Algebra Summer Math Packet - Altamont School
Pre‐Algebra Summer Math PacketTo help students retain math concepts and skills we are requiring students to complete this Pre‐AlgebraSummer Math Packet. The skills required to answer the questions in this packet are ones that shouldhave been mastered by students in previous math courses. Some of the skills are also covered in thefirst chapter of the Pre‐Algebra textbook. The packet contains a brief review and example problems foreach skill.Students should complete all of the questions for each lesson.Please note:1. Working through these problem sets is mandatory.2. All work should be completed on separate sheets of paper. Answers should be written on thepacket.3. Students should bring completed problems sets with them to turn in on the first day their mathclass meets next school year.a. Students do not need to print out the answer pages that are included with the packet.4. Students should check their work upon completion.a. The answers to the questions are located at the back of this packet. If a studentanswers a question incorrectly, he/she should return to the work shown, attempt to findthe source of the error(s), and correct the problem.5. Students should NOT use calculators on any portion of this packet.6. Students will be given a homework grade for completion of this packet.
Name �——————SECTIONWhole Numbers, Decimals,and IntegersLesson 4: Adding and Subtracting DecimalsTo add and subtract decimals, line up the decimal points. Then add or subtractas with whole numbers and bring down the decimal point.EXAMPLE 1Add. 6.45 1 8.86.451 8.8015.25EXAMPLE 2Line up the decimal points vertically.Write zeros as needed. Add.Line up the decimal points.HINTWhen adding or subtractingdecimals, be sure thedecimal point in the answeris directly below the decimalpoint in the problem.Subtract. 12.50 2 1.25 12.502 1.25 11.251. WHOLE1. WHOLENUMBERSNUMBERS4. Adding1. PlaceandValueSubtracting1Date ————————————Line up the decimal points vertically.Subtract.Line up the decimal points.Practice: First TryCopyright by McDougal Littell, a division of Houghton Mifflin Company.Add.1.3.681 0.942.0.071 17.823. 25.491 3.474. 12.491 2.795.10.531 1.066.30.031 2.097. 10.301 62.508. .081 .959. 5.50 1 .8910. 12.8 1 4.4111. 59.38 1 21.51Subtract.12. 12.002 6.5013.8.7622 0.38114.10.3942 0.89815. 19.992 8.6416.8.302 5.7317.52.522 25.2518. 20.502 10.2519. 14.992 5.5020. 17.001 2 5.521. 20 2 14.9822. 25.17 2 19.62McDougal Littell Middle School MathRemediation Book Lesson 1.47
Name �——————1Whole Numbers, Decimals,and Integers1. WHOLE1. WHOLENUMBERSNUMBERS6. Multiplying1. Place Valuewith DecimalsSECTIONDate ————————————Lesson 6: Multiplying with DecimalsWhen multiplying with decimals, the number of decimal places in theproduct is equal to the total number of decimal places in the factors.EXAMPLE 1Multiply. 6.253 3 82 426.2533850.024EXAMPLE 2Count 3 decimal places in the factor: 6.253.The product has 3 decimal places.Multiply. 14.50 3 0.06HINTThe number of digits to theright of the decimal point inthe product is the sum of thenumber of digits to the rightof the decimal point in thefactors.23 14.503 0.062 places1 2 places .87004 placesCopyright by McDougal Littell, a division of Houghton Mifflin Company. .87Practice : First TryMultiply.1.3.23 52.0.053 93.0.73 64.3.013 95.3.13 0.36.1.253 4.47.4.53 0.88.0.63 0.099.3 16.49510.3 8.692811. 3.503 0.0412. 12.003 0.913. 0.2 3 8214.3.986 3 315. 0.06 3 516. 92.6 3 1.3217.0.99 3 1.518. 0.374 3 0.3McDougal Littell Middle School MathRemediation Book Lesson 1.611
Name �——————SECTIONWhole Numbers, Decimals,and IntegersLesson 8: Dividing with DecimalsIf the divisor is a whole number, write a decimal point in the quotientdirectly above the decimal point in the dividend.If the divisor is a decimal number, move the decimal point to the rightuntil the divisor is a whole number. Then move the decimal in the dividendthe same number of places to the right. Write a decimal point in the quotientdirectly above the new decimal point in the dividend.EXAMPLE 11. WHOLE1. WHOLENUMBERSNUMBERS8. 1.DividingPlace Valuewith Decimals1Date ————————————Divide. 1.98 by 4. Round to the nearest cent.Copyright by McDougal Littell, a division of Houghton Mifflin Company.The decimal point in the quotient is above thedecimal point in the dividend.0.4954 qw1.9802019216382362022 00EXAMPLE 2Write zeros as needed to keep going.034504345Round thequotient to thenearest cent.9 3 4 5 36 .495 A .50Check0.4953 41.985 3 4 5 20Divide. 318 4 0.6Move this decimal until thedivisor is a whole number.0.6 qw318.0RewriteThen move thisdecimal point thesame number ofplaces. Writezeros as needed.5306 qw3180230182180020005 3 6 5 303 3 6 5 1803650Check5303 0.6318.0Practice: First TryDivide.1. 2 qw6.342. 5 qw97.153. 0.3 qw9.814. 0.04 qw10.6McDougal Littell Middle School MathRemediation Book Lesson 1.815
Name �——————SECTION6Date ————————————AlgebraLesson 1: Writing ExpressionsA variable is any letter that represents an unknown number.A numerical expression has numbers and operations.A variable expression also has variables.It is sometimes called an algebraic expression.EXAMPLE 1Copyright by McDougal Littell, a division of Houghton Mifflin Company.WordsSymbolsfour times ten4 104 3 10the sum of two and five215(2 1 5)nine divided by the difference ofsix and one9 4 (6 2 1)4(10)9621}HINTNotice in theexamples shownhere that someoperations canbe representedby more thanone symbol.6. ALGEBRA1. Writing ExpressionsEXAMPLE 2Here are some numerical expressions.Here are some variable expressions.WordsSymbolsthe product of seven and n7 na minus b plus foura2b14the quotient of a number and twox4273n7(n)x2}Practice: First TryWrite symbols for the given words.1. the sum of eight and six2. twenty divided by five3. the product of x and y4. two times a number5. five times three6. the sum of nine and two divided by 77. 8 times the sum of b and 38. 6 divided by the difference of x and 19. the difference of nine and five10. the product of ten and fortyMcDougal Littell Middle School MathRemediation Book Lesson 6.1167
Name �——————SECTION6Date ————————————AlgebraLesson 6: Evaluating ExpressionsTo evaluate a variable expression, substitute the given value for the variable(s).Then use the order of operations to evaluate.EXAMPLE 1Evaluate 2x 2 4 when x 5 5.6. ALGEBRA6. Evaluating Expressions2x 2 4 5 2(5) 2 4 5 10 2 4 5 6Substitute 5 for x. Use the order of operations.EXAMPLE 2Evaluate 14 1 n2 when n 5 6.14 1 n2 5 14 1 62 5 14 1 36 5 50Substitute 6 for n. Use the order of operations.Copyright by McDougal Littell, a division of Houghton Mifflin Company.EXAMPLE 3Evaluate 3a2 2 b when a 5 2 and b 5 5.HINTIf using a calculator toevaluate, don’t assumeit will do order ofoperations correctly.Substitute 5 for b.3a2 2 b 5 3(2)2 2 5 5 3(4) 2 5 5 12 2 5 5 7Substitute 2 for a.Use the order of operations.Practice: First TryEvaluate the expression.1. y 2 4 when y 5 92. a 1 7 when a 5 113. 3x when x 5 5z4. } when z 5 1825. n2 when n 5 46. 9 2 p3 when p 5 1n7. m 1 } when m 5 4 and n 5 1058. 2x 1 y when x 5 3 and y 5 19. a2 2 b2 when a 5 6 and b 5 410. s 1 50 t when s 5 13 and t 5 3McDougal Littell Middle School MathRemediation Book Lesson 6.6177
Name �——————SECTION6Date ————————————AlgebraLesson 5: Order of OperationsSome expressions have more than one operation. A set of rules called theorder of operations tells us how to evaluate them.When an expression has more than one operation, do the operations in thefollowing order.Order of Operations1. Evaluate expressions inside parentheses.3. Multiply and divide from left to right.4. Add and subtract from left to right.EXAMPLE(5 2) 1 62 4Parentheses5316 42Exponents5 3 1 36 4Multiply, DivideCopyright by McDougal Littell, a division of Houghton Mifflin Company.5 3 1 144Add, Subtract5 147HINTIf there is addition andsubtraction in the sameexpression, do them fromleft to right. For example,in 18 2 4 1 2, do thesubtraction first. In18 1 2 2 4, do theaddition first. The sameis true for multiplicationand division.6. ALGEBRA5. Order of Operations2. Evaluate expressions with exponents.You can use the sentence “Please excuse my dear Aunt Sally” to helpyou remember the order of operations.Practice: First TryFor each expression, tell which operation you would do first.1. 43 1 9 2 32.20 2 (4 1 7)3. 24 4 6 1 74. 6 2 1 1 55.(3 2 1) 1 426. 24 2 32Evaluate the expression. Use the order of operations.7. 10 3 (6 2 2)10. (12 1 4) 4 228.11.52 2 (4 1 3)(9 2 1)(2 1 6)9. 12 4 4 3 2312. 8 1 7 2 1 4McDougal Littell Middle School MathRemediation Book Lesson 6.5175
Name �——————SECTION1Date NUMBERSNUMBERS11.1. PlaceIntegersValueWhole Numbers, Decimals,and IntegersLesson 11: IntegersThe set of numbers in the box are integers.Negative integers are less than 0, and positiveintegers are greater than 0. Zero is an integerthat is neither positive nor negative. . . , 24, 23, 22, 21, 0, 1, 2, 3, 4, .You can graph integers on a number line.EXAMPLE 1 3 2 101234Graph –6 and –1 to compare them. 7 6 5 4 3 226 is less than –1. 10121 is greater than 26.26 , 21Copyright by McDougal Littell, a division of Houghton Mifflin Company. 4HINTThe numbers increase as youmove from left to right on anumber line.21 . 26Two numbers are opposites if they are the same distance from0 on a number line, but are on opposite sides of 0. The absolutevalue of a number is the distance between the number and 0 ona number line. The absolute value of a number n is written n .EXAMPLE 2The numbers 23 and 3 are opposites.The absolute value of 23 is 3.3 unitsThe absolute value of 3 is 3. 4Write 23 5 3 and 3 5 3. 3 2 13 units01234Practice: First TryComplete with , , or 5.1. 24 252. 22 23. 1 234. 27 245. 0 266. 28 0Write the absolute value of each integer.7. 5 58. 22 510. 4 511. 21 59. 24 512. 0 5McDougal Littell Middle School MathRemediation Book Lesson 1.1121
Name �——————SECTION1Date NUMBERSNUMBERS12.1. PlaceAddingValueIntegersWhole Numbers, Decimals,and IntegersLesson 12: Adding IntegersYou can use absolute value or a number line to add integers.EXAMPLE 1Add. –3 (–2)Find absolute values:U 23 U 5 3 and U 22 U5 2Add absolute values:31255Attach a negative sign:–5Write the sum:–3 1 –2 2 –5 2 6EXAMPLE 2 5 4 3 3 2 1012Add. –5 2U 25 U 5 5 and U 2 U5 2Find absolute values:Subtract absolute values: 5 – 2 3Copyright by McDougal Littell, a division of Houghton Mifflin Company.HINTTo add two negativeintegers, add theirabsolute values. Theanswer is negative.Attach a negative sign:–3Write the sum:–5 2 –3 5HINTTo add a negative integerand a positive integer,subtract their absolutevalues. The answer has thesign of the integer with thegreater absolute value. 2 6EXAMPLE 3 5 4 3 2 1012Add. –3 5Find absolute values:U 23 U 5 3 and U 5 U5 5Subtract absolute values:5–3 2The answer is positive:2Write the sum:–3 5 2HINTUse a number line tocheck your answer. 3 5 4 3 2 101234McDougal Littell Middle School MathRemediation Book Lesson 1.1223
Name �——————Date ————————————LESSON 00.001. WHOLE NUMBERSMore Copy if Needed12. Adding IntegersPracticeAdd. Use the number line if it helps you. 10 9 8 7 6 5 4 3 2 10123456789101. 4 1 1 21 2 52. 22 1 1 22 2 53. 5 1 1 28 2 54. 23 1 3 55. 24 1 1 23 2 56. 25 1 7 57. 26 1 2 58. 1 1 1 26 2 59. 21 1 1 29 2 510. 24 1 9 511. 23 1 1 25 2 512. 8 1 1 27 2 513. When Alison went to bed, the temperature was –8 C. If it drops 10 degreesovernight as predicted, what will be the temperature?14. In an electronic game, Nate scored the following points: 120, 230, 210, 150,240, 220, 220, 110. What was his final score?15. What is the sum of any integer n and its opposite?16. What is the sum of any integer n and zero?PuzzleWrite the integers –4, –3, –2, –1, 0, 1, 2, 3, 4 in the magic square. Every horizontal,vertical, and diagonal sum must equal zero. Two numbers have already been written for you.3224McDougal Littell Middle School MathRemediation Book Lesson 1.12Copyright by McDougal Littell, a division of Houghton Mifflin Company.Extend Your Skills
Name �——————SECTIONWhole Numbers, Decimals,and IntegersLesson 13: Subtracting IntegersTo subtract an integer, you add its opposite. Rewrite the subtraction expressionas addition. Then follow the rules for addition of integers.The opposite of a negative number is positive, and the opposite of a positivenumber is negative.EXAMPLE 1Subtract. 2 2 6Use addition:EXAMPLE 2412 6Write the difference:4 2 1 –2 2 5 6Subtract. 24 2 2Use addition:Copyright by McDougal Littell, a division of Houghton Mifflin Company.2 2 6 5 24Subtract. 4 2 1 –2 2Use addition:EXAMPLE 3HINTTo add integers,see pages 23–24.2 1 1 –6 2 24Write the difference:1.1. WHOLEWHOLE NUMBERSNUMBERS13.1.SubtractingPlace Value Integers1Date ————————————24 1 1 –2 2 26Write the difference:24 2 2 5 26Practice : First TryMatch each subtraction expression with its addition expression.1. 3 2 1 –8 22. 3 2 83. 23 2 84. 23 2 1 –8 2A. 3 1 1 –8 2B. 23 1 8C. 3 1 8D. 23 1 1 –8 2Subtract. Use the number line if it helps you. 10 9 8 7 6 5 4 3 2 10123456789105. 24 2 7 5 1 56. 1 2 8 5 1 57. 3 2 1 –1 2 5 1 58. 27 2 1 –2 2 5 1 5McDougal Littell Middle School MathRemediation Book Lesson 1.1325
Name �——————1Whole Numbers, Decimals,and IntegersLesson 14: Multiplying and Dividing IntegersWhen you multiply two positive numbers or two negativenumbers, the product is positive.When you multiply a positive number and a negativenumber, the product is negative.Use the same sign rules when you divide with positiveand negative numbers.EXAMPLE 1Multiply.2 3 8 5 16positivepositivenegativeCopyright by McDougal Littell, a division of Houghton Mifflin Company.2 3 1 28 2 5 –16positivepositive22 3 1 28 2 5 16EXAMPLE 2HINTBefore you multiplyor divide, look at thesigns and determinewhat the sign of theanswer will be.1. WHOLE1. WHOLENUMBERSNUMBERS14. Multiplying1. Place Valueand DividingSECTIONDate venegative22 3 8 5 216negativenegativenegativepositiveDivide.12 4 3 5 4positive12 4 1 23 2 5 –4positivepositivepositive212 4 1 23 2 5 4negativenegativepositivenegative212 4 3 5 24negativenegativenegativepositivePractice: First TryMultiply.1. 4 3 1 24 2 52. 26 3 5 53. 27 3 1 22 2 54. 6 3 10 55. 211 3 3 56. 28 3 1 21 2 58. 12 4 1 22 2 59. 29 4 1 23 2 5Divide.7. 40 4 1 25 2 510. 214 4 1 21 2 511. 232 4 8 512. 81 4 1 29 2 5McDougal Littell Middle School MathRemediation Book Lesson 1.1427
Name �——————SECTION6Date ————————————AlgebraLesson 18: Points in the Coordinate PlaneYou can locate points in a coordinate plane. A horizontal x-axis and avertical y-axis intersect at the origin, dividing the plane into four quadrants,numbered I, II, III, and IV.II5y-axisAF1C(0, 0) origin 5 4 3 2 1 O 1 2G 3 4 5III1 235 x-axis4HINTWhen drawing acoordinate planealways label the axesand the origin.EIV6. ALGEBRA18. Coordinate Plane4D32BICopyright by McDougal Littell, a division of Houghton Mifflin Company.To locate a point in the coordinate plane, use an ordered pair. The numbersin an ordered pair (x, y) are coordinates, with the x-coordinate followed bythe y-coordinate.EXAMPLEIn the coordinate plane above, locate point A. Starting at the origin,count 3 units left and 2 units up. Point A is located at (23, 2).Practice: First TryUse the coordinate plane above. Write the coordinatesfor each point.1. B2. C3. D4. E5. F6. GDraw a coordinate plane. Draw and label each point at thelocation indicated.7. U (21, 4)10. X (25, 22)8. V (3, 3)11. Y (2, 0)9. W (0, 23)12. Z (4, 23)McDougal Littell Middle School MathRemediation Book Lesson 6.18201
Name �——————Date ————————————Practice: Second TryWrite the coordinates for each point.2.B3. C4.D5. E6.Fy5432FC7. G9. I8.10.HJ16. ALGEBRA18. Coordinate PlaneM14. (2, 4)15. (3, 24)16. (0, 3)17. (23, 25)18. (22, 0)19. (3, 0)20. (25, 3)Ey54S3212. (24, 23)13. (0, 0)A 5 4 3 2 1 O1 2 1H 2J 3DG 4 5Write the point for the given coordinates.11. (5, 23)IWR1 234 5 xTPImagine a neighborhood on a coordinate grid, with your home at the originand the top of the page as due north.21. If you travel 3 blocks west, then 5 blocks north to get to school, whatquadrant is your school in?22. If you travel 2 blocks east, then 1 block south to get to your friend’shouse, what quadrant is your friend’s house in?23. If you travel 2 blocks west, then 4 blocks south to get to the store, whatquadrant is the store in?PuzzleDraw a coordinate plane. Draw points as indicated. Then connect them in order usingstraight lines. What figure do you get?202McDougal Littell Middle School MathRemediation Book Lesson 6.185 xBExtend Your Skills(23, 3) to (3, 0) to (23, 23) to (0, 3) to (3, 23) to (23, 3)4Q1 5 4 3 2 1 O 1 2U 3 4N 53Copyright by McDougal Littell, a division of Houghton Mifflin Company.1. A
Name �——————SECTION6Date ————————————AlgebraLesson 12: Solving One-Step EquationsOne-step equations can be solved using any of the four basic operations.Use the inverse operation, or opposite operation of what is in the equation.Inverse tiplicationDivisionDivisionMultiplicationYou can use all four operations to solve one-step equations.Using Additiona – 2 5 10a – 2 1 2 5 10 1 2 Add.a 5 12Check: 12 2 2 5 10 Using MultiplicationCopyright by McDougal Littell, a division of Houghton Mifflin Company.HINTSee Lessons 10, 11 formore practice on solvingone-step equations.n} 5 10n 2} 2 5 10 2 Multiply.2n 5 2020Check: }5 10 2Using Subtractiony 1 2 5 10y 1 2 2 2 5 10 2 2 Subtract.y58Check: 8 1 2 5 10 6. ALGEBRA12. Solving One-StepEXAMPLEOperationUsing Division2x 5 10102x} 5 } Divide.22x55Check: 2(5) 5 10 Practice: First TrySolve the equation. Check your solution.1. x – 1 5 82. m 2 6 5 63. c 1 3 5 74. 6d 5 24r5. } 5 926. 2n 5 67. 9z 5 278. h 4 3 5 79. y 1 9 5 15a10. } 5 5611. c 2 19 5 2012. t 1 8 5 18McDougal Littell Middle School MathRemediation Book Lesson 6.12189
Name �——————SECTION6Date ————————————AlgebraLesson 13: Solving Two-Step EquationsUse two operations to solve a two-step equation. To determine whichoperation to undo first, use the order of operations in reverse.EXAMPLE 1Solve the equation.2x 2 1 5 72x 5 82x282}5}x54Add 1 to each side.Simplify.Divide each side by 2.HINTFirst, use addition orsubtraction. Then,use multiplication ordivision.Simplify.Check: 2(4) 2 1 5 7 EXAMPLE 2Solve the equation.n5}1256Copyright by McDougal Littell, a division of Houghton Mifflin Company.6. ALGEBRA13. Solving Two-Step2x 2 1 1 1 5 7 1 1n5}12225622n5}54n5} 554 5n 5 20Subtract 2 from each side.Simplify.Multiply each side by 5.HINTRemember tocheck yoursolution in theoriginal equation.Simplify.201256 Check: }5Practice: First TrySolve each equation. Check your solution.1. 3y 2 4 5 52. 2a 1 5 5 13m3. } 2 1 5 64b4. } 2 3 5 195. 6c 2 7 5 11y6. } 1 12 5 185McDougal Littell Middle School MathRemediation Book Lesson 6.13191
Answer KeySection 1Whole Numbers, Decimals, and IntegersLesson 4 (pp. 7–8)Practice:First Try1. 4.62 2. 17.893. 28.96 4. 15.28 5. 11.59 6. 32.127. 72.80 8. 1.03 9. 6.39 10. 17.2111. 80.89 12. 5.50 13. 8.381 14. 9.49619. 9.4920. 11.50121. 5.0215. 11.3516. 2.5717. 27.2718. 10.2522. 5.55Second Try1. 6.62 2. 15.22 3. 16.34. 13.17 5. 45.3 6. 0.523 7. 12.118. 26.53 9. 34.4 10. 27.24 11. 195.5412. 69.1216. 7.2620. 21.5017. 8.7218. 9.0219. 14.2513. 9.7914. 15.2721. 46.2322. 6.56415. 40.6623. 8.42924. 45.77 25. 10.05 26. 106.75 27. 36.3128 a. 24.59 28 b. 5.41 29. 115.25PuzzleFill up the 0.3 liter container first. Pour it into the 0.5 liter container. Fill up the 0.3 liter container again, andfill up the res
6 2 1 EXAMPLE 2 Here are some variable expressions. Words Symbols the product of seven and n 7 n 7 3 n 7(n) a minus b plus four a 2 b 1 4 the quotient of a number and two x 4 2 x} 2 McDougal Littell Middle School Math Remediation Book Lesson 6.1 HINT Notice in the examples shown here that some operations can be represented by more than one .
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Summer Math Packet 2019 Rising Pre-Algebra (Math 8) Poe Middle School If you are taking Pre-Algebra next year, this is the packet for you! summer to keep your math skills sharp before the next Complete the following problems each week over the school year. You may use a calculator, but be sure to show all your steps with each problem and to label
Summer Packet 2021: Pre-Algebra College Prep *** Students Entering 7th or 8th Grade Pre-Algebra Purpose: This packet is designed to help students stay on track over the summer and enter 7th grade confident and prepared for a great school year. Math teachers have selected 6 skills that are important for the students’ success in Pre-Algebra.
Algebra 1 Summer Packet Get ready for Algebra with Ms. Murano! In this packet you will find a review of the most important topics you learned in 7th Grade Accelerated Math this year. Reviewing these topics over the summer will help you be prepared for Algebra I in September! There is a brief review of each important topic with problems that are
The purpose of this summer math packet is to provide you with notes and practice problems to help you review what you learned in sixth grade math. The summer math packet will NOT be graded. However, you are responsible for this material. Within the first few days of Math 7, you will be assessed on the math skills
contained in this packet. The packet allows us to start directly into the Algebra 2 curriculum. This course requires each student to complete a review packet. The packet must be turned into the office no later than 2:30 pm on August 22, 2019. After successful completion of the packet, you will take a basic Algebra 1 test on the first day of school.
