students will use indirect methods of measurement to solve a problem.

MA.B.2.4.2

IRSX020X: (9) Students will solve problems involving units of measure, conversions, and rated measures (e.g., miles per hour, feet per second). IRSX021X: (10) Students will solve problems involving conversions and rated measures.

MA.B.2.4.2

Takes a picture of a student and a taller object, measures picture heights of both, and actual height of student. Then, using proportions, finds the actual height of the taller object. (Same taller object for all students – comparison of answers) Takes a picture of student and a taller object, measures picture heights of both, and actual height of student. Then using proportions, finds the actual height of the taller object. Explain reasonableness of answer. Finds how many feet per second a car travels going at a speed of 80 miles per hour. (Algebra To Go Handbook 291) Finds the currency exchange rate of U.S. dollars with at least 2 countries. (Algebra To Go Handbook 290)

M5

3,4

M5 W5 –expository

2,3,4

M5

3,4

M5

3,4

Sunshine State Standard (Benchmark)

The Student

Content Statement

Assessment

Goal 3 Standards

Completes AIM Higher – FCAT Math – Level H –Challenge on two- and three- dimensional shapes pages 149 – 152.

M6

3,4

Completes AIM Higher – FCAT Math – Level J – Challenges on triangles pages 123-130 and circles pages 145-148.

M6

3,4

Draws an irregular polygon that tessellates.

M7

3,4

Using tangrams, finds and compares triangles, parallelograms, trapezoids, and polygons (convex and concave).

M7

3,4

Creates card sets on circles, parabolas, etc., their properties and graphs, then matches them; ALSO AIM Higher – FCAT Math – Level J – Challenge on Planes and Solids pages 167 – 170.

M7

3,4

The Student

Sample Performance Descriptions

6. The student describes draws, identifies, and analyzes two- and three-dimensional shapes. MA.C.1.4.1 MA.C.1.4.1

7.

IRSX022X: (9) Students will use geometric properties and relationships to determine numeric and/or definitional characteristics of geometric shapes. IRSX023X: (10) Students will use geometric properties and relationships to determine and/or explain numeric and definitional characteristics of geometric shapes.

The student visualizes and illustrates ways in which shapes can be combined, subdivided, and changed.

MA.C.2.4.1 MA.C.2.4.1 MA.C.2.4.2

IRSX024X: (9) Students will apply geometric concepts, properties, formulas, and/or relationships to solve problems. IRSX025X: (10) Students will recognize, represent, apply, and/or explain geometric concepts, properties, formulas, and relationships to solve problems. IRSX026X: (10) Students will analyze and apply geometric properties to solve problems involving planar cross-sections.

8. The student uses coordinate geometry to locate object in both two and three dimensions and to describe objects algebraically. MA.C.3.4.1

MA.C.3.4.1 MA.C.3.4.2

MA.C.3.4.2

IRSX027X: (9) Students will apply geometric properties, formulas, and relationships in the coordinate plane to solve real-world and mathematical problems, including ratio, proportion, and right triangle geometry. IRSX028X: (10) Students will represent, apply, and/or explain geometric properties, formulas, and relationships to solve a problem. IRSX029X: (9) Students will apply algebraic properties, including distance, midpoint, slope, parallelism, and perpendicularity, to interpret graphs or solve problems in a rectangular coordinate system. IRSX030X: (10) Students will interpret graphs and solve problems by applying, verifying, and/or explaining algebraic properties in a rectangular coordinate system.

Explains how to find the height where a ladder meets a building.

M8 W5 – expository

2,3,4

Completes Algebra To Go Resource book – pages 100 – 101 “A Ladder of Love”

M8 W5 – expository

2,3,4

Completes Algebra To Go Resource book – pages 126 – 127 “An Acute Cabin”

M8

3,4

Completes Algebra To Go Resource book – pages 88 – 89 “Are We in Line?”

M8

3,4

Sunshine State Standard (Benchmark)

The Student

Content Statement

Assessment

Goal 3 Standards

Completes Algebra To Go Resource book – pages 208 – 209 “Pascal’s Triangle”

M9

3,4

Completes Algebra To Go Resource book – pages 56 – 57 “And the Winner Is …”

M9

3,4

Using various tables (input – output charts), the students can find the change and explain the result.

M9 W5 – expository

3,4

Completes Algebra To Go Resource book – Teacher’s Notes – page 32 “What would happen in a baseball game if the rules were changed?” Example – 4 outs in an inning, batter out after 1 strike, batter walks after 2 balls, game has 12 innings

M9 W5 – expository

2,3,4

Completes Lessons 1 – 7 in Hands On Equations.

M10

3,4

Completes Algebra To Go Resource book – pages 76 – 77 “The Quadratic Salutation”

M10

3,4

M11 W5 - expository

2,3,4

The Student

Sample Performance Descriptions

9. The student describes, analyzes, and generalizes a wide variety of patterns, relations, and functions. MA.D.1.4.1 MA.D.1.4.1 MA.D.1.4.2

MA.D.1.4.2

IRSX031X: (9) Students will analyze, identify, and/or generalize relationships or functions to solve problems or continue patterns. IRSX032X: (10) Students will analyze, identify, and/or generalize relationships or functions to solve problems or continue patterns. IRSX033X: (9) Students will determine the result of changing a parameter in a given situation or function or determine the required change in a parameter to achieve the desired outcome. IRSX034X: (10) Students will determine and/or explain the result of changing a parameter in a given situation or function or determine the required change in a parameter to achieve the desire outcome.

10. The student uses expressions, equations, inequalities, graphs, and formulas to represent and interpret situations. MA.D.2.4.2 MA.D.2.4.2

IRSX035X: (9) Students will interpret and/or solve realworld problems involving expressions, linear equations or linear inequalities or manipulating literal equations. IRSX036X: (10) Students will interpret and/or solve realworld problems involving expressions, equations, inequalities, and/or systems of equations and inequalities by formulating, solving, and/or graphing equations.

11. The student understands and uses the tools of data analysis for managing information. MA.E.1.4.1 MA.E.1.4.1 MA.E.1.4.2

MA.E.1.4.2

IRSX037X: (9) Students will interpret and/or predictions based on displayed data or identify accurate displays of given data. IRSX038X: (10) Students will display, analyze, and/or interpret data.

Analyzes a double bar graph from magazines, newspaper, Internet, etc. Completes a M & M lab to collect, organize, and display data.

M11

3,4

IRSX039X: (9) Students will calculate and/or interpret measures of central tendency and/or range for sets of data or determine the most meaningful measure to describe the data for give situations. IRSX040X: (10) Students will calculate and/or interpret measures of central tendency and/or range for sets of data or determine the most meaningful measure to describe the data for given situations.

Conducts a class survey of heights in inches and in centimeters, organize the data in appropriate graph and applies statistical measures.

M11

3,4,8

Conducts a survey about which flavor of ice cream, organize data, and applies statistical measures.

M11

3,4,8

Sunshine State Standard (Benchmark)

The Student

Content Statement

The Student

Sample Performance Descriptions

Assessment

Goal 3 Standards

12. The student identifies patterns and makes predictions from an orderly display of data using concepts of probability and statistics. MA.E.2.4.1

MA.E.2.4.1

IRSX041X: (9) Students will use a variety of methods, including counting procedures, tables, and tree diagrams, to determine the probability of a given simple event or independent, compound events. IRSX042X: (10) Students will determine the probability of a given event or events.

Given digits 1 –5, determines how many different area codes are possible for both situations: repetition and no repetition. (Glencoe Skill, Exercises, and Applications Workbook – Skills 69 –70 Unit 10 Activity 1) Predicts the probability of a team winning the World Series, Super Bowl, NCAA Final Four, Stanley Cup, NBA championship based on team records at their halfway point.

M12

3,4

M13

3,4

M12 M13

3,4

M12 M13 R4 W5 – expository

2,3,4

13. The student uses statistical methods to make inferences and valid arguments about real-world situations. MA.E.3.4.1

IRSX043X: (9) Students will analyze and interpret data that result from statistical experiments.

MA.E.3.4.1

IRSX044X: (10) Students will analyze and interpret data that result from statistical experiments or identify and/or explain design components or flaws in statistical experiments.

Given various data from the Internet or another source, determines the appropriate graph to display the data accurately. (Glencoe Skills, Exercises, and Applications Workbook – Skills 54 – 55 Unit 8 Activity 5) Given various graphs from magazines, newspapers, Internet, etc, explains how another graph may be more useful and how could the data be used differently.

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

;

1

USING 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 Knowledge (recalling-eliciting factual answers) Comprehension (grasping meaning, translating, interpreting, extrapolating) Application (using knowledge in situations that are new, unfamiliar, or have a new slant)

ACTIONS Ask, cite, count, define, indicate, inquire, know, list, locate, name, recite, state, tabulate, tell Associate, classify, compare, convert, describe, explain, extrapolate, give examples, identify, interpret, match, measure, put in order, recognize, report, restate, specify, stipulate, summarize, translate Apply, calculate, compute, demonstrate, do , estimate, find, illustrate, manipulate, relate, simulate, solve, use, utilize

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

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

Evaluation (judging, evaluating according to some set criteria)

1

6-8-00

QUESTION STEMS Who, What, Why, When, Where, How, How much, What does it mean, Which one, Match, Choose 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 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 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 How would you test, Propose an alternative, Develop a plan, Design a model, Compose a song or play, Formulate a theory or hypothesis What fallacies, consistencies or inconsistencies appear, Find the errors in, Which is more important, more logical, more appropriate

FLORIDA COMPREHENSIVE ASSESSMENT TEST ALIGNMENT

Reading Content Tested / Grade 8

Mathematics Content Tested

Writing Content Tested

FCAT Reading is an assessment of the Sunshine State Standards in reading. The Literature content area contains passages such as fictional stories, poems and folk tales. The information content area contains passages such as magazine and newspaper articles about science, history or other topics. FCAT Reading assesses the following areas:

FCAT Mathematics is an assessment of the Sunshine State Standards in mathematics. FCAT mathematics assesses content from the following areas:

FCAT Writing is an assessment of the Sunshine State Standards in writing. For this assessment, the student produces, 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:

R1 R2

interpreting the meaning of text based on context clues analyzing words and text, drawing conclusions, using context and word structure clues, and recognizing organizational patterns

R3

determining stated or implied main ideas or essential messages

R4

identifying the author’s purpose and/or point of view

R5

checking validity and accuracy of information from research (including recognizing facts and opinions, strong vs. weak arguments, and the influence of an author’s personal views on text)

R6

recognizing the use of comparison and contrast within a test

R7

recognizing complex elements of text, including plot, theme, setting, character development, conflicts, and resolution

R8

understanding how character and plot development, point of view, and tone are used in various selections

R9

recognizing cause and effect

R10

comparing and/or contrasting characters, settings, and events as presented in various texts

R11

locating, organizing, and interpreting written information for a variety of purposes

R12

using a variety of reference materials, including indexes, magazines, newspapers, and journals, to gather information for a variety of purposes

Number Sense, Concepts, and Operations M1

identifying operations (+, -, x, ÷) and effects of operations

W1

maintains clear focus of main ideas, theme, or unifies point in one or more paragraphs

M2

determining estimates

W2

M3

knowing how numbers are represented and used

demonstrates organization and development of topic (beginning, middle, end) in one or more paragraphs

W3

uses quality details (examples, illustrations) to support appropriate depth and thoroughness of topic

converting

W4

utilizes correct writing conventions (punctuation, capitalization, spelling) and sentence structure

Geometry and Spatial Sense M6 describing, drawing, identifying, and analyzing two- and three-dimensional shapes

W5

reflects a variety of question response methods/types: Persuasive – the purpose of this type of writing is to convince the reader to accept a particular point of view or to take a specific action

Measurement M4 recognizing measurements measurement M5

comparing, contrasting, measurements

and and

units

M7

visualizing and illustrating changes in shapes

M8

using coordinate geometry

of

Algebraic Thinking M9 describing, analyzing, and generalizing patterns, relations, and functions M10

writing and using expressions, inequalities, graphs, and formulas

equations,

Data Analysis and Probability M11 analyzing, organizing, and interpreting data M12

identifying patterns and making inferences, and valid conclusions

M13

using probability and statistics

predictions,

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

FLORIDA COMPREHENSIVE ASSESSMENT TEST ALIGNMENT

Reading Content Tested / Grade 10

Mathematics Content Tested

Writing Content Tested

FCAT Reading is an assessment of the Sunshine State Standards in reading. The Literature content area contains passages such as fictional stories, poems and folk tales. The information content area contains passages such as magazine and newspaper articles about science, history or other topics. FCAT Reading assesses the following areas:

FCAT Mathematics is an assessment of the Sunshine State Standards in mathematics. FCAT mathematics assesses content from the following areas:

FCAT Writing is an assessment of the Sunshine State Standards in writing. For this assessment, the student produces, 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:

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

R5

making and confirming inferences from what is read, including interpreting diagrams, graphs, and statistical illustrations. 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

Number Sense, Concepts, and Operations M1

identifying operations (+, -, x, ÷) and effects of operations

W1

maintains clear focus of main ideas, theme, or unifies point in one or more paragraphs

M2

determining estimates

W2

M3

knowing how numbers are represented and used

demonstrates organization and development of topic (beginning, middle, end) in one or more paragraphs

W3

uses quality details (examples, illustrations) to support appropriate depth and thoroughness of topic

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 writing is to convince the reader to accept a particular point of view or to take a specific action

Measurement M4

recognizing measurements measurement

M5

comparing, contrasting, measurements

and and

units

of

converting

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

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

M9

describing, analyzing, and generalizing patterns, relations, and functions

R10

selecting and using appropriate study and research skills and tools according to the type of information being gathered or organized

M10

writing and using expressions, equations, inequalities, graphs, and formulas

M11

analyzing, organizing, and interpreting data

R11

analyzing the validity and reliability of primary source information and using the information appropriately

M12

identifying patterns and making predictions, inferences, and valid conclusions

R12

synthesizing information from multiple sources to draw conclusions

M13

using probability and statistics

Algebraic Thinking

Expository – the purpose of this type of writing is to inform, clarify, explain, define, or instruct by giving 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

Circumference

a mathematical sentence in which two expressions are connected by an equality symbol 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 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. 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 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 Diameter

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 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 Face

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 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

Hypothesis

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

Algebraic expression Algebraic order of operations Break

Height (h)

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

Linear equation Midpoint of a line segment 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 Organize data

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)]. 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

Prism Probability, empirical

a three-dimensional figure (polyhedron) with congruent, polygonal bases and lateral faces that are all parallelograms. 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 any of the four regions formed by the axes in a rectangular coordinate system

Quadrant 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 (

Radicand Radius

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

) used before a number to show that the number is radicand

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

a , where b ≠ 0) b

Rational number

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

Real numbers

All rational and irrational numbers

22 7

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

Scientific notation

Sequence

Solid figures

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

Similar figures

x-intercept y-intercept

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

1 ) 4

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 Grade 8 Reference Sheet excludes AU