SkillsTutor Math C

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ContentsGetting Started . 1-1SkillsTutor Math Lessons . 1-2SkillsTutor Math Problem Solving Lessons . 1-2Quizzes . 1-3Tests . 1-3Worksheets . 1-3SkillsTutor Math Lesson Summaries . 2-1Math C . 2-2Worksheets . 3-1Answer Keys. 4-1Math C . 4-2Assignment Sheets . 5-1

Getting StartedSkillsTutor Math provides extensive coverage of the skills students need to improve basic mathematics skills. Thiscoverage is provided through a variety of engaging activities. Each level of SkillsTutor Math provides students withbasic skills lessons, problem solving lessons, quizzes, tests, and worksheets.The SkillsTutor management system (OTS) provides several important features: Test students’ skills with pretests and posttests to make initial assessments and to gauge student progress Prescribe activities based on students’ pretest results Monitor student scores and completion of activities Produce reports for individual students and classes Provide online and print documentation, including printable activity sheets which extend the computerlessons to classroom or home activitiesThis guide outlines the content and activities of SkillsTutor Math. Information on the management system (OTS)is provided under separate cover in the User’s Guide.Classroom Guide1–1

Getting StartedMath CSkillsTutor Math LessonsIn SkillsTutor Math, each lesson has two parts: Warm-Up and Review.The Warm-UpThe Warm-Up begins with a real-life problem using the skills covered in the lesson. After students read the paragraph, they click Go On to continue.The Warm-Up then uses the problem from the preceding screen as a basis for introducing students to the kinds ofactivities that will be presented in the Review. Students see the format of the questions and any special manipulatives or tools that will be available to help them answer the questions. Students answer the question and use thetools directly.The ReviewThe Review gives students practice problems. Clicking Hint provides students with a clue about how to completethe question. Students enter an answer and then click Check.If any question is answered incorrectly, students are given some feedback about why their answer was incorrect.Then they are guided through answering the question.SkillsTutor Math Problem-Solving LessonsThe Problem-Solving Lessons begin with an overview of the 4-Step Problem-Solving Plan. The steps of the planare as follows: Understand the Problem, Make a Plan, Solve the Problem, and Look Back. The steps provide a basicstructure to the problem-solving process and offer students a methodology for solving application problems.Each lesson consists of application problems that necessitate the use of the mathematical skills taught in the lessons immediately preceding the Problem-Solving Lesson. The lesson begins with an initial problem presentedin a setting that engages the student. Students are guided through the solution of this problem using the 4-StepProblem-Solving Plan. Students are then given the opportunity to review any part of the plan before moving on tothe practice problems, where they solve a variety of application problems on their own. In addition to solving theproblems, students answer questions that ask them to consider various methods of solution and require them touse critical thinking to extend their understanding of what they’ve learned. Feedback is provided for all responses.1–2SkillsTutor

Math CGetting StartedQuizzesAfter finishing a set of lessons, students are given a Quiz. When they answer a question, SkillsTutor Math givesfeedback. Students must select the correct answer before they can move on to the next question. Click Next to seethe next question.TestsFor each level, SkillsTutor Math offers content-area pretests and posttests modeled on standardized tests. Likethe questions for quizzes, the test questions are presented in multiple choice format to give students practice inanswering standardized-test questions. After each test, students have the opportunity to review the questions theymissed. Feedback is provided for each missed question.WorksheetsSkillsTutor Math contains reproducible worksheets for each lesson. The worksheets may be used to extend thecomputer activity or as a homework assignment.Each worksheet provides word problems for added practice and challenges students with a creative writing or artistic exercise. The focus is on applications and connections with other areas of the curriculum.Electronic versions are provided with the online documentation and may be printed from your computer.Classroom Guide1–3

Getting Started1–4Math CSkillsTutor

Math Lesson SummariesIn this section of the manual, you will find the lesson summaries for each of the lessons in Math C, which includeslessons that are targeted for grades 7 and 8.For all levels, lessons are grouped into units that reflect the general concepts covered in the lesson activities. Theseunits appear in the following order:Math CUnderstanding NumbersUsing DecimalsUsing Fractions and PercentsUsing GeometryWorking with DataThe lesson summaries are meant to provide, at a quick glance, a description of the concepts covered in the lessonas well as an example activity from the lesson.Classroom Guide2–1

Math Lesson SummariesMath CLevel C Lesson SummariesLesson #Lesson TitleRules/SummaryExampleUnderstanding Numbers12Place Value and Scientific Notation Students use a place value chart to learn about expandedand scientific notation. The place values range from 108 to10-4. Students are asked to type the numeral for a numberrepresented in expanded or scientific notation.Type the standard numeral for this expandednotation.(3 x 108) (5 x 107)Word Names and ScientificNotationType the scientific notation for this word name.Students write scientific notation to represent word names.Whole numbers, or positive exponents, go to 108. Decimalnumbers, or negative exponents, go to 10-4.Answer: 350,000,000Seven thousand three hundred forty-twoten-thousandthsAnswer: 7.342 x 10-13Comparing and OrderingNumbersStudents use a number line to compare positive integers,negative integers, and decimal numbers with up to threedecimal places. The lesson presents three types ofquestions:1 Students enter the correct symbol ( , , ) tocompare two numbers.2 Students enter a number between two given numbers.3 Students order numbers from least to greatest value.The Sea of Rains’ temperature is -14 F. TheSea of Clouds’ temperature is -26 F. Whichplace on the moon has a higher temperature?Answer: Sea of Rains. -14 F -26 FUsing Decimals1Addition of DecimalsStudents add decimal numbers to the ten-thousandthsType the sum. Then drag the decimalplace. Each problem has two to four addends. The sums are point into the sum.decimal numbers to the tenths, hundredths, thousandths,and ten-thousandths place.4.0496 7.321011.37062Subtraction of DecimalsStudents subtract numbers having up to four decimalplaces. All problems require students to place the decimalpoint in the difference. Special emphasis is given toregrouping across zeros and subtracting a decimal numberfrom a whole number.Type the difference. Then drag the decimalpoint into the difference.The Gift of SongThe guided solution to the initial problem involves usingaddition and subtraction of decimals in a scenario involvingmeasurements of time and the making of an audiotape.The practice problems include questions pertaining to increases and decreases in stock prices, balancing a checkingaccount, and a variety of problem-solving strategies.If Paul continues to train in the same way(increasing his distance by 0.4 miles eachday), in which week of his training will hefirst run more than 20 miles in one day?Multiplication of DecimalsStudents multiply decimal numbers. Problems show atwo-digit to four-digit decimal number as the first factor.Multipliers are one-digit or two-digit whole numbers ordecimal numbers. Special emphasis is given to problemswhere products require zeros as place holders in orderto obtain the correct number of decimal places. Productsare decimal numbers to the hundredths, thousandths, orten-thousandths place.Type the product. Then drag the decimal pointinto the product.PS132–25.095– 0.1454.9500.017x 0.7.0119SkillsTutor

Math CMath Lesson SummariesLevel C Lesson SummariesLesson #Lesson TitleRules/SummaryExample4Division of DecimalsStudents divide decimal numbers by decimals and wholeType the quotient. Then drag the decimal pointnumbers. Problems show a two-digit, three-digit, or fourin the quotient into place.digit decimal (to the thousandths place) or whole numberdivided by a one-digit or two-digit divisor. Special emphasisis given to problems having more decimal places in thedivisor than in the dividend. The quotients are two-digit,three-digit, or four-digit whole numbers or decimal numbersto the tenths, hundredths, or thousandths place. The lessonpresents two types of problems:1 The divisor is a whole number.2 The divisor and dividend are decimals.5Number SequencesStudents see number sequences with missing numbers. Stu- Look at the path. The numbers on the pathdents must identify the missing number by finding the rule form a sequence. One number is missing. Typefor the sequence. Number sequences are based on one-step the missing number into the path.or two-step rules of addition, subtraction, multiplication,and division of whole numbers and decimals.Pedal PowerThe guided solution to the initial problem involves usingmultiplication and division of decimals to solve a probleminvolving a bike-a-thon. The solution also requires use ofthe formula relating distance, rate, and time. The practiceproblems include questions pertaining to area, round-tripdistance, and rate affected by a current, and critical thinking questions in which students extend their understandingof these concepts.You’ve been training all summer, and the bigday is here! It’s your first bike-a-thon! Thecourse is divided into three minicourses, each14.1 miles long. You’ve decided to bike allthree. If you want to finish in 4.5 hours, whatwill your average speed need to be (in milesper hour)?Type this fraction in simplest form.PS2Using Fractions and Percents1Equivalent FormsStudents find equivalent forms. The lesson presents threetypes of questions:1 Students enter the simplest form of a fraction. Denominators in the simplified form range from 2 to 20.2 Students enter the fraction form of a mixed number.Whole numbers go up to 12, and denominators rangefrom 2 to 20.3 Students enter the decimal form of a percent. Percentscan include decimals (e.g., 25.4%).2Addition of FractionsStudents add fractions and mixed numbers. All problemsType the sum.have two addends, and the fractions have denominators up You may need to click on one or more ofto 21. Some problems are specifically designed to require the helpers at the bottom of the screen.the student to find a common denominator. All otherproblems consist of fractions with the same denominator.The sums of the fractions may be improper fractions.Classroom Guide2–3

Math Lesson SummariesMath CLevel C Lesson SummariesLesson #3Rules/SummaryExampleSubtraction of FractionsStudents subtract fractions and mixed numbers. Thefractions have denominators up to 15. Some problemsare specifically designed to require the student to find acommon denominator. All other problems consist of fractions with the same denominator. The top fraction may besmaller than the second fraction, requiring the renaming of1 from the whole number.Type the difference.You may need to click on one or more ofthe helpers at the bottom of the screen.Pass the PopcornThe guided solution to the initial problem involves writingand solving an equation used to model a scenario involvinga weekly work schedule. The equation contains mixednumerals, and its solution requires both addition andsubtraction. The practice problems include questions pertaining to perimeter, liquid measurement, and modeling areal-world situation using an equation, and critical thinkingquestions in which students extend their understanding ofthese concepts.Pam is adding a second garden (with the samedimensions) next to the first. If she wantsto enclose the two gardens with one fencearound the perimeter, how would this affect theamount of fencing she needs to buy?4Multiplication of FractionsStudents multiply simple fractions, whole numbers, andmixed numbers. Denominators in the factors go up to 10.Denominators in the product are limited to 60. Problemsappear in horizontal format. All problems have two factors.These factors can be any combination of simple fractions,whole numbers, and mixed numbers.Type the product.You may need to click on one or more ofthe helpers at the bottom of the screen.5Division of FractionsStudents divide simple fractions, whole numbers, andmixed numbers. Denominators in the problems go upto 10. Denominators in the quotient are limited to 60.Problems appear in horizontal format. The dividend anddivisor can appear as any combination of simple fractions,whole numbers, and mixed numbers.Type the quotient.You may need to click on one or more ofthe helpers at the bottom of the screen.Rolling In DoughThe guided solution to the initial problem involves usingmultiplication and division of fractions to solve a probleminvolving measurements of ingredients for a cookie recipe.The practice problems include questions pertaining to capacity,selection of the appropriate operation, and elimination ofunnecessary information, and critical thinking questions inwhich students extend their understanding of mixed numeralsas multipliers and divisors.You measure the total amount of flourbrought by the students and find that youhave 44 13 cups. Each cookie recipe callsfor 2 13 cups of flour. How many batchescan be made? You’ll also need to check tosee if you have enough sugar for all thosebatches. Each batch requires 34 cup ofsugar. How much sugar will be needed?PS1PS22–4Lesson TitleSkillsTutor

Math CMath Lesson SummariesLevel C Lesson SummariesLesson #6789PS2Classroom GuideLesson TitlePercent of a NumberFinding the WholeFinding the PercentUsing PercentsKick Up Your HeelsRules/SummaryExampleStudents find the percent of a number. Many of thequestions are presented in the context of a real-life wordproblem. Such problems may involve calculating theinterest on a loan, commission on a sale, earnings on aninvestment, or sales tax. Percents can be in the range from1% to 99%, can be greater than 100%, or can includedecimal values such as 4.5%.The commission on a sale is 20%. How muchcommission is earned on a sale of 830.00?Students find the whole when the percent and part areknown. Many of the questions are presented in the contextof a real-life word problem. Such problems may involvecalculating the total amount of a loan when the interest isknown, calculating the amount of a sale when the commission is known, or calculating the price of an item when thesales tax is known. Percents can be in the range from 1%to 99%, can be greater than 100%, or can include decimalvalues such as 4.5%.Interest of 122.40 was charged on a loan.If the interest rate was 18%, what was theoriginal amount of the loan?Students find the percent when the whole and the partare known. Many of the questions are presented in thecontext of a real-life word problem. Such problems mayinvolve calculating the interest rate on a loan, the rate ofcommission being paid, the tax rate, or the percent earnedon an investment. Percents can be in the range from 1%to 99%, can be greater than 100%, or can include decimalvalues such as 4.5%.On an investment of 670.00, 1621.40was earned. What percent was earned onthe investment?Students see problems similar to those in the three precedinglessons. They are asked to find the percent of a number,the whole (when the percent and part are known), or thepercent (when the whole and part are known). Many ofthe questions are in the context of a word problem. Someproblems have one-step solutions. Others require a two-stepsolution such as calculating the total cost of an item includingtax or finding the final cost of an item that has beendiscounted. Percents can be in the range from 1% to 99%,can be greater than 100%, or can include decimal valuessuch as 4.5%.The cost of your dinner was 70.20. Youwant to leave a 20% tip. What is the finalcost, including tip?The guided solution to the initial problem involvescalculation of percent increase and finding the percent ofa number in a scenario involving student participation ina Dance-a-thon. The practice problems include questionspertaining to percent decrease, discount, and populationgrowth, and critical thinking questions in which studentsextend their understanding of these concepts.As secretary of the Student Council, one of yourjobs is to keep records of the annual fundraisers. Your records show that 125 studentsparticipated in last year’s Dance-a-thon. Thisyear, 145 students participated. What percentincrease does this represent? If the same percent increase is expected next year, how manystudents can be expected to participate at nextyear’s Dance-a-thon?Answer: 0.20 x 830.00 166.00Answer: 122.40 0.18 680.00Answer: 1621.40 670.00 2.42 242%Answer:0.20 x 70.20 14.04 70.20 14.04 84.242–5

Math Lesson SummariesMath CLevel C Lesson SummariesLesson #Lesson TitleRules/SummaryExampleUsing Geometry1AnglesStudents identify complementary and supplementaryWhat is the relationship between angles Aangles and compute the missing angle of a complementary and B?or supplementary pair of angles.Answer: Supplementary2Parallel LinesStudents identify the properties of angles created by twoparallel lines that have been cut by a transversal andcompute the measurement of those angles.What is the corresponding angle paired with 1?Answer: 53CongruenceStudents compute the measurements of correspondingsides and angles of congruent figures. Congruent figureshave undergone transformations.Quadrilateral ABCD Quadrilateral EFGH.Find the measure of H.Answer: 115 4SimilarityStudents compute the measurements of correspondingsides and angles of similar figures. Solving for the lengthof a corresponding side may involve proportions. Similarfigures may have undergone transformations.Quadrilateral ABCD Quadrilateral EFGH.Find the measure of H.Answer: 137 2–6SkillsTutor

Math CMath Lesson SummariesLevel C Lesson SummariesLesson #5Lesson TitleRules/SummaryExampleTransformationsStudents use specific instructions to draw the image of afigure that has undergone a translation (slide) or a reflection (flip) over a line of reflection.Perform a translation on the figure. Slide thefigure 4 units to the right and 2 units down.1Bar GraphsStudents cycle through a set of four questions for eachbar graph. Graphs are double or triple bar graphs and mayrequire simple interpolation. The four types of questionsrequire students to interpret the bar graphs:1 Students click on a bar that shows a particular value.2 Students click on a label or bar to indicate the “least” or“greatest” value.3 Students enter a number to represent the differencebetween two values.4 Students enter a number to indicate the sum of values.2Line GraphsStudents cycle through a set of four questions for each line Type the total number of votes for 1992.graph. The graphs include double and triple line graphs.Some points on the graphs fall between the labels on the yaxis, so students must estimate point values. The four typesof questions require students to interpret the line graphs:1 Students click on a point that shows a particular value.2 Students click on a point to indicate the “least” or“greatest” value.3 Students type the numerical difference between thevalues of two points.4 Students type the total number of the items beingmeasured for a certain time period.3Circle GraphsStudents cycle through a set of three questions for eachFind how many students chose soda or tea.circle graph. The sections of the graphs are labeled withpercents. Each circle has four or five sections and representsup to 80 observations. The three types of questions requirestudents to interpret the circle graphs:1 Students click on a section of the graph to indicate“least” or “most.”2 Students enter a number to answer “how many chose”a certain category.3 Students enter a number to answer “how many chose”either of two specified categories.Working with DataClassroom GuideClick on the bar that has the least value.2–7

Math Lesson Summaries2–8Math CSkillsTutor

WorksheetsThis section contains reproducible worksheets for each lesson in Math C. These worksheets may be used by students to extend the classroom activity or as a homework assignment. The worksheet provides word problems foradded practice and challenges students with a creative writing or artistic exercises. The focus is on applications andconnections with other areas of the curriculum.Classroom Guide3–1

NameNameDateDatePlace Value and Scientific NotationLesson 1Use powers of ten to identify place value.Joe’s idol is his uncle, an astronomer who works for NASA. For Joe to follow in his uncle’s footsteps, hemust understand numbers written in scientific notation.1. Write the standard numeral for each number represented in scientific notation:PlanetAverage Distance from the SunMiles inMiles inScientific Notation Standard Numeral FormMercury3.59 107Venus6.7 107Earth9.29 107Mars1.42 108Jupiter4.83 108Saturn9.14 108Uranus1.78 109Neptune2.79 109Pluto3.68 10122. Bacteria growing in an experiment on the space shuttle were measured in millimeters as follows. Writethe standard numeral for each:7.38 10-2 4.2 10-4 5.6 10-3 1.33 10-1 smART Idea: Make a drawing or model of our solar system. Be sure to represent the distances betweenplanets accurately. 2004 Achievement Technologies, Inc.Understanding NumbersLevel C, Understanding NumbersSkillsTutor

NameNameDateDateWord Names and Scientific NotationLesson 2Use place value to identify the name of a number.You are helping a scientist write an article on some research she’s been doing. You first write all the numbersin words as she dictates them. Then she asks you to translate the words into scientific notation for the article:Word Namesixty-five millionScientific Notation6.5 107two hundred twenty-five thousandfifty thousandfour hundred million, nine hundred thousandthirty-two thousandthssix thousandthsfive hundred seventy-one thousandthseighty-nine hundred-thousandthsfive hundred seventy-one thousandtwo hundred four thousandthsWrite Idea: How did you convert “sixty-five million” to scientific notation? Write an explanation that mightclarify this process for a confused friend. 2004 Achievement Technologies, Inc.SkillsTutor Level C, Understanding NumbersUnderstanding Numbers

NameNameDateDateComparing and Ordering NumbersLesson 3Use a number line to compare and order numbers.Suppose you are working as an electrician’s helper in your new summer job. You have to make a lot ofcomparisons of integers. Following is a sample of the comparisons you must make on your first day on thejob.1. Complete each number sentence by inserting a symbol: , , or 2. After consulting an operations manual, you must select a voltage between two limits. Select an integerbetween each of the given pairs, and write it in the box beneath. 3. You also have to determine which circuit has the highest voltage. Place each group of integers in orderfrom least to greatest.–6 , 8 ,– 4 , 30 ,– 9 ,– 10 , 1–99 ,– 101 ,– 66 ,– 65Write Idea: Ask at home if you can see the electric bill. Did you use more or less electricity this month thanlast month? How can you tell? Why do you think there was a change in the amount of electricity used? Whatcould you do to conserve more electricity? 2004 Achievement Technologies, Inc.Understanding NumbersLevel C, Understanding NumbersSkillsTutor

NameNameDateDateAddition of DecimalsLesson 1Use addition to find the total.Imagine you are a reporter covering the Olympics. You are reporting on the women’s gymnasticscompetition. As soon as each individual’s scores are given, you record them in a table for your story.1. This table shows the top five competitor’s scores in each of four exercises. Find the total score for eachgymnast and complete the table. Who had the highest total score? Circle the orExerciseMary Ann GibbonsUSA19.9519.7019.6019.925Laura SzaboRomania19.8519.5019.8519.925Ecaterina PaucaRomania19.62519.57519.8519.625Julie McSharryUSA19.72519.9519.07519.65Simona CutinaRomania19.7019.72519.12519.75Total Score2. If the total scores for the other USA team members were 78.10, 77.55, 77.10, and 77.60, what was thescore for the entire, six-member USA team?3. If the scores for the other Romanian team members were 77.90, 77.70, and 77.60, what was the score forthe entire, six-member Romanian team?4. Compare the team scores for the USA and Romanian teams. Which team scored higher? By how manypoints?smART Idea: Choose a graphing method to display the total score for each gymnast in the table above.Which method did you choose? Is it easier to compare the scores when they are in a table or in a graph? Whyis that? 2004 Achievement Technologies, Inc.SkillsTutor Level C, Using DecimalsUsing Decimals

NameNameDateDateSubtraction of DecimalsLesson 2Use subtraction to find the difference.If you were a currency trader, you would be checking the exchange rates daily. The following table shows theamount of foreign currency equal to one U.S. dollar at three points in time. Use the table for the questionsbelow. For each, show your subtraction.FOREIGN CURRENCY EQUAL TO U.S. DOLLARExchange RateToday6 Months Ago1 Year AgoAustralian dollarFrench francGreek drachmaJapanese yenIrish puntItalian 77.31. At which time would you get more Australiandollars for one U.S. dollar: one year ago ortoday? How much more?4. At which time would you get more Italian lirafor one U.S. dollar: one year ago or today?How much more?2. At which time would you get more Japaneseyen for one U.S. dollar: six months ago ortoday? How much more?5. At which time would you get more Greekdrachmas for one U.S. dollar: six months agoor today? How much more?3. At which time would you get more Frenchfrancs for one U.S. dollar: six months ago ortoday? How much more?6. At which time would you get more Irish puntfor one U.S. dollar: one year ago or today?How much more?Write Idea: Select one of the above currencies. Assume that you had invested in that currency at the rateindicated in the table for “one year ago.” Compare that rate to the exchange rate listed in a current newspaperand describe whether or not you made a good investment. 2004 Achievement Technologies, Inc.Using DecimalsLevel C, Using DecimalsSkillsTutor

NameNameDateDateMultiplication of DecimalsLesson 3Use multiplication to combine groups or parts of the same size.You are helping your neighbor work on her lawn. She has asked you to figure out how muchit will cost to buy the seed and fertilizer.1. Below is a diagram of the yard. Compute the area of the yard.57.5 ft.82 ft.2. At Harkins Hardware, you find the information shown in the following table. Calculatethe amount of materials you will need and their costs. Then record these numbers in thetable. Assume that the sales tax is 5% (0.05) of the price.ItemPriceCoverageGrass seed 2.25/lb.200 sq. ft. per lb.Fertilizer 8.00/bag5000 sq. ft. per bagNumber ofUnits NeededCost (includingtax)Write Idea: You notice that the grass seed costs a lot more than the fertilizer. What is theapproximate ratio of the two costs? Could you have gotten cheaper grass seed? Should youbuy the cheaper type? Why or why not? Is there another way to save money? Write aparagraph explaining your thoughts on this topic. 2004 Achievement Technologies, Inc.SkillsTutor Level C, Using DecimalsUsing Decimals

NameNameDateDateDivision of DecimalsLesson 4Use division to make groups or parts of equal size.Your teacher asked you to take notes on the various ways you saw decimals being used last week. Below area few things you noticed, with follow-up questions. Show your calculations under each question.1. Your

1 Place Value and Scientific Notation Students use a place value chart to learn about expanded and scientific notation. The place values range from 108 to 10-4. Students are asked to type the numeral for a number represented in expanded or scientific notation. Type the standard numeral for this exp

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