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CONTENTSStandardsLetter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivDomain 1: OPERATIONS AND ALGEBRAIC THINKING . . . 5Writing Numerical Expressions . . . . . . . . . . . . . . . . . . 6Lesson 15.OA.2Lesson 2Evaluating Numerical Expressions . . . . . . . . . . . . . . 135.OA.1Lesson 3Relating Numerical Expressions . . . . . . . . . . . . . . . . 215.OA.3Domain 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30DOMAIN 2: NUMBER AND OPERATIONS IN BASE TEN . . . . 37Comparing the Values of the Digits of a Number . . . 38Lesson 45.NBT.1Lesson 5Multiplying and Dividing by Powers of 10 . . . . . . . . 455.NBT.2Lesson 6Reading and Writing Decimals . . . . . . . . . . . . . . . . . 525.NBT.3.aLesson 7Comparing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . 595.NBT.3.bLesson 8Rounding Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.NBT.4Lesson 9Multiplying Whole Numbers . . . . . . . . . . . . . . . . . . . 745.NBT.5Lesson 10Dividing Whole Numbers . . . . . . . . . . . . . . . . . . . . . . 835.NBT.6Lesson 11Adding and Subtracting Decimals . . . . . . . . . . . . . . 935.NBT.7Lesson 12Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . 1035.NBT.7Lesson 13Dividing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.NBT.7Domain 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128DOMAIN 3: NUMBER AND OPERATIONS – FRACTIONS . . . . 129Lesson 14 Adding and Subtracting Fractions andMixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Lesson 155.NF.1Solving Problems with Addition andSubtraction of Fractions . . . . . . . . . . . . . . . . . . . . . . 1405.NF.2Lesson 16Interpreting Fractions as Division . . . . . . . . . . . . . . 1485.NF.3Lesson 17Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . 1555.NF.4.aLesson 18Area of Rectangles . . . . . . . . . . . . . . . . . . . . . . . . . . 1635.NF.4.bLesson 19Comparing Products to Factors . . . . . . . . . . . . . . . . 1735.NF.5.a, 5.NF.5.bDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCPerformance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35ii312NASE Mth G5 D1 PDF.indd 220/02/14 5:14 PM
StandardsLesson 20Solving Problems with Multiplying Fractionsand Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 1805.NF.6Lesson 21Dividing Unit Fractions with Whole Numbers . . . . 1885.NF.7.a, 5.NF.7.bLesson 22Solving Problems with Division of Unit Fractionsand Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . 1975.NF.7.cDomain 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210DOMAIN 4: MEASUREMENT AND DATA . . . . . . . . . . . . . . . 211Lesson 23 Converting Measurement Units . . . . . . . . . . . . . . . . 2125.MD.1Lesson 24Line Plots with Fractions . . . . . . . . . . . . . . . . . . . . . . 2205.MD.2Lesson 25Understanding Volume . . . . . . . . . . . . . . . . . . . . . . 2295.MD.3.a, 5.MD.3.b, 5.MD.4Lesson 26Volume of Rectangular Prisms . . . . . . . . . . . . . . . . . 2375.MD.5.a, 5.MD.5.bLesson 27Adding Volumes of Rectangular Prisms . . . . . . . . . 2455.MD.5.cDomain 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCDuplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCPerformance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258DOMAIN 5: GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Lesson 28 Graphing on Coordinate Planes . . . . . . . . . . . . . . . 2605.G.1Lesson 29Solving Problems with Coordinate Planes . . . . . . . 2685.G.2Lesson 30Classifying Two-Dimensional Figures . . . . . . . . . . . 2765.G.3, 5.G.4Domain 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291Math Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297iii312NASE Mth G5 D1 PDF.indd 320/02/14 5:14 PM
LESSON3Relating Numerical ExpressionsStudent Edition pages 21–29LESSON OVERVIEWStandardObjectives5.OA.3Students will: Generate numerical patterns given a rule and identify relationshipsbetween patternsKey Terms Make connections between different representations of patternscoordinate planecorrespondingtermsordered pairDiscussion QuestionsMaterials Represent the relationship between two patterns using orderedpairs and graph them on a coordinate planeMP1MP7MP8rulesequenceterm Explain the relationship between a list of ordered pairs and agraph created by the ordered pairs. Math Tool: Grids, p. C3 How do you know when a sequence of numbers does nothave a pattern or rule? Math Tool: Coordinate Grids, p. C19Student Edition p. 299Student Edition p. 331 Explain one method you use to determine if a sequence isa pattern.DifferentiationLesson Support With each problem, provide a visualof the pattern. Have students use a four-quadrantgraphic organizer to view the different representationsof the patterns. Quad 1—the pattern; Quad 2—rule;Quad 3—ordered pairs; Quad 4—the graph.Lesson Extension Have students find the 10th and20th terms of a pattern and explain how they foundthe terms. Ask: How did the rule help you in finding the10th and 20th terms?1 GETTING THE IDEALesson OpenerOn the board provide three representations oftwo related simple patterns—the patterns, theordered pairs, and a graph. Ask: How are the threerepresentations related?The three representations will provide visuals of thenew vocabulary. Use this as an opportunity to discussthe vocabulary presented in this lesson. Student6Domain 1: Operations and Algebraic Thinkinganswers will give you an opportunity to assess theirunderstanding and identify any misconceptions. ELL Support The word order is a homonym.Different meanings for order include:A set of instructions:Your orders are to clean your room.An arrangement:The numbers were put in order from least to greatest.Duplicating this page is prohibited by law. 2015 Triumph Learning, LLC
u Example 1This example requires students to relate thecorresponding terms of two patterns. Assist studentsin identifying the relationship. Ask: What can you doto 4 to get 12? Explore all options—multiply by 3 oradd 8. Ask: Do either of those options apply to thenext pair of corresponding terms? Have students tryout both options. Have them test their rule on theother pairs. Journal Prompt MP3 MP4 A rule is a statementthat tells you what is and is not allowed. In this lesson youare finding rules between patterns. Where else do youencounter rules?u Example 3Domain 1The cognates for order in Spanish are ordenar (verb) andel orden (noun).This example shows how corresponding terms intwo related patterns can be plotted on a coordinateplane. If necessary, review how to plot the orderedpairs on a grid. Ask: What point is a good startingplace when graphing ordered pairs? Why?Ask: When graphing, which direction should youmove first—left to right, or bottom to top? Does itmatter? Common Errors Errors occur when students switchthe order of corresponding terms in creating and plottingordered pairs. Emphasize the importance of organizingthe information presented in tables. Explore this error byhaving students compare points such as (3, 15) and(15, 3).u Example 2This example is similar to Example 1, except thatstudents must first generate the patterns. Thisexample includes patterns with the same numbers.Have students create a table to distinguish betweenthe two.2 Coached exampleHave students use a four quadrant graphic organizerto display the different requirements of the problem.Quad 1—the given table; Quad 2—the rule; Quad3—ordered pairs; Quad 4—the graph. Whenfinished, discuss the connection among the fourrepresentations of the problem. Journal Prompt How much tomato sauce would youneed if you had 32 basil leaves? Explain how you foundyour answer.For answers, see page A3.3 LESSON PRACTICEAs students are working, pay special attention toproblem 7, which requires students to form orderedpairs and graph them on the coordinate plane. Askstudents to explain how they know they are correct.For answers, see page A4.Duplicating this page is prohibited by law. 2015 Triumph Learning, LLC312NATE Mth G5 2R.indd 7Lesson 3: Relating Numerical Expressions730/01/14 7:17 PM
Lesson35.OA.3Relating Numerical Expressions1 Getting the ideaA pattern is a sequence of numbers in an ordered list. Each number in the pattern is calleda term. The first 5 terms of a pattern are shown below.8, 16, 24, 32, 40, You can generate numerical patterns using given rules, identify relationships of thecorresponding terms between two patterns, and graph the patterns on a coordinate plane.Example 1Write a rule for each pattern. Then identify the relationship between the two patterns.4, 8, 12, 16, 20, 12, 24, 36, 48, 60, StrategyStep 1Compare terms to identify rules and relationships in the patterns.Identify a rule in each pattern.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCDetermine what you can do to the first term to get the second term.Check that the rule applies to every term in the pattern.44,48,412,416,20, You can add 4 to a term to get the next term. The rule is add 4.1212,1224,1236,1248,60, You can add 12 to a term to get the next term. The rule is add 12.Lesson 3: Relating Numerical Expressions 21312NASE Mth G5 D1 2R.indd 2113/01/14 11:53 AM
Step 2Identify corresponding terms in each pattern.You can list the sets of corresponding terms.Step 34812162012243648604, 128, 2412, 3616, 4820, 60Compare corresponding terms.Compare the terms in the second pattern to the corresponding termsin the first pattern.12 and 4: 12 is 3 times 4 or 8 more than 4.24 and 8: 24 is 3 times 8, but not 8 more than 8.Step 4Check the remaining terms and identify a relationship.Terms in the second pattern are 3 times the corresponding terms inthe first pattern.SolutionThe rule is add 4 for the first pattern and add 12 for the second pattern.The terms in the second pattern are 3 times the corresponding terms inthe first pattern.Example 2Use the given rules and the starting numbers to generate the first 5 terms in two differentnumerical patterns. Then identify the relationship between corresponding terms in the patterns.Second pattern: Add 8, starting with 8.StrategyStep 1Use counting by multiples to generate the patterns. Then comparethe corresponding terms.Generate the numerical patterns.Count by multiples of 2 for the first pattern: 2, 4, 6, 8, 10Count by multiples of 8 for the second pattern: 8, 16, 24, 32, 40Step 2List the corresponding terms in the two patterns.2, 8224, 16 6, 248, 3210, 40Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCFirst pattern: Add 2, starting with 2.Domain 1: Operations and Algebraic Thinking312NASE Mth G5 D1 2R.indd 2213/01/14 11:53 AM
Step 3Identify the relationship between corresponding terms.In the first two corresponding terms, 8 is 4 3 2 and 16 is 4 3 4.Check each of the corresponding terms to make sure the relationshipapplies to all of the terms.The terms in the second pattern are 4 times the corresponding termsin the first pattern.SolutionThe two numerical patterns are 2, 4, 6, 8, 10 and 8, 16, 24, 32, 40. The termsin the second pattern are 4 times the corresponding terms in the first pattern.An ordered pair is used to locate a point on the coordinate plane. The ordered pair (2, 5)is located 2 units to the right of the origin and 5 units up. You can make ordered pairs fromcorresponding terms of two patterns to graph the patterns.Example 3The table shows the cost of buying screen-print T-shirts in packs of three.Number of T-shirts3691215Cost ( )1530456075Identify the relationship between the cost of the T-shirts and the number of T-shirts. Formordered pairs for the relationship and then graph the relationship on a coordinate plane.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCStrategyStep 1Use the numbers in the table to identify the relationship, write ordered pairs,and graph the ordered pairs.Identify the relationship between the cost of T-shirts and the number of T-shirts.Identify a relationship between the corresponding terms for the first twoterms in the pattern.15 is 5 times 3 T-shirts.30 is 5 times 6 T-shirts.The cost of T-shirts in dollars is5 times the number of T-shirts.Check that the remaining terms have the same relationship.Lesson 3: Relating Numerical Expressions 23312NASE Mth G5 D1 2R.indd 2313/01/14 11:53 AM
Step 2Form ordered pairs.Write ordered pairs for the corresponding terms in the table:(number of T-shirts, cost).The ordered pairs are (3, 15), (6, 30), (9, 45), (12, 60), (15, 75).Step 3Graph the ordered pairs on the coordinate plane.Plot a point for each of the ordered pairs.Draw a line through the points.Cost ofT-Shirtsy9080Cost ( )706050403020100369121518xNumber of T-ShirtsThe relationship between the corresponding terms in the patterns is thatthe cost in dollars is 5 times the number of T-shirts. The ordered pairs are(3, 15), (6, 30), (9, 45), (12, 60), (15, 75). The graph is shown in Step 3.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLCSolution24Domain 1: Operations and Algebraic Thinking312NASE Mth G5 D1 2R.indd 2413/01/14 11:54 AM
2 COACHED EXAMPLEThe table shows the number of basil leaves and amount of tomato sauce used in apasta recipe.Number of Basil Leaves48121620Tomato Sauce (in fl oz)816243240Identify the relationship between the amount of tomato sauce and the number of basilleaves in the recipe. Form ordered pairs for the relationship, and graph the orderedpairs on the coordinate plane.Identify a relationship between the corresponding terms for the first two terms in the pattern.8 fl oz of tomato sauce istimes 4 basil leaves.times 8 basil leaves.16 fl oz of tomato sauce isThe terms in the pattern for tomato sauce arepattern for basil leaves.times the corresponding terms in thetimes the number of basil leaves.The amount of tomato sauce in fluid ounces isForm ordered pairs. (basil leaves, tomato sauce)The ordered pairs are (,), (,), (,), (,), (,).Graph the ordered pairs on a coordinate plane.yPasta RecipeTomato Sauce (in fl oz)Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLC4036322824201612840246810 12 14 16 18 20xNumber of Basil LeavesLesson 3: Relating Numerical Expressions 25
3 LESSON PRACTICE1Use each rule and starting number to generate two numerical patterns.,Pattern A: Add 3, starting with 0.Pattern B: Add 18, starting with 0.,,,,,,,Identify the relationship between the two patterns.2Rami generated two numerical patterns.5, 10, 15, 20, 25, 10, 20, 30, 40, 50, .The rule for the first pattern isThe rule for the second pattern is.Identify the relationship between the two patterns.Mandy made turquoise paint by mixing drops of green tint and blue tint in jars ofwhite paint. The table shows how many drops Mandy used.Drops of Green Tint246810Drops of Blue Tint48121620Circle the rule for each statement.add 1add 2The rule for green tint is add 2 . The rule for blue tint is add 4 .add 4Identify the relationship between the two colors of tint.26add 8Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLC3Domain 1: Operations and Algebraic Thinking312NASE Mth G5 D1 2R.indd 2613/01/14 11:54 AM
4Omar generated two numerical patterns.10, 20, 30, 40, 50, 50, 100, 150, 200, 250, Which describes the patterns? Circle all that apply.A. The terms in the second pattern are 5 times the correspondingterms in the first pattern.B. The terms in the first pattern are one-half the correspondingterms in the second pattern.C. The rule for the first numerical pattern is add 40.D. The rule for the first numerical pattern is add 10.E. The rule for the second numerical pattern is add 50.F.5The rule for the second numerical pattern is add 100.Identify the relationship between the two numerical patterns.3, 6, 9, 12, 15, Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLC12, 24, 36, 48, 60, 6Select True or False for each statement about the two numerical patterns.20, 40, 60, 80, 100, 5, 10, 15, 20, 25, A. Add 15 is the rule for the first pattern. True FalseB. Add 20 is the rule for the first pattern. True FalseC. Add 5 is the rule for the second pattern. True FalseD. The terms in the first pattern are 4 times thecorresponding terms in the second pattern. True FalseLesson 3: Relating Numerical Expressions 27312NASE Mth G5 D1 2R.indd 2713/01/14 11:54 AM
7A company sells bags of marbles in sets. Each set contains 2 bags and 40 marbles.Generate two numerical patterns using the rules for the number of bags and thenumber of marbles in a set. The starting number for each is given.Number of bags: 2,Number of marbles: 40,,,,,,Write ordered pairs for the two numerical patterns. Graph the ordered pairs on acoordinate plane.yMarble SetsNumber of Marbles220200180160140120100806040200132456789 10 11 12xNumber of BagsUse the numbers in the box to complete the statements about the two number patterns.Numbers may be used once, more than once, or not at all.25, 50, 75, 100, 150, 50, 100, 150, 200, 250, Which describes the patterns? Circle all that apply.The rule for the first pattern is add.5The terms in the second pattern aretimes the corresponding terms in the first pattern.25The rule for the second pattern is add282.50Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLC8Domain 1: Operations and Algebraic Thinking312NASE Mth G5 D1 2R.indd 2813/01/14 11:54 AM
9Ed generated two numerical patterns. The rules are add 4, starting with 0 forthe first pattern, and add 8, starting with 0 for the second pattern.0, 4, 8, 12, 16, 0, 8, 12, 20, 28, Did Ed generate correct patterns? Use words or numbers to justify your answer.Duplicating any part of this book is prohibited by law. 2015 Triumph Learning, LLC10Look at the two numerical patterns. Select Yes or No for each statement.15, 30, 45, 60, 75, 60, 120, 180, 240, 300, A. The terms in the second pattern are 2 timesthe corresponding terms in the first pattern. Yes NoB. The terms in the second pattern are 4 timesthe corresponding terms in the first pattern. Yes NoC. The rule for the first pattern is add 15. Yes NoD. The rule for the second pattern is add 30. Yes NoLesson 3: Relating Numerical Expressions 29312NASE Mth G5 D1 2R.indd 2913/01/14 11:54 AM
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