MATHEMATICS CURRICULUM GUIDE - Volusia County...

High School

MATHEMATICS CURRICULUM GUIDE

Intensive Mathematics Course Number 1204000 /IRS

HS Intensive 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 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 1204000/IRS Sunshine State

Standard (Benchmark)

Content Statement

The Student

Sample Performance Descriptions

The Student

Assessment

Goal 3 Standards

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

MA.A.1.4.2 IRSX001X: (9) Students will compare, order, and determine the relative size of real numbers.

Creates “piles” of pennies, paper, etc, showing the physical size of 10, 100, 1000, etc.

M3 3,4

MA.A.1.4.2 IRSX002X: (10) Students will compute, identify, and/or compare the relative size of real numbers.

Matches (different forms) numerals from index cards to correct position on a number line.

M3 3,4

MA.A.1.4.4 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.

Compares NFL, NBA, MLB or NHL salaries in scientific notation.

M3 3,4

MA.A.1.4.4 IRSX004X: (10) Students will identify and/or represent numbers in equivalent forms.

Creates card sets – various fractions, percents, decimals, radicals, and play a matching game.

M3 3,4

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 IRSX005X: (9) Students will determine, analyze, and/or

identify the effects or results of mathematical operations (including appropriate inverse operations) on real numbers.

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

M1 3,4

MA.A.3.4.1 IRSX006X: (10) Students will analyze and identify the effects or results of mathematical operations.

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).

M1 3,4,8

MA.A.3.4.2 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.

Finds the numbers 1 – 100 using any one digit 4 times. M1 3,4

MA.A.3.4.2 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.

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

M1 3,4

MA.A.3.4.3 IRSX009X: (9) Students will solve real-world problems using appropriate computation with real numbers.

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

M1 R9

2,3,4

MA.A.3.4.3 IRSX010X: (10) Students will solve real-world problems using appropriate computation.

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

M1 R9

2,3,4

Sunshine State Standard

(Benchmark)

Content Statement

The Student


The Student

Assessment

Goal 3 Standards

3. The student uses estimation in problem solving and computation. MA.A.4.4.1 IRSX011X: (9) Students will use an appropriate

estimation strategy or determine the reasonableness of results.

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

M2 3,4

MA.A.4.4.1 IRSX012X: (10) Students will demonstrate or explain the strategies used to estimate a solution or determine and explain the reasonableness of results.

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

M2 3,4

4. The student measures quantities in the real world and uses the measures to solve problems. MA.B.1.4.1 IRSX013X: (9) Students will use and derive formulas to

solve problems involving perimeter, area, surface area, circumference, or volume.

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

MA.B.1.4.1 IRSX014X: (10) Students will solve a problem by using and/or deriving formulas for perimeter, circumference, area, surface area, or volume.

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

MA.B.1.4.2 IRSX015X: (9) Students will solve problems by using formulas (derived or standard) for rate, distance, time, or angle measures.

Investigates dividing the face of the clock into angles. M4 3,4

MA.B.1.4.2 IRSX016X: (10) Students will solve problems by using and/or deriving formulas for rate, distance, time, angle measures, or are lengths.

Create a spinner given a specific number of sections. (Glencoe Skills, Exercises, and Applications Workbook – Skill 52 Unit 10 Activity 3).

M4 3,4

MA.B.1.4.3 IRSX017X: (9) Students will use an appropriate proportion to solve real world measurement problems, which may include similar figures or scale drawings.

Creates a scale drawing of their “dream” house with at least 1 bathroom, a kitchen, 2 bedrooms, etc.

M4 3,4

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.

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)

M5 3,4

MA.B.2.4.1 IRSX019X: (10) Students will use indirect methods of measurement to solve a problem.

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.

M5 W5 –expository

2,3,4

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).

Finds how many feet per second a car travels going at a speed of 80 miles per hour. (Algebra To Go Handbook 291)

M5 3,4

MA.B.2.4.2 IRSX021X: (10) Students will solve problems involving conversions and rated measures.

Finds the currency exchange rate of U.S. dollars with at least 2 countries. (Algebra To Go Handbook 290)

M5 3,4


(Benchmark)

Content Statement

The Student


The Student

Assessment

Goal 3 Standards

6. The student describes draws, identifies, and analyzes two- and three-dimensional shapes. MA.C.1.4.1 IRSX022X: (9) Students will use geometric properties and

relationships to determine numeric and/or definitional characteristics of geometric shapes.

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

M6 3,4

MA.C.1.4.1 IRSX023X: (10) Students will use geometric properties and relationships to determine and/or explain numeric and definitional characteristics of geometric shapes.

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

M6 3,4

7. The student visualizes and illustrates ways in which shapes can be combined, subdivided, and changed. MA.C.2.4.1 IRSX024X: (9) Students will apply geometric concepts,

properties, formulas, and/or relationships to solve problems.

Draws an irregular polygon that tessellates. M7 3,4

MA.C.2.4.1 IRSX025X: (10) Students will recognize, represent, apply, and/or explain geometric concepts, properties, formulas, and relationships to solve problems.

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

M7

3,4

MA.C.2.4.2 IRSX026X: (10) Students will analyze and apply geometric properties to solve problems involving planar cross-sections.

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

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 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.

Explains how to find the height where a ladder meets a building. M8 W5 – expository

2,3,4

MA.C.3.4.1 IRSX028X: (10) Students will represent, apply, and/or explain geometric properties, formulas, and relationships to solve a problem.

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

M8 W5 – expository

2,3,4

MA.C.3.4.2 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.

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

M8 3,4

MA.C.3.4.2 IRSX030X: (10) Students will interpret graphs and solve problems by applying, verifying, and/or explaining algebraic properties in a rectangular coordinate system.

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

M8

3,4


(Benchmark)

Content Statement

The Student


The Student

Assessment

Goal 3 Standards

9. The student describes, analyzes, and generalizes a wide variety of patterns, relations, and functions. MA.D.1.4.1 IRSX031X: (9) Students will analyze, identify, and/or

generalize relationships or functions to solve problems or continue patterns.

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

M9 3,4

MA.D.1.4.1 IRSX032X: (10) Students will analyze, identify, and/or generalize relationships or functions to solve problems or continue patterns.

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

M9 3,4

MA.D.1.4.2 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.

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


3,4

MA.D.1.4.2 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.

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


2,3,4

10. The student uses expressions, equations, inequalities, graphs, and formulas to represent and interpret situations. MA.D.2.4.2 IRSX035X: (9) Students will interpret and/or solve real-

world problems involving expressions, linear equations or linear inequalities or manipulating literal equations.

Completes Lessons 1 – 7 in Hands On Equations. M10 3,4

MA.D.2.4.2 IRSX036X: (10) Students will interpret and/or solve real-world problems involving expressions, equations, inequalities, and/or systems of equations and inequalities by formulating, solving, and/or graphing equations.

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

M10 3,4

11. The student understands and uses the tools of data analysis for managing information. MA.E.1.4.1 IRSX037X: (9) Students will interpret and/or predictions

based on displayed data or identify accurate displays of given data.

Analyzes a double bar graph from magazines, newspaper, Internet, etc. M11 W5 - expository

2,3,4

MA.E.1.4.1 IRSX038X: (10) Students will display, analyze, and/or interpret data.

Completes a M & M lab to collect, organize, and display data.

M11 3,4

MA.E.1.4.2 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.

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

MA.E.1.4.2 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 survey about which flavor of ice cream, organize data, and applies statistical measures.

M11 3,4,8


(Benchmark)

Content Statement

The Student


The Student

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 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.

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)

M12 3,4

MA.E.2.4.1 IRSX042X: (10) Students will determine the probability of a given event or events.

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.

M13 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. 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)

M12 M13

3,4

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 graphs from magazines, newspapers, Internet, etc, explains how another graph may be more useful and how could the data be used differently.

M12 M13 R4

W5 – expository

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

FLORIDA COMPREHENSIVE ASSESSMENT TEST ALIGNMENT

Reading Content Tested / Grade 8 FCAT Reading is an assessment of the Sunshine StateStandards in reading. The Literature content areacontains passages such as fictional stories, poems andfolk tales. The information content area containspassages such as magazine and newspaper articles aboutscience, history or other topics. FCAT Reading assessesthe following areas: R1 interpreting the meaning of text based on

context clues R2 analyzing words and text, drawing conclusions,

using context and word structure clues, andrecognizing 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 andopinions, strong vs. weak arguments, and theinfluence 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 invarious selections

R9 recognizing cause and effect R10 comparing and/or contrasting characters,

settings, and events as presented in varioustexts

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

Mathematics Content Tested FCAT Mathematics is an assessment of the Sunshine StateStandards in mathematics. FCAT mathematics assessescontent 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 Data Analysis and Probability 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

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

Grade 8 Reference Sheet excludes AU

MATHEMATICS CURRICULUM GUIDE - Volusia County...

Documents

Transcript of MATHEMATICS CURRICULUM GUIDE - Volusia County...