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Table of Contents Introduction. ..................................................................................................... 5 Unit 1 Ratios and Percents............................................................................................... 7 6.RP.1 6.RP.3.a 6.RP.2, 6.RP.3.b 6.RP.3.d 6.RP.3.c Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Review Ratios......................................................................... 8 Equivalent Ratios.................................................... 12 Rates........................................................................ 16 Measurement Conversions.....................................20 Percents................................................................... 24 Ratios and Percents................................................ 28 Unit 2 Operations. ............................................................................................................ 31 6.NS.2 6.NS.1 6.NS.3 6.NS.3 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Review Dividing Whole Numbers....................................... 32 Dividing Fractions................................................... 36 Adding and Subtracting Decimals.........................40 Multiplying and Dividing Decimals.......................44 Operations...............................................................48 Unit 3 Factors and Multiples......................................................................................... 51 6.NS.4 6.NS.4 Lesson 1 Greatest Common Factors...................................... 52 Lesson 2 Least Common Multiples........................................ 56 Review Factors and Multiples.............................................60 Unit 4 Positive and Negative Numbers.....................................................................63 6.NS.5 6.NS.6.a, c 6.NS.6.b, c; 6.NS.8 6.NS.7.a, b 6.NS.7.c, d Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Review Integers....................................................................64 Rational Numbers on Number Lines.....................68 Coordinate Graphing.............................................. 72 Comparing Integers................................................ 76 Absolute Value........................................................80 Positive and Negative Numbers.............................84 Unit 5 Expressions. ........................................................................................................... 87 6.EE.1; 6.EE.2.a, b 6.EE.1, 6.EE.2.c 6.EE.3, 6.EE.4 FLM CCSS Gr6_FM.indd 3 Lesson 1 Lesson 2 Lesson 3 Review Writing Expressions................................................88 Evaluating Expressions...........................................92 Operation Properties.............................................. 96 Expressions........................................................... 100 10/4/10 3:19:30 PM Unit 6 Equations and Inequalities............................................................................ 103 6.EE.5 6.EE.6 6.EE.7 6.EE.8 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Review Equations and Inequalities.................................. 104 Writing Equations................................................ 108 Solving Equations................................................. 112 Representing Inequalities..................................... 116 Equations and Inequalities...................................120 Unit 7 Relationships Between Two Variables........................................................123 6.EE.9 6.EE.9 Lesson 1 Functions............................................................... 124 Lesson 2 Graphing Relationships........................................128 Review Relationships Between Two Variables.................132 Unit 8 Geometry..............................................................................................................135 6.G.1 6.G.2 6.G.4 6.G.3, 6.NS.8 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Review Area.......................................................................136 Volume................................................................. 140 Nets and Surface Area......................................... 144 Coordinate Geometry...........................................148 Geometry............................................................... 152 Unit 9 Data and Statistics.............................................................................................155 6.SP.1 6.SP.2, 6.SP.3 6.SP.5.a–d 6.SP.5.a–d 6.SP.4 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Review Collecting Data.....................................................156 Data Distributions.................................................160 Measures of Central Tendency............................ 164 Measures of Spread..............................................168 Representing Data................................................ 172 Data and Statistics................................................ 176 Practice Test............................................................................................................... 179 Glossary...................................................................................................................... 191 FLM CCSS Gr6_FM.indd 4 10/4/10 3:19:30 PM Lesson 2 The product of a number and its reciprocal is always 1. To multiply fractions, multiply the numerators. Then multiply the denominators. 8 2 4 234 3 3 5 5 5 15 335 To change a mixed number to a fraction greater than 1, multiply the whole number part by the denominator. Then add the numerator. This becomes the new numerator of the fraction. The denominator stays the same. To change a fraction greater than 1 to a mixed number, divide the numerator by the denominator. Write the remainder as a fraction. 36 Dividing Fractions 6.NS.1 To divide fractions, multiply by the reciprocal of the second fraction. The numerator and denominator of a reciprocal switch places. What is the reciprocal of each number? 5 1 6 2 8 Switch the numerator and the denominator. 5 6 1 8 The reciprocal of is . 5 6 The reciprocal of is 5 8. 1 8 2 2 1 As a fraction, 2 5 1 . The reciprocal of 1 is . 2 3 3 What is the quotient of 4 8 ? 4 3 First rewrite as multiplication using the reciprocal of . 8 3 8 The reciprocal of is , so the equivalent multiplication 8 3 3 8 expression is 4 3 3 . Multiply and reduce to lowest terms if necessary. 3 8 24 3 3 5 12 5 2 4 3 3 The quotient of 4 4 8 5 2. UNIT 2 Operations © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. FLM CCSS Gr6_U2.indd 36 10/5/10 10:56:11 AM Read each problem. Circle the letter of the best answer. 2 SAMPLE Travis has a 6-foot long rope. He ties a knot in the rope every 3 foot. How many knots are tied in the rope? A 4 B 8 C 9 D 12 The correct answer is C. To find the number of knots, divide 6 6 2 by . First write 6 as the fraction . Use it to write the division 1 3 6 6 2 2 problem: 1 4 3 . Multiply by the reciprocal of and reduce: 3 1 3 3 18 2 5 2 5 9 knots. Choice A is not correct because the numbers are multiplied, not divided. Choices B and D are not correct because a mathematical error was made. 5 1What is the reciprocal of ? 4 1 C 5 4 D 5 A 4 B 4 3 5 4 What is the quotient of 10 4 12 ? 4 A 8 5 B 11 2Which number sentence shows the product of a number and its reciprocal? 2 A 3 0 5 0 7 2 7 B 3 2 5 1 7 2 4 8 markers are placed equal distances apart to help guide hikers. How far is one marker from the next? 5 A mi 10 1 C 32 mi B mi 5 2 D 5 mi 32 D 25 18 1 C 2 acres 2 D 2 acres 3 A acre 3 B acre 9 D 7 3 7 5 49 4 3A hiking trail is 5 -mile long. A total of 4 evenly into 3 pieces. What is the size of each piece of land? 2 2 C 6 2 5A piece of land is 3 acre. It is divided C 3 1 5 7 7 2 5 1 1 6A bottle contains 8 cups of juice. The juice 3 is poured into glasses that hold 4 cup each. How many glasses can be filled with the juice? 2 A 6 C 10 3 B 8 4 3 D 12 UNIT 2 Operations 37 © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. FLM CCSS Gr6_U2.indd 37 10/5/10 10:56:12 AM Read each problem. Write your answer. 3 1 SAMPLE Carmen walked 2 miles in hour. What was her average walking 4 2 speed, in miles per hour? Answer ____________________________________ 3 1 by . Change the To find the average walking speed, divide 2 4 2 1 23211 5 mixed number to a fraction: 2 5 5 2 . Now divide: 2 2 5 3 5 4 20 10 10 1 2 4 4 5 2 3 3 5 6 5 3 . The fraction 3 5 10 4 3 5 3 . The 3 1 average walking speed was 3 miles per hour. 3 2 7It rained a total of 3 inch in 4 hours. What was the average amount of rainfall each hour? Show your work. Answer ________________________ 8A recipe makes a total of 5 cups of pudding. A serving of pudding 3 is cup. How many servings of pudding does the recipe make? 4 Show your work. Answer ________________________ 1 9Horses are measured in units called hands. One hand equals 3 foot. 1 A horse is 5 feet tall. How tall is this horse in hands? Show your work. 3 38 Answer ________________________ UNIT 2 Operations © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. FLM CCSS Gr6_U2.indd 38 10/5/10 10:56:13 AM Read the problem. Write your answer to each part. 10Jada surveyed some students to see which tool they most favored for communicating with friends. The results of her survey are shown in this circle graph. FAVORITE COMMUNICATION TOOL Text Messages 5 12 1 5 Phone 1 20 Letters 1 3 E-mail Part AWhat is the reciprocal of each fraction in the circle graph? Answer ____________________________________ Part BA total of 50 students said they favored text messages to communicate with friends. How many total students did Jada survey? Show your work or explain how you know. What division expression can be used to answer this question? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ UNIT 2 Operations 39 © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. FLM CCSS Gr6_U2.indd 39 10/5/10 10:56:14 AM