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ContentsForeword .6Chapter 6: Ratios and ProportionsIntroduction .7Ratios and Rates .12Solving Problems Using Equivalent Rates .15Solving Proportions: Cross Multiplying .17Why Cross-Multiplying Works .23Unit Rates .24Proportional Relationships .29Graphing Proportional Relationships–MorePractice .35More on Proportions .37Scaling Figures .41Floor Plans .47Maps .51Significant Digits .57Chapter 6 Mixed Review .59Chapter 6 Review .62Chapter 7: PercentIntroduction .67Review: Percent .72Solving Basic Percentage Problems .75Percent Equations .78Circle Graphs .83Percentage of Change .85Percentage of Change: Applications .88Comparing Values Using Percentages .92Simple Interest .96Chapter 7 Mixed Review .102Chapter 7 Review .105Sample worksheet fromwww.mathmammoth.com3
Chapter 8: GeometryIntroduction .107Angle Relationships .114Angles in a Triangle .119Basic Geometric Constructions .124More Constructions .130Drawing Problems .135Circumference of a Circle .142Area of a Circle .145Proving the Formula for the Area of a Circle .148Area and Perimeter Problems .150Surface Area .155Conversions Between Customary Units of Area .159Conversions Between Metric Units of Area .162Slicing Three-Dimensional Shapes .165Volume of Prisms and Cylinders .172Chapter 8 Mixed Review .176Chapter 8 Review .179Chapter 9: Pythagorean TheoremIntroduction .187Square Roots .190Equations That Involve Taking a Square Root .194The Pythagorean Theorem .199The Pythagorean Theorem: Applications .204Proof of the Pythagorean Theorem .211Chapter 9 Mixed Review .212Chapter 9 Review .215Chapter 10: ProbabilityIntroduction .218Probability .223Probability Problems from Statistics .226Experimental Probability .228Counting the Possibilities .231Using Simulations to Find Probabilities .237Probability of Compound Events .243Chapter 10 Mixed Review .247Chapter 10 Review .250Sample worksheet fromwww.mathmammoth.com4
Chapter 11: StatisticsIntroduction .252Review of Data Analysis .256Random Sampling .261Using Random Sampling .265Comparing Two Populations .272Comparing Two Samples .280Chapter 11 Mixed Review .286Chapter 11 Review .290Sample worksheet fromwww.mathmammoth.com5
ForewordMath Mammoth Grade 7-A and Grade 7-B worktexts comprise a complete math curriculum for seventh grademathematics studies. This is a pre-algebra course after which students can continue to an Algebra 1 curriculum.The curriculum meets and actually exceeds the Common Core Standards (CCS) for grade 7. The two major areaswhere it exceeds those standards are linear equations (chapter 5) and the Pythagorean Theorem (chapter 9). Linearequations are covered in more depth than the CCS requires, and the Pythagorean Theorem belongs to grade 8 in theCCS. You can access a document detailing the alignment information either on the Math Mammoth website or inthe download version of this curriculum.Part B starts out with a study of ratios and proportions (chapter 6). Students study unit rates, proportions,proportional relationships and graphing, scaling geometric figures, floor plans, and mapsThe next chapter provides thorough lessons on the concept of percent. Students learn to solve a wide variety ofproblems involving percentages, including percentage of change, percentages of comparison, and simple interestproblems.Geometry is our focus in chapter 8. Students draw geometric figures using a a protractor and a ruler, and they alsolearn some basic geometric constructions. The other themes of this chapter are various angle relationships, area andthe perimeter of a circle, conversions between units of area and of volume, surface area, volume, and cross-sectionswhen solids are sliced with a plane.Chapter 9 covers square roots, the Pythagorean Theorem, and its applications. I have included the PythagoreanTheorem in order to make the curriculum work as a pre-algebra course, and you can omit the entire chapter 9 if youare following the Common Core Standards for grade 7.Chapter 10 is an introduction to probability. Besides learning the basic idea behind probability as the ratio offavorable events to all possible events, students compare experimental probabilities to theoretical ones inprobability simulations and even design some on their own.Lastly, in chapter 11, the curriculum covers statistical concepts. The major areas of study are random sampling andlearning to compare two populations using some basic statistical measures and graphs.Part 7-A covers an introduction to basic concepts of algebra, integers, one-step equations, fractions and decimals,and linear equations.I wish you success in teaching math!Maria Miller, the authorSample worksheet fromwww.mathmammoth.com6
Chapter 6: Ratios and ProportionsIntroductionChapter 6 reviews the concept, which has already been presented in previous grades, of the ratio of two quantities.From this concept, we develop the related concepts of a rate (so much of one thing per so much of another thing)and a proportion (an equation of ratios). We also study how tables of equivalent ratios can help to solve problemswith rates, and how cross-multiplying can help to solve problems with proportions.The lesson Unit Rates defines the concept of the unit rate, shows how to calculate one, and gives practice at doingso, including practice with complex fractions. We also consider rates as two quantities that vary, graph thecorresponding equation in the coordinate grid, and tie in the concept of unit rate with the concept of slope.The concept of direct variation is introduced in the lesson Proportional Relationships. Writing and graphingequations gives a visual understanding of proportionality. In two following lessons on proportions, students alsopractice solving rate problems in different ways, using the various methods they have learned throughout thechapter.The lessons Scaling Figures, Floor Plans, and Maps give useful applications and more practice to master theconcepts of proportions.Before the Chapter Review there is also an optional lesson, Significant Digits, that deals with the concept of theaccuracy of a measurement and how it limits the accuracy of the solution. It is optional because significant digits isnot a standard topic for seventh grade, yet the concept in it is quite important, especially in science.The Lessons in Chapter 6pagespanRatios and Rates .123 pagesSolving Problems Using Equivalent Rates .152 pagesSolving Proportions: Cross Multiplying .176 pagesWhy Cross-Multiplying Works . 231 pageUnit Rates . 245 pagesProportional Relationships .296 pagesGraphing Proportional Relationships–More Practice .352 pagesMore on Proportions .374 pagesScaling Figures . 416 pagesFloor Plans .474 pagesMaps .516 pagesSignificant Digits .572 pagesChapter 6 Mixed Review .593 pagesChapter 6 Review .625 pagesSample worksheet fromwww.mathmammoth.com7
Helpful Resources on the InternetLanguage of Algebra - Video Lessons by MariaA set of free videos that teach the topics in this book - by the author ra/pre-algebra-videos.php#algebraEquivalent ratiosRatio Pairs Matching GameMatch cards representing equivalent ratios.Easy: http://nrich.maths.org/4824 Challenge: http://nrich.maths.org/4821Equivalent Ratios Workout10 online practice ice/S1U2L1/S1U2L1Pract.htmlRatio StadiumA multi-player online racing game for matching equivalent ratios. The student with the fastest rate of correctanswers will win the atio-stadium/All About Ratios - QuizAn interactive five-question quiz about equivalent ratios presented with pictureshttp://math.rice.edu/ lanius/proportions/quiz1.htmlRatios and ratesRate lesson from BrainingCampA comprehensive interactive lesson on the concepts of ratio, rate, and constant speed (for 6th and 7th grades).Includes an animated lesson, a virtual manipulative, and questions and problems to tios Activity from BBC BitesizeAn animated and narrated tutorial about ratios and scale models with some quiz questions along the activityPractice with RatiosAn online quiz from Regents Exam Prep Center that includes both simple and challenging questions and wordproblems concerning EBRA/AO3/pracRatio.htmExploring Rate, Ratio and Proportion (Video Interactive)The video portion of this resource illustrates how these math concepts play a role in photography. The interactivecomponent allows students to explore ratio equivalencies by enlarging and reducing images to compare an originalratio and a target ex.html?l 0&ID1 AB.MATH.JR.NUMB&ID2 AB.MATH.JR.NUMB.RATEIf the link above doesn't work, use this x.html?l 0&ID1 AB.MATH.JR.NUMBFirst choose Rate/Ratio/Proportion, and then Exploring Rate, Ratio, and Proportion.Self-Check Quiz from GlencoeA five-question multiple-choice quiz about comparing with ratios and rates. By reloading the page you will getdifferent ls/cgi-bin/msgQuiz.php4?isbn 1-57039-855-0&chapter 8&lesson 1Sample worksheet fromwww.mathmammoth.com8
Free RideAn interactive activity about bicycle gear ratios. Choose the front and back gears, which determines the gear ratio.Then choose a route, pedal forward, and make sure you land exactly on the five .aspx?ID 178Ratio Quiz from BBC SkillswiseA multiple-choice quiz about the concept of ratio. You can take the quiz online or download it as a PDF or doc -e1and2-quizPractice with RatiosA set of 11 word problems that involve ratios. You can reveal the answer and the full solution at your ra/ao3/pracRatio.htmRatio Quiz from SyvumA 10-question online quiz about ratios and problem mat/math review/arithmetic 5.tdf?0Three-Term RatiosPractice the equivalency of ratios by filling in the missing numbers in three-term ratios(for example, 2:7:5 : 105 : ) where the three numbers represent the amounts of red, blue, or green colors innine different photographs. After finishing the activity you get to assemble a picture puzzle from the /mejhm/index.html?l 0&ID1 AB.MATH.JR.NUMB&ID2 AB.MATH.JR.NUMB.RATE&lesson html/object interactives/3 term ratio/use it.htmlIf the link above doesn't work, use this x.html?l 0&ID1 AB.MATH.JR.NUMBFirst choose Rate/Ratio/Proportion, and then either 3-Term Ratios.ProportionsRatios and ProportionsA tutorial with interactive practice exercises about ratios and onsPractice with ProportionsAn online quiz from Regents Exam Prep BRA/AO3/pracProp.htmChallenge BoardChoose questions from the challenge board about rates, ratios, and ://www.quia.com/cb/101022.htmlRags to Riches - ProportionsSolve proportions and advanced towards more and more difficult questions.http://www.quia.com/rr/35025.htmlDirt Bike ProportionsA racing game where you need to find the unknown in a simple proportion. This game would actually work equallywell for practicing equivalent fractions because the proportions are quite atio and Proportion Game From BBC SkillswiseWrite the simplified ratio of red to black marbles. Answer simple questions about ratios and le worksheet fromwww.mathmammoth.com9
Proportions Battleship GameSolve proportions whenever you get a ‘hit’ on enemy ships in the classic battleship game.http://www.quia.com/ba/83811.htmlHow Much Is a Million?This is a lesson plan for a hands-on activity where students count grains of rice in a cup, weigh that amount of rice,and then build a proportion to figure out the weight of 1 million grains of rice.http://illuminations.nctm.org/Lesson.aspx?id 2674Scale drawings and mapsRatio and ScaleAn online unit about scale models, scale factors, and maps with interactive exercises and cs/demo/units/KCA024.htmlSelf-Check Quiz from GlencoeA five-question multiple-choice quiz about scale drawings. By reloading the page you will get different ls/cgi-bin/msgQuiz.php4?isbn 0-02-833050-1&chapter 8&lesson 3MapsA tutorial with worked out examples and interactive exercises about how to calculate distances on the map or inreal life based on the map's es/book7/bk7i19/bk7 19i3.htmScale Drawings and Models - Word ProblemsSolve word problems involving scale drawings and models. You can choose between multiple-choice, matchanswers, or flashcard style ingsandmodelsUse Proportions To Solve Problems Involving Scale DrawingsA set of word problems. You can choose how they are presented: as flashcards, as a quiz where you matchquestions and answers, as a multiple choice quiz, or a true/false quiz. You can also play a game (Jewels) ale Drawings - Problem Solving and Constructing Scale Drawings Using Various ScalesA comprehensive lesson with several worked out examples concerning scale -Common-Core/section/12.0/Constructing Scale DrawingsPractice making scale drawings on an interactive grid. The system includes hints and the ability to check /e/constructing-scale-drawingsInterpreting Scale DrawingsSolve word problems involving scale drawings in an online practice environment. The system includes hints andthe ability to check /e/interpreting-scale-drawingsSample worksheet fromwww.mathmammoth.com10
Significant digitsSig Fig RulesDrag Sig J. Fig to cover each significant digit in the given number.http://www.sigfig.dreamhosters.com/Practice on Significant FiguresA multiple-choice quiz that also reminds you of the rules for significant nt/uploads/2012/07/SigFig.htmlSignificant digits quizA 10-question multiple-choice quiz about significant digits.http://www.quia.com/quiz/114241.html?AP rand 1260486279Sample worksheet fromwww.mathmammoth.com11
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Unit RatesRemember that a rate is a ratio where the two terms have different units, such as 2 kg/ 0.45 and 600 km/5 h.In a unit rate, the second term of the rate is one (of some unit).For example, 55 mi/1 hr and 4.95/1 lb are unit rates. The number “1” is nearly always omitted so those rates areusually written as 55 mi/hr and 4.95/lb.To convert a rate into an equivalent unit rate simply divide the numbers in the rate.Example 1. Mark can ride his bike 35 km in 1 ½hours. What is the unit rate?Example 2. A snail can slide through the mud 5 cm in20 minutes. What is the unit rate?To find the unit rate, we use the principles of divisionby fractions to divide 35 km by 1 ½ h. The units “km”and “hours” are divided, too, and become “km perhour” or “km/hour.”Here, it is actually not clear whether we should givethe unit rate as cm/min or cm/hr. Let’s do both.(1) To get the unit rate in cm/min, we simply divide5 cm 20 min. We get the fraction 5/20. We alsodivide the units to get “cm/min.” So we get3235 km 35 km/h 35 km/h231 1/2 h 5 cm 20 min 5/20 cm/min 1/4 cm/minOr use decimals: 5 cm/20 min 25/100 cm/min70km/h 23 ⅓ km/h.3 0.25 cm/min.We could also use decimal division:35 km 1.5 h 23.333. km/h.(2) For centimeters per hour, we multiply both termsof the rate by 3 to get an equivalent rate of 15 cmin 60 minutes, which is 15 cm in 1 hour.So the unit rate is 23 ⅓ km per hour.1. Find the unit rate.a. 125 for 5 packagesb. 6 for 30 envelopesc. 1.37 for ½ hourd. 2 ½ inches per 4 minutese. 24 m2 per 3/4 gallon2. A person is walking 1/2 mile every 1/4 hour. Choose the correct fraction for the unit rate and simplify it.1412miles per hour orSample worksheet fromwww.mathmammoth.com1214miles per hour24
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Chapter 7: PercentIntroductionIn this chapter we review the concept of percent as “per hundred” or as hundredth parts and how to convert betweenfractions, decimals, and percents. Solving Basic Percentage Problems is another lesson intended for review of sixthgrade topics, focusing on finding a known percentage of a number (such as 21% of 56) or finding a percentagewhen you know the part and the total.We take a little different perspective of these concepts in the lesson Percent Equations. Students write simpleequations for situations where a price increases or decreases (discounts). This lesson also explains what a percentproportion is. Personally, I prefer not to use percent proportion but to write the percentage as a decimal and thenwrite an equation. I feel that approach adapts better to solving complex problems than using percent proportion.Here is a quick example to show the difference between the two methods. Let’s say an item is discounted by 22%and it now costs 28. Then, the new price is 78% of the original. If we let p be the price of the item before thediscount, we can write the percent proportion 28/p 78/100 and solve for p. If, we write the percentage 78% asthe decimal 0.78, we get the equation 0.78p 28. Personally, I consider percent proportion to be an optional topic,and the reason I have included it here is to make this curriculum fully meet the Common Core Standards forseventh grade.The lesson Circle Graphs provides students a break from new concepts and allows them to apply the concept ofpercent in a somewhat familiar context. Next, we delve into the percentage of change. Students sometimes view thepercentage of change as a totally different concept as compared to other percentage topics, but it is not that at all.To calculate the percentage of change, we still use the fundamental idea of percentage part/total, only this time,the “part” is how much the quantity in question changes (the difference) and the “total” is the original quantity.Tying in with percentage of change, students also learn to compare values using percentages, such as how manypercent more or less one thing is than another. Once again, this is not really a new concept but is based on thefamiliar formula percentage part/total. The percentage difference (or relative difference) is the fraction (actualdifference)/(reference value).Simple Interest is a lesson on the important topic of interest, using as a context both loans and savings accounts.Students learn to use the formula I prt in a great variety of problems and situations.The text concludes with a review lesson of all of the concepts taught in the chapter.The Lessons in Chapter 7pagespanReview: Percent .723 pagesSolving Basic Percentage Problems .753 pagesPercent Equations .785 pagesCircle Graphs .832 pagesPercentage of Change .853 pagesPercentage of Change: Applications .884 pagesComparing Values Using Percentages .924 pagesSimple Interest .966 pagesChapter 7 Mixed Review .1023 pagesChapter 7 Review .1052 pagesSample worksheet fromwww.mathmammoth.com67
Helpful Resources on the InternetPercent videos by MariaVideos on percent-related topics that match the lessons in this phpPercentages, fractions, and decimalsVirtual Manipulative: PercentagesAn interactive tool where you fill in any two of the three boxes (whole, part, and percent), and it will calculate themissing part and show the result visually in two ways.http://nlvm.usu.edu/en/nav/frames asid 160 g 2 t 1.htmlMission: MagnetiteHacker tries to drop magnetite on Motherboard. To unlock a code to stop him, match up percentages, fractions, andimages showing fractional parts in five different sets of rcent/index.htmlFractions and Percent Matching GameA simple matching game: match fractions and percentages.http://www.mathplayground.com/matching fraction percent.htmlFraction/Decimal/Percent JeopardyAnswer the questions correctly, changing between fractions, decimals, and r PowerGrow flowers and harvest them to make money in this addictive order-’em-up game. Practice ordering decimals,fractions, and percentages. The game starts with ordering decimals (daisies), and proceeds into fractions (tulips powerMatching Fractions, Decimals, and PercentagesA simple matching memory game.http://nrich.maths.org/1249Sophie's DominoesPlace dominoes that contain either numbers or a percentage of a number (such as 15% of 300) in the correct orderin the work /212/mod resource/content/1/doms.swfPercent Goodies: Fraction-Decimal-Percent ConversionsPractice conversions between fractions, decimals and percents. There are three levels of difficulty and instantscoring for each. Note that fractions must be written in lowest /Sample worksheet fromwww.mathmammoth.com68
Percentage of a numberPercent worksheetsCreate an unlimited number of free customizable percent worksheets to ath.net/worksheets/percentages-words.phpPenguin WaiterA simple game where you calculate the correct tip to leave the waiter (levels “easy” and “medium”), the percentagethat the given tip is (level “hard”), or the original bill (level “Super Brain”).http://www.funbrain.com/penguin/Percent JeopardyAn interactive jeopardy game where the questions have to do with a percentage of a quantity.http://www.quia.com/cb/42534.htmlMath At the MallPractice percentages while shopping at a virtual mall. Find the percentage of discount and the sales price, calculatethe interest earned at the bank, compare health memberships at the gym and figure out how much to tip your waiterat the Happy all2.htmlMatching Percentage of a NumberMatch cards that ask for a percentage of a number (such as 75% of 40) with the values. The game is fairly easy andcan be completed using mental centage/MatchingPercentNumber.htmDiscount DoorsCalculate the price after the .php/214/mod resource/content/1/doors.swfThe Percentage GameThis is a printable board game for 2-3 players that practices questions such as“20 percent of is 18” or “ is 40 percent of eA Conceptual Model for Solving Percent ProblemsA lesson plan that uses a 10 x 10 grid to explain the basic concept of percent and to solve various types ofpercentage problems. The lesson includes seven different word problems to solve. Please note their solutions areincluded on the same px?id L249Percentages of SomethingThis is a simple illustration to help students understand the meaning of percent. Choose a way to illustratepercentages and then drag percentages into the 16perc-game-percentages-of-somethingSample worksheet fromwww.mathmammoth.com69
Percent of changePercent of Change MatchingMatch five flashcards with given increases or decreases (such as “25 is decreased to 18”) with five percentages ching-182854Percent ShoppingChoose toys to purchase. In level 1, you find the sale price when the original price and percent discount are known.In level 2, you find the percent discount (percent of change) when the original price and the sale price are known.http://www.mathplayground.com/percent shopping.htmlRags to Riches: Percent Increase or DecreaseAnswer simple questions about percent increase or decrease and see if you can win the grand prize in the game.http://www.quia.com/rr/230204.htmlPercentage Change 1A self-marking quiz with 10 questions about percentage change. The link below goes to level 1 quiz, and at thebottom of that page you will find links to level 2, 3, 4, 5 and 6 quizzes.http://www.transum.org/software/SW/Starter of the day/Students/PercentageChange.aspPercentage increase and decrease 4 in a lineThe web page provides a game board to print. Players take turns picking a number from the left column, andin
Math Mammoth Grade 7-A and Grade 7-B worktexts comprise a complete math curriculum for seventh grade mathematics studies. This is a pre-algebra course after which students can continue to an Algebra 1 curriculum. The curriculum meets and actually exceeds the Common Core Standards (CCS) for grade 7. The two major areas
Math Course Progression 7th Grade Math 6th Grade Math 5th Grade Math 8th Grade Math Algebra I ELEMENTARY 6th Grade Year 7th Grade Year 8th Grade Year Algebra I 9 th Grade Year Honors 7th Grade Adv. Math 6th Grade Adv. Math 5th Grade Math 6th Grade Year 7th Grade Year 8th Grade Year th Grade Year ELEMENTARY Geome
Math Mammoth Grade 4-A and Grade 4-B worktexts comprise a complete math curriculum for the fourth . Choose the 3rd grade book to approximately match Math Mammoth 4. The books include answer key, worked examples, practice problems, and . zEducation Place Brain Teasers Has a separat
Teacher of Grade 7 Maths What do you know about a student in your class? . Grade 7 Maths. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Primary. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 . Learning Skill
skip grade 4 math and take grade 5 math while still in grade 4 Student A, now in grade 4, qualifies for SSA and enrolls in the accelerated course, which is grade 5 math Student A, after completing grade 5 math while in grade 4, takes the grade 4 End‐of‐Grade test Grade‐Level Grade 3 Grade 4 Grade 4
Foreword Math Mammoth Grade 5-A and Grade 5-B worktexts comprise a complete math curriculum for the fifth grade mathematics studies that meets and exceeds the Common Core Standards. Fifth grade is the time to focus on fra
Math Mammoth Grade 3-A and Grade 3-B worktexts comprise a complete math curriculum for third grade mathematics studies that meets and exceeds the Common Core standards. Third grade is a time for learning and mastering two (mostly
Math Mammoth Grade 1-A and Grade 1-B worktexts comprise a complete math curriculum for the first grade mathematics studies. This curriculum is aligned to the Common Core standards. The four main areas of study for first grade are: 1. The concepts of addition and subtr
Math Mammoth Grade 1-A and Grade 1-B worktexts comprise a complete math curriculum for the first grade mathematics studies. This curriculum is aligned to the Common Core standards. The four main areas of study for first grade are: 1. The concepts of addition and subtr