TEST INFORMATION BOOKLET

Massachusetts Testsfor Educator Licensure ®TESTINFORMATIONBOOKLET03 General CurriculumMA-SG-FLD003-04Massachusetts Department of Education

Table of ContentsHow to Prepare for the Tests.............................................................................................................. 1Overview of the Subject Matter Tests............................................................................................... 2Development of the Subject Matter Tests......................................................................................... 3Structure of the Content of the Tests................................................................................................. 3Description of the General Curriculum Test..................................................................................... 6Using the Test Objectives ................................................................................................................. 6Developing a Study Outline.............................................................................................................. 7Identifying Resources ....................................................................................................................... 8Approaching the Test Items ............................................................................................................... 12Multiple-Choice Item Formats.......................................................................................................... 12Multiple-Choice Item Format One: The Single Test Item............................................................ 12Multiple-Choice Item Format Two: Test Items with Stimulus Material ...................................... 14Open-Response Item Formats ........................................................................................................... 15Scoring Open-Response Items .......................................................................................................... 16Sample Test Administration Documents........................................................................................... 18Sample Test Directions ..................................................................................................................... 18Sample Directions for the Open-Response Item Assignments.......................................................... 19Sample Answer Document................................................................................................................ 20The Day of the Test Administration .................................................................................................. 26Preparing for the Test Administration............................................................................................... 26Test-Taking Tips............................................................................................................................... 26After the Test Administration ............................................................................................................ 28Score Reporting................................................................................................................................. 28Interpreting Your Score Report......................................................................................................... 28General Curriculum (03) .................................................................................................................... 29Test Overview Chart ......................................................................................................................... 31Test Objectives.................................................................................................................................. 32Sample Test Items............................................................................................................................. 38Answer Key and Sample Response................................................................................................... 47Test Information Booklet Order Form

General Curriculum(Field 03)Test Overview ChartTest ObjectivesSample Test ItemsAnswer Key and Sample Response29

Test Overview Chart:General Curriculum (03)SubareasApproximateNumber ofMultiple-Choice ItemsI. Language Arts 21–23Number ofOpen-ResponseItemsII. Mathematics 20–22III. History and Social Science 20–22IV. Science and Technology/Engineering 20–22V. Child Development 14–16VI. Integration of Knowledge and Understanding 2The General Curriculum test is designed to assess the candidate's knowledge of the elementary subjectmatter required for a Massachusetts Elementary teaching license and other licenses as defined in theRegulations for Educator Licensure and Preparation Program Approval, 603 CMR 7.06, "Subject MatterKnowledge Requirements for Teachers." This subject matter knowledge is delineated in theMassachusetts Department of Education's Regulations.The General Curriculum test assesses the candidate's proficiency and depth of understanding of thesubject at the level required for a baccalaureate major, according to Massachusetts standards. Candidatesare typically nearing completion of or have completed their undergraduate work when they take the test.The multiple-choice items on the test cover the subareas as indicated in the chart above. The openresponseitems may relate to topics covered in any of the subareas and will typically require breadth ofunderstanding of the elementary field and the ability to relate concepts from different aspects of the field.Responses to the open-response items are expected to be appropriate and accurate in the application ofsubject knowledge, to provide high-quality and relevant supporting evidence, and to demonstrate asoundness of argument and understanding of the elementary field.31

Test Objectives:General Curriculum (03)Massachusetts Tests for Educator LicensureFIELD 03: GENERAL CURRICULUMTEST OBJECTIVESSubareaMultiple-ChoiceRange ofObjectivesApproximateTestWeightingI. Language Arts 01–05 17%II. Mathematics 06–09 17%III. History and Social Science 10–13 17%IV. Science and Technology/Engineering 14–16 17%V. Child Development 17–18 12%80%Open-ResponseVI. Integration of Knowledge and Understanding 19 20%32

Test Objectives: General CurriculumSUBAREAS:LANGUAGE ARTSMATHEMATICSHISTORY AND SOCIAL SCIENCESCIENCE AND TECHNOLOGY/ENGINEERINGCHILD DEVELOPMENTINTEGRATION OF KNOWLEDGE AND UNDERSTANDINGLANGUAGE ARTS 1 [17%]0001 Understand the history and structure of the English language.For example: major developments in the history of the English language (e.g., invention ofthe printing press, standardization of written language, development of dictionaries); majorlinguistic origins of the English language (e.g., Anglo-Saxon roots, Celtic influences, Greekand Roman elements); derivatives and borrowings; differences between oral and writtenEnglish (e.g., level of formality, diversity of oral dialects, uniformity of written language);fundamental language structures (i.e., phonology, morphology, syntax, and semantics); partsof speech (e.g., noun, verb, adjective, adverb, conjunction, preposition); sentence types(e.g., simple, compound, complex) and sentence purposes (e.g., declarative, imperative,interrogative); and rules of English grammar and conventions of editedAmerican English.0002 Understand American literature and selected literature from classical and contemporaryperiods.For example: historically or culturally significant works, authors, and themes of U.S.literature; selected literature from classical and contemporary periods; literature of othercultures; elements of literary analysis (e.g., analyzing story elements, interpreting figurativelanguage); and varied focuses of literary criticism (e.g., the author, the context of the work,the text, the response of the reader).0003 Understand literary genres, elements, and techniques.For example: basic literary terminology (e.g., flashback, foreshadowing); characteristicsof different genres and types of literature (e.g., myths, folk tales,fiction, nonfiction, drama, poetry); elements of fiction (e.g., plot, character, setting,theme, voice); types of poetry (e.g., lyric, narrative, haiku); characteristics of poetryand poetic techniques (e.g., meter, rhyme, alliteration, figurative language); and types ofdrama (e.g., comedy, tragedy) and common dramatic devices (e.g., suspense,soliloquy).1. Knowledge of the following content will be measured on a separate Foundations of Reading test for allprospective Early Childhood, Elementary, and Special Education teachers: 1) reading theory, research, andpractice; 2) development of an oral and reading vocabulary; 3) theories on the relationship between beginningwriting and reading; 4) approaches and practices for developing skills in using writing tools; and 5) theoriesof first- and second-language acquisition and development.33

Test Objectives: General Curriculum0004 Understand literature for children, including genres, literary elements, and literarytechniques.For example: major works and authors of children's literature; genres of children'sliterature and their characteristics; major themes associated with children's literature;analysis of rhetorical and literary devices (e.g., analogies, metaphors, symbolism) inchildren's literature; comparison of different styles and communicative purposes inchildren's literature; criteria for evaluating children's literature (e.g., reading level, literaryquality, richness of vocabulary, appealing plot, interesting information, illustrations,gender preferences, variety of settings and characters); analysis of excerpts ofchildren's literature in relation to style, theme, or voice; and uses of children's literature(e.g., providing exposure to high-quality language, enhancingother areas of the curriculum, fostering cross-cultural understanding).0005 Understand how to apply writing skills and strategies for various purposes.For example: knowledge and use of prewriting strategies, including techniques forgenerating topics and developing ideas (e.g., brainstorming, semantic mapping, outlining,reading and researching); formal elements of good writing (e.g., paragraphing, topicsentences, cohesive transitions); revising written texts to improve unity, coherence, andlogical organization; editing written work to ensure conformity to conventions of editedAmerican English (e.g., grammar, punctuation, spelling of homophones such asthere/their/they're); techniques and stylistic requirements for writing for various purposes(e.g., to respond, inform, analyze, persuade, entertain), including factors related to theselection of topic and mode of written expression; clarifying intended audience; and use ofvarious techniques to convey meaning (e.g., precise vocabulary, figurative language,illustrations).MATHEMATICS [17%]0006 Understand and apply number properties and number representations.For example: number sense; cardinal, ordinal, and negative numbers; properties of realnumbers (e.g., commutative, distributive); the structure of the base ten number system(e.g., place value, decimal expansions); the expanded form of a number; the applicationof number concepts to count, compare, sort, order, and round numbers; equivalentforms of fractions, decimals, and percents; various equivalent symbolic representationsof numbers (e.g., scientific notation, exponents); number theory concepts (e.g., primeand composite numbers); and the process of converting among graphic, numeric,symbolic, and verbal representations of numbers.0007 Understand and apply number operations to represent and solve problems.For example: relationships among mathematical operations (e.g., multiplicationand division as inverse operations); order of operations; procedures for enhancingcomputational fluency; standard algorithms for basic arithmetic operations; the useof number properties to analyze nonstandard computational algorithms; provingnumber facts and relationships; representing operations using concrete models; multiplesolutions; solving problems involving integers, fractions, decimals, ratios andproportions, and percents; strategies to estimate quantities (e.g., front end, rounding,regrouping); the relationships between number operations and algebra; and the use ofmathematical reasoning to solve problems involving numbers and number operations.34

Test Objectives: General Curriculum0008 Understand and apply patterns, relations, algebra, and principles of geometry.For example: recognizing and extending patterns using a variety of representations(e.g., manipulatives, figures, numbers, algebraic expressions); relationship betweenstandard algorithms and fundamental concepts of algebra and geometry; the applicationof concepts of variable, function, and equation to express relationships algebraically;deriving algebraic expressions to represent real-world situations; the use of tables andgraphs to explore patterns, relations, and functions; solving equations and inequalities;properties of lines and angles; attributes of two- and three-dimensional geometricfigures; the application of the concepts of similarity and congruence tosolve problems; geometric transformations; the classification of figures accordingto symmetries; and connections between algebra and geometry (e.g., the use ofcoordinate systems).0009 Understand and apply concepts and methods of measurement, data analysis,statistics, and probability.For example: the use of both standard and nonstandard units of measurementto describe and compare phenomena; appropriate instruments, units, andprocedures for solving various measurement problems (e.g., problems involvingtime, length, area, angles, volume, mass, temperature); estimation and conversionof measurements within the customary and metric systems; the collection, organization,and communication of information using appropriate graphic and nongraphicrepresentations (e.g., frequency distributions and percentiles); the use of measures ofcentral tendency and spread to analyze data; problems involving simple probabilities;and predictions based on simulations, theory, or data from the real world.HISTORY AND SOCIAL SCIENCE [17%]0010 Understand major developments in the history of the United States.For example: lives of indigenous peoples before the arrival of Europeans; Europeanexploration and settlement of North America; the Revolutionary War and the formationof the national government; slavery; the Civil War and Reconstruction; the settlement ofthe West; the transformation from an agrarian to an industrial economy (e.g.,immigration, the rise of entrepreneurship, the development of science and technology);the Progressive Era and the New Deal; the emergence of the United States as a worldpower (e.g., the era of U.S. overseas expansion, World War I, World War II, the ColdWar); the Civil Rights movement; the Women's movement; the Vietnam War; thePersian Gulf War; the effects of the collapse of the Soviet Union and subsequent eventson U.S. leadership in world affairs; and international terrorism.35

Test Objectives: General Curriculum0011 Understand the governmental system of the United States; the principles, ideals,rights, and responsibilities of U.S. citizenship; and the fundamental principles andconcepts of economics.For example: purposes of government; functions of federal, state, and localgovernment in the United States; the branches of government and their roles; formsof local self-government in Massachusetts and the United States (e.g., town meeting,city government); how laws are enacted and enforced; the political process in the UnitedStates and the role of political parties; fundamental concepts and principles ofcapitalism (e.g., private property, wage labor, supply and demand, the global economy);democratic principles and values contained in the Declaration of Independence, theU.S. Constitution, and the Constitution of the Commonwealth of Massachusetts(e.g., the rule of law, due process, equal protection of the laws, majority rule, protectionof minority rights); and responsibilities of U.S. citizens (e.g., respecting others' rights,obeying laws and rules, paying taxes, jury duty, voting).0012 Understand major developments in world history.For example: characteristics of early human civilizations; major eras, developments,and turning points in Western civilization (e.g., ancient Israel, the emergence of Greekcivilization, the rise and fall of the Roman Empire, the Middle Ages, the Renaissanceand Reformation, the Age of Discovery, the scientific revolution, the Enlightenment, theage of revolution, World Wars I and II); and the impact of industrialization, nationalism,communism, and religion on modern world history.0013 Understand basic geographic concepts, phenomena, and processes, and the majorgeographic features and regions of the United States and the world.For example: basic concepts of geography (e.g., location, place, movement); the use ofglobes, maps, and other resources to access geographic information; global features(e.g., continents, hemispheres, latitude and longitude, poles); major physical featuresand regions of Massachusetts, the United States, and world areas; and the relationshipbetween geographic factors (e.g., climate, topography) and historical and currentdevelopments (e.g., human migrations, patterns of settlement, economic growth anddecline).SCIENCE AND TECHNOLOGY/ENGINEERING [17%]0014 Understand and apply basic concepts and principles of life science to interpret andanalyze phenomena.For example: basic characteristics and needs of living things; basic concepts andprocesses related to cells and organisms; plant structures, functions, and processes(e.g., photosynthesis); the systems of the human body; basic principles of genetics andheredity; and how organisms interact with one another and their environments.0015 Understand and apply basic concepts and principles of physical and earth sciences tointerpret and analyze phenomena.For example: the composition and structure of matter (e.g., atoms, molecules); propertiesand states of matter; forms of energy (e.g., electrical, magnetic, sound, light); basicconcepts related to the motion of objects (e.g., inertia, momentum); components andstructure of the solar system; climate and weather; and forces that shape the earth'ssurface.36

Test Objectives: General Curriculum0016 Understand the foundations of scientific thought, the historical development of majorscientific ideas and technological discoveries, and the principles and procedures ofscientific inquiry and experimentation.For example: the development of scientific thinking (e.g., the process of observation,classification, and notation of evidence developed by the ancient Greeks, the scientificrevolution of the seventeenth century, the concepts of uncertainty and relativity introducedin the early twentieth century); the history of major scientific and technological discoveriesand inventions; cultural and historical factors that have promoted or discouraged scientificdiscovery and technological innovation; basic concepts of scientific experimentation(e.g., hypothesis, control, variable, replication of results); and health and safety measuresrelated to scientific inquiry and experimentation.CHILD DEVELOPMENT [12%]0017 Understand child development from birth through the elementary years.For example: major theories of child development; characteristics and processes ofcognitive, language, physical, social, and emotional development during the elementaryyears; developmental progressions and ranges of individual and cultural variation incognitive, language, physical, social, and emotional development; factors that mayfacilitate or impede a child's development in various domains; major learning theories;processes by which children acquire knowledge and construct meaning;interrelationships between cognitive development and other developmental domains;and principles and procedures for promoting students' cognitive, language, physical,social, and emotional development.0018 Understand child development and learning in students with exceptionalities.For example: types of disabling conditions, developmental delays, indices of advancedacademic or artistic talent; effects of exceptionalities on cognitive, physical, social, andemotional development and functioning; significance of various exceptionalities forlearning; identification of students with exceptionalities; criteria and procedures forselecting, creating, and modifying materials and equipment to address students'exceptionalities; legal requirements for providing education to students with disablingconditions; and purposes and procedures for developing and implementingIndividualized Education Plans (IEPs) or 504 Accommodation Plans.INTEGRATION OF KNOWLEDGE AND UNDERSTANDING [20%]In addition to answering multiple-choice items, candidates will prepare written responses toquestions addressing content from the preceding objectives, which are summarized in theobjective below.0019 Prepare an organized, developed analysis on a topic related to one or more of the firstfive elementary subareas (Language Arts, Mathematics, History and Social Science,Science and Technology/Engineering, and Child Development).(Refer to objectives 0001 through 0018 and associated descriptive statements.)37

Sample Test Items:General Curriculum (03)1. Read the passage below from Kidnapped, a novel by Robert Louis Stevenson; then answer thequestion that follows.In this passage, the narrator, a boy named Davie, is attempting to climb a dangerous old tower.This was a grand stair! I thought. And with the thought a gust of a kind of angry courage came into myheart. My uncle had sent me here, certainly to run great risks, perhaps to die. I swore I would settle that'perhaps,' if I should break my neck for it; I got me down upon my hands and knees; and as slowly as asnail, feeling before me every inch, and testing the solidity of every stone, I continued to ascend the stair.The darkness, by contrast with the flash, appeared to have redoubled; nor was that all, for my ears werenow troubled and my mind confounded by the great stir of bats in the top part of the tower, and the foulbeasts, flying downward, sometimes beat upon my face and body.Which of the following statements bestdescribes the author's use of a literarydevice in this passage?A. Flashbacks highlight the contrastbetween the character's past andpresent circumstances.B. Personification intensifies thethreatening tone of the narrative.C. Descriptive details relating to thesetting create a mood of suspense andforeboding.D. Comic irony undercuts theseriousness of the narrator's situation.38

Sample Test Items: General Curriculum2. Use the excerpt below from an essay bya fourth-grade student to answer thequestion that follows.1In my opinion, dogs are the smartestanimals. 2 Dogs can learn to do lots ofstuff, like chasing a ball and sitting. 3 Catsdon't really like to learn things, most ofthe time. 4 Some dogs can roll over andbark when you tell them. 5 I saw on TVthere was a dog that saved a family from afire. 6 My friend has a cat. 7 It just sits inthe window when it is sunny. 8 This iswhy I want a dog more than a cat.Which of the following changes wouldmost improve the coherence of theexcerpt?A. Clarify the reference of the pronounit in Sentence 7.B. Place Sentence 3 after Sentence 5.C. Provide more evidence for the claimin Sentence 3.D. Place Sentence 8 after Sentence 1.39

Sample Test Items: General Curriculum3. Use the passage below to answer the question that follows.Think of two tasks and determine whether or not the order in whichyou do them matters. For example, does it matter whether you washyour face first or brush your teeth first? Does it matter whether youbrush your teeth first or eat your chocolate cookie first?This passage would be most helpful ingaining a deeper understanding of whichof the following mathematical concepts?A. commutative versus noncommutativesystemsB. cardinal numbers versus ordinalnumbersC. congruence versus similarityD. equations versus functions40

Sample Test Items: General Curriculum4. Use the incomplete proof below of a number trick to answer thequestion that follows.Step Statement Expression1 Pick any number. n2 Multiply it by three. 3n3 Add six to the result. 3n + 64 Divide by three.5 Subtract the number picked first. 2The table above shows an incomplete algebraic proof of a numbertrick that always results in the number 2, regardless of which numberis initially picked. Which of the following expressions shouldappear in Step 4 to complete the proof?A. n + 2B. n + 6C. 3n + 2D. 3n + 341

Sample Test Items: General Curriculum5. Which of the following best describesthe historical context in the United Statesduring the 1830s in which Horace Manncalled for universal education?A. A wide range of organizationswith a strong commitment toself-improvement had arisen tochampion various reform causes.B. The evangelicalism of an earlierperiod had given way to a religiousrationalism that stressed theimportance of learning.C. Restrictive voting laws continuedto prevent many citizens fromparticipating in elections.D. Changes in the U.S. economy hadsubstantially increased the number ofjobs requiring some form of highereducation.6. The concept of "natural rights" is acornerstone of both the U.S. Declarationof Independence (1776) and the FrenchDeclaration of the Rights of Man and theCitizen (1789). Which of the followingbest reflects how participants in theAmerican and French revolutionsunderstood this concept?A. In the state of nature, each personwould be able to exercise his or hernatural rights without interference.B. A government may have the power torestrict the exercise of an individual'snatural rights but cannot take thoserights away.C. Governments that do not protect theircitizens' natural rights have neverbeen able to claim the allegiance oftheir citizens.D. Natural rights are absolute andcannot be legitimately regulatedby government.42

Sample Test Items: General Curriculum7. An introduced species of insect isattacking hemlock trees in a forest. Theinsect eats the needles on a tree, killing thetree outright or weakening it so that it maydie in a few years from drought or otherenvironmental stress. However, there isconsiderable variation in the susceptibilityof individual hemlocks to the insects.Some trees possess a gene that allowsthem to produce a bittertoxin that discourages the insects fromeating the needles. Other trees in theforest lack this gene. If this insectpredation continues, it is likely that futurepopulations of hemlocks in the area willbe less susceptible to damage because:A. new mutations in the offspring ofsusceptible trees will lead to thespread of genes for producing thetoxin throughout the population.B. susceptible trees that survive insectattack will be able to produce thetoxin and will pass this ability on totheir offspring.C. trees that can produce the toxin willhave more offspring than trees thatcannot, and the gene for producingthe toxin will increase in thepopulation.8. At the age of five or six, children typicallybegin to experience a significant change inregard to their social development. Whichof the following statements best describesthe developmental progression that occursat this time?A. At the beginning of this period, mostchildren prefer to work cooperativelyin groups to solve problems; by theend of this period, most prefer towork independently.B. At the beginning of this period, thedesire to please peers tends to bemost important; by the end of thisperiod, the desire to please adults isforemost.C. At the beginning of this period,children tend to seek mainly samesexfriends; by the end of this period,most children have roughly equalnumbers of male and female friends.D. At the beginning of this period,children value relationships withadults above all others; by the end ofthis period, friends have becomeincreasingly important.D. insects carrying plant tissue from onetree to another will transmit the genefor producing the toxin from resistantto susceptible trees.43

Sample Test Items: General Curriculum9. Which line of the table below accurately matches a planet with its characteristics?Line Planet Characteristics1 Venus The planet closest to the sun, this planet is almost the same size as theearth, but lacks an atmosphere and rotates very slowly on its axis.2 Uranus The fifth planet from the sun, this is the second largest planet and has athick atmosphere that reflects sunlight and causes the planet to shinebrightly in the night sky.3 Jupiter The planet that is farthest from the sun, this planet is the largest in the solarsystem and is composed primarily of water vapor and methane gas.4 Mars The fourth planet from the sun, this planet has a mass only one-tenth thatof the earth and has a thin atmosphere composed mostly of carbon dioxide.A. Line 1B. Line 2C. Line 3D. Line 444

Sample Test Items: General Curriculum10. Which line on the table below correctly matches a major learning theory with the view of learningassociated with that theory?Line Learning Theory Description of Theory1 Behaviorism (B. F. Skinner) Learning occurs through connections establishedbetween stimulus inputs and responses; desirablelearning strategies and behaviors in children can beincreased with reinforcers.2 Cognitive-DevelopmentalTheory (Jean Piaget)3 Social Learning Theory(Albert Bandura)4 Sociocultural Theory(Lev Vygotsky)Learning occurs through observation and imitation ofmodels; as children become older, they become moreselective in the behaviors they imitate.Learning occurs in eight distinct stages of psychosocialdevelopment as children use new skills andattitudes to resolve conflicts related to psychologicalneeds.Learning occurs in stages characterized by particularways of thinking; children acquire knowledge throughactive construction and multiple opportunities toconnect new ideas to previous experiences.A. Line 1B. Line 2C. Line 3D. Line 445

Sample Test Items: General Curriculum11. Read the problem below; then complete the exercise that follows.A rectangle has a width of 8 units and a length of 12 units.• If the width of the rectangle increases by 25% and the length of the rectangle increases by 33 1 3 %,what is the ratio of the original perimeter to the increased perimeter, and the ratio of the originalarea to the increased area?• Express your answers as fractions reduced to lowest terms.Use your knowledge of mathematics to create a response in which you analyze and solve this problem. Inyour response you should:• describe two prerequisite mathematical skills necessary for solving this problem;• identify two mathematical concepts involved in solving this problem; and• solve the given problem showing your work and justifying the steps you used in arriving atyour solution.Be sure to show your work and explain the reasoning you used to complete the above exercise.46

Answer Key and Sample Response:General Curriculum (03)QuestionNumberCorrectResponseTest Objective1. C Understand literary genres, elements, and techniques.2. B Understand how to apply writing skills and strategies for various purposes.3. A Understand and apply number properties and number representations.4. A Understand and apply patterns, relations, algebra, and principles of geometry.5. A Understand major developments in the history of the United States.6. B Understand major developments in world history.7. C Understand and apply basic concepts and principles of life science to interpret and analyzephenomena.8. D Understand child development from birth through the elementary years.9. D Understand and apply basic concepts and principles of physical and earth sciences to interpret andanalyze phenomena.10. A Understand child development from birth through the elementary years.AcknowledgmentsQuestionNumber1. [Public Domain] Stevenson, R. (1965). Kidnapped. New York: Grosset and Dunlap. p. 38.47

Answer Key and Sample Response: General CurriculumThe sample response below reflects a strong knowledge and understanding of the subject matter.12168 810 1012original rectangle16new rectangleThe perimeter of a rectangle is the distance around it, i.e. the sum of the lengths of thesides. For the original rectangle this is 8 + 12 + 8 + 12 = 40. The area of a rectangle is thenumber of square units inside it and can be found by multplying the length of the rectangle byits width. In this case the area is 8 x 12 = 96 square units.The new rectangle has a width that is 25% greater than the width of the original1 1rectangle. Since 25% is equivilent to4 and ( x 8) is equal to 2, the width of the new rectangle41is 8 + 2 = 10. The length of the new rectangle is 33 % greater than the length of the original311 1rectangle. Since 333 % is equivilent to 3 , and ( x 12) is equal to 4, the length of the new3rectangle is 12 + 4 = 16.The perimeter of the new rectangle is the sum of the lengths of the sides, 10 + 16 +10 +16 = 52.The area of the new rectangle is the product of the length and width, 10 x 16 = 160 square units.The ratio of the original perimeter to the new perimeter is 40:52 which can be expressed as4010the fraction52 . This reduces to . The ratio of the area of the original rectangle to the area13963of the new rectangle is160 , which reduces to 5 .Two prerequisite mathematical skills for solving this problem include how to calculate theperimeter of a rectangle (addition), and how to simplify fractions to lowest terms (dividingnumerator and denominator by common factors).Two mathematical concepts involved in solving this problem include understanding theeffect that increasing the lengths of the sides of a rectangle has on its perimeter and area,and understanding the relationship between percents and fractions.48