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EACH CHAPT ER INCLUDES: • Prescriptive targeted strategic intervention charts. • Student activity pages aligned to the Common Core State Standards. • Complete lesson plan pages with lesson objectives, getting started activities, teaching suggestions, and questions to check student understanding. Grade 5 Targeted Strategic Intervention Grade 5, Chapter 8 Based on student performance on Am I Ready?, Check My Progress, and Review, use these charts to select the strategic intervention lessons found in this packet to provide remediation. Am I Ready? If Students miss Exercises… Then use this Strategic Intervention Activity… Concept 1-6 8-A: Identify Missing Factors Factors 7-11 8-B: Multiplication Facts Through 8 8-C: Division Facts Through 9 12-13 8-D: Points on a Number Line Where is this concept in My Math? Prep for 5.NF.2 Grade 4, Chapter 3, Lesson 7 Multiplication and division 5.NBT.5 Chapter 2, Lesson 9; Chapter 3, Lesson 3 Graph decimals on a number line 5.NBT.3 Chapter 1, Lesson 7 Check My Progress 1 Where is this concept in My Math? If Students miss Exercises… Then use this Strategic Intervention Activity… Concept 4-5 8-E: Identify the Shaded Part Interpret fractions as division 5.NF.3 Chapter 8, Lesson 1 6-7 8-F: Multiples, Factors, and Greatest Common Factor Find the GCF Prep for 5.NF.2 Chapter 8, Lesson 2 8-10 8-G: Simplifying Fractions Write fractions in simplest form 5.NF.5b Chapter 8, Lesson 3 Review Where is this concept in My Math? If Students miss Exercises… Then use this Strategic Intervention Activity… Concept 9-10 8-H: Factors, Common Factors, and Greatest Common Factor GCF Prep for 5.NF.2 Chapter 8, Lesson 2 11-12 8-I: Use a Multiplication Table to Divide Simplest form of fractions 5.NF.5b Chapter 8, Lesson 3 13-14 8-J: Multiples of a Number LCM Prep for 5.NF.2 Chapter 8, Lesson 5 15-17 8-K: Shade and Compare Fractions Compare fractions 5.NF.5b Chapter 8, Lesson 6 18-23 8-L: Identify Fractions and Decimals Write fractions as decimals 5.NF.5b Chapter 8, Lesson 8 Name Identify Missing Factors Lesson 8-A Use basic multiplication facts. What Can I Do? I want to find a missing factor. Write the missing factor. 2× ? = 10 Think: 2 times what number is equal to 10? Find the multiplication fact for 2 with a product of 10. 2×1=2 2×2=4 2×3=6 2×4=8 2 × 5 = 10 So, 5 is the missing factor. Write each product. Then write each missing factor. 1. 3 × 4 = = 12 4× = 20 Write each missing factor. 3. 2 × = 14 4. 5 × = 15 5. 4 × = 16 6. 3 × = 24 7. 6 × = 24 8. 4 × = 36 9. 7 × = 63 10. 5 × = 20 Copyright © The McGraw-Hill Companies, Inc. 3× 2. 4 × 5 = Name Identify Missing Factors Lesson 8-A Lesson Goal • Use basic multiplication facts to find a missing factor. What the Student Needs to Know Use basic multiplication facts. What Can I Do? I want to find a missing factor. 2× ? = 10 Think: 2 times what number is equal to 10? Find the multiplication fact for 2 with a product of 10. • Recall basic multiplication facts from 1 to 9. 2×1=2 2×2=4 2×3=6 2×4=8 2 × 5 = 10 Getting Started Remind students that they usually multiply two factors to get a product. Here they will have the product and one of the factors and have to find the other factor. Say: • Let’s see how we can find a missing factor. When I see 2 × __ = 6, and I immediately recognize a missing factor, that’s all there is to the problem. If I don’t recognize it immediately, there is a simple method to use. • I can set up a list of facts for 2. I write out 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6. Since 2 × 3 = 6, 3 is the missing factor. Write the missing factor. So, 5 is the missing factor. Write each product. Then write each missing factor. 2. 4 × 5 = 20 1. 3 × 4 = 12 3× 4 = 12 4× 5 = 20 Write each missing factor. 3. 2 × 7 = 14 4. 5 × 3 = 15 5. 4 × 4 = 16 6. 3 × 8 = 24 7. 6 × 4 = 24 8. 4 × 9 = 36 9. 7 × 9 = 63 10. 5 × 4 = 20 Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-A What Can I Do? Read the question and the response. Then discuss the example. Ask: • What do we do if we don’t recognize the missing factor in 2 × __ = 10? (Make a list of facts for 2.) • How far do you have to go to find the factor? (2 × 5) Try It • Have students read each of the exercises and use a list of facts, if necessary, to find each of the missing factors. Power Practice • Have students complete the practice items. Then review each answer. 244_S_G5_C08_SI_119817.indd 244 7/12/12 5:35 PM WHAT IF THE STUDENT NEEDS HELP TO Recall Basic Multiplication Facts from 1 to 9 Complete the Power Practice • Have the student use physical counters to make groups of objects. • Have the student write out lists of multiplication facts and keep them in his or her math journal/ notebook to use as a reference. • Discuss each incorrect answer. Review how the student can check his or her answers by using counters or a list of multiplication facts. Name Multiplication Facts Through 8 Lesson 8-B Use equal groups. Use doubling. Find 6 × 5. Find 8 × 8. Draw 6 groups of 5 circles. You can double a 4s fact to find an 8s fact. What Can I Do? I want to practice multiplication facts through 8. 4 × 8 = 32 Double the product. 32 + 32 = 64 So, 8 × 8 = 64. There are 30 circles in all. So, 6 × 5 = 30. Use equal groups or doubling to multiply. 1. 8 × 5 = Multiply. 3. 8 × 2 = 4. 7 × 5 = 5. 6 × 8 = 6. 7 × 3 = 7. 7 × 7 = 8. 6 × 9 = Copyright © The McGraw-Hill Companies, Inc. 2. 7 × 6 = Name Multiplication Facts Through 8 Lesson 8-B Lesson Goal • Use equal groups or doubling to practice multiplication facts through 8. Use doubling. Use equal groups. Find 6 × 5. Find 8 × 8. Draw 6 groups of 5 circles. You can double a 4s fact to find an 8s fact. What the Student Needs to Know What Can I Do? I want to practice multiplication facts through 8. 4 × 8 = 32 Double the product. • Recall basic addition and multiplication facts. Getting Started • Ask students to draw and count a group of 3 objects. Then ask: • How can you find out how many are in 6 groups of 3 objects? (Draw 5 more groups of 3 objects, then count the total number.) 32 + 32 = 64 So, 8 × 8 = 64. There are 30 circles in all. So, 6 × 5 = 30. Use equal groups or doubling to multiply. 2. 7 × 6 = 42 1. 8 × 5 = 40 What Can I Do? Read the question and the response. Then discuss the first example. Ask: • In the first example, what would you draw to show equal groups? (6 groups of 5 circles) • How many circles are there in all? (30) • What multiplication sentence shows this? (6 × 5 = 30) Read and discuss the second example. Ask: • What method are you going to use to solve this? (doubling a 4s multiplication fact) • What multiplication sentence will you use first? (4 × 8 = 32) • How do you double the product? (by adding 32 + 32) Try It • Have students read Exercise 1: 8 × 5 = ____. Ask whether to use equal groups or doubling a 4s fact to multiply. (doubling) • Now, have students read and go through the steps on the second exercise. Power Practice • Have students complete the practice items. Then review each answer and method. Multiply. 3. 8 × 2 = 16 4. 7 × 5 = 35 5. 6 × 8 = 48 6. 7 × 3 = 21 7. 7 × 7 = 49 8. 6 × 9 = 54 Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-B 246_S_G5_C08_SI_119817.indd 246 7/12/12 5:38 PM WHAT IF THE STUDENT NEEDS HELP TO Recall Basic Addition and Multiplication Facts Complete the Power Practice • Practice addition and multiplication facts 10 to 15 minutes daily until the student can recall the sums for the addition facts and the products for the multiplication facts with ease. • Discuss each incorrect answer. • Have the student model any fact he or she missed. Name Division Facts Through 9 Lesson 8-C Use any division strategy to find 24 ÷ 6. What Can I Do? Use a related multiplication fact. Think: How many 6s make 24? I want to divide one number by another number. 4 × 6 = 24, so 24 ÷ 6 = 4 Use an array. Use repeated subtraction. Subtract 6 four times. 24 - 6 = 18 18 - 6 = 12 12 - 6 = 6 6-6=0 So, 24 ÷ 6 = 4. Make 6 equal groups of 4. So, 24 ÷ 6 = 4. Skip count backward on a number line. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 So, 24 ÷ 6 = 4. Use a related multiplication fact to find the quotient. 1. × 7 = 28, so 28 ÷ 7 = 2. × 6 = 30, so 30 ÷ 6 = Copyright © The McGraw-Hill Companies, Inc. Skip count backward by 6 four times. Name Lesson Use an array to find each quotient. 3. 27 ÷ 3 = 8-C 4. 15 ÷ 3 = Use repeated subtraction to find each quotient. 5. 9 ÷ 3 = 6. 30 ÷ 5 = Subtract: Subtract: Skip count backward to find each quotient. 8. 42 ÷ 6 = 7. 45 ÷ 5 = Count backward: Count backward: Copyright © The McGraw-Hill Companies, Inc. Find each quotient. Use any strategy. 9. 8 ÷ 4 = 10. 20 ÷ 4 = 11. 48 ÷ 8 = 12. 35 ÷ 5 = 13. 36 ÷ 6 = 14. 40 ÷ 5 = 15. 28 ÷ 4 = 16. 12 ÷ 6 = 17. 49 ÷ 7 = 18. 8 64 19. 9 81 20. 7 21 21. 4 16 22. 4 24 23. 7 42 24. 8 32 25. 4 36 USING LESSON 8-C Name Division Facts Through 9 Lesson Goal • Use any division strategy to divide using basic facts through 9. What the Student Needs to Know Lesson 8-C Use any division strategy to find 24 ÷ 6. What Can I Do? Use a related multiplication fact. Think: How many 6s make 24? I want to divide one number by another number. 4 × 6 = 24, so 24 ÷ 6 = 4 • Use related multiplication facts. • Use repeated subtraction. • Skip count backward. Use an array. Use repeated subtraction. Subtract 6 four times. 24 - 6 = 18 18 - 6 = 12 12 - 6 = 6 6-6=0 So, 24 ÷ 6 = 4. Getting Started What Can I Do? Read the question and the response. Then discuss each example. Ask: • Can you use a related multiplication fact to find the answer to 24 ÷ 6? (Yes.) • Which fact do you know that will help you solve this division? (6 × 4 = 24 and 4 × 6 = 24) Make 6 equal groups of 4. So, 24 ÷ 6 = 4. Skip count backward on a number line. Skip count backward by 6 four times. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 So, 24 ÷ 6 = 4. Use a related multiplication fact to find the quotient. 1. 4 × 7 = 28, so 28 ÷ 7 = 4 2. 5 × 6 = 30, so 30 ÷ 6 = 5 Copyright © The McGraw-Hill Companies, Inc. Find out what students know about division strategies. Write the division fact 36 ÷ 9 on the board. Say: • Of the four strategies, using a related multiplication fact, an array, repeated subtraction, or skip counting backward on a number line, which ones would be easiest to use for this example? (related multiplication fact and repeated subtraction) • What related multiplication fact can you name to solve this division fact? (9 × 4 = 36 or 4 × 9 = 36) How can you use the related multiplication fact to solve the division fact 36 ÷ 9? (If 4 × 9 = 36, then 36 ÷ 9 must be 4.) So, 36 ÷ 4 = ? . (9) • How can you use repeated subtraction to solve 36 ÷ 9? (Start at 36 and subtract 9 to get 27. Then subtract 9 again to get 18. Subtract 9 from 18 to get 9, and then subtract 9 from 9 to get 0. Nine was subtracted 4 times to reach zero.) So, what is the quotient of 36 ÷ 9? (4) 248_249_S_G5_C08_SI_119817.indd 248 7/12/12 5:50 PM WHAT IF THE STUDENT NEEDS HELP TO Use Related Multiplication Facts • Have the student use a multiplication table to create related multiplication and division facts on index cards. Have the student choose facts that are troublesome for him or her and write a related pair of facts on each card. • Have the student practice these facts daily until he or she can recall them with ease. Use Repeated Subtraction • Have the student use counters to perform repeated addition such as 3 + 3 + 3 + 3 + 3 = 15 • Then have the student “undo” the repeated addition with repeated subtraction. For the example above, subtract 15 - 3 = 12; 12 - 3 = 9; 9 - 3 = 6; 6 - 3 = 3; and 3 - 3 = 0. Name Lesson Use an array to find each quotient. 9 3. 27 ÷ 3 = 8-C 5 4. 15 ÷ 3 = Use repeated subtraction to find each quotient. 3 5. 9 ÷ 3 = 6. 30 ÷ 5 = Subtract: 9 - 3 = 6, 6 - 3 = 3, 6 Subtract: 30 - 5 = 25, 25 - 5 = 20, 3-3=0 20 - 5 = 15, 15 - 5 = 10, 10 - 5 = 5, 5 - 5 = 0 Skip count backward to find each quotient. 8. 42 ÷ 6 = 9 7. 45 ÷ 5 = Try It 7 Count backward: Count backward: 45, 40, 35, 30, 25, 20, 15, 10, 5, 0 42, 36, 30, 24, 18, 12, 6, 0 Copyright © The McGraw-Hill Companies, Inc. Find each quotient. Use any strategy. 9. 8 ÷ 4 = 2 10. 20 ÷ 4 = 5 11. 48 ÷ 8 = 6 12. 35 ÷ 5 = 7 13. 36 ÷ 6 = 6 14. 40 ÷ 5 = 8 15. 28 ÷ 4 = 7 16. 12 ÷ 6 = 2 17. 49 ÷ 7 = 7 18. 8 64 8 19. 9 81 9 20. 7 21 3 21. 4 16 4 24 22. 4 6 23. 7 42 6 24. 8 32 4 25. 4 36 9 248_249_S_G5_C08_SI_119817.indd 249 7/12/12 5:50 PM WHAT IF THE STUDENT NEEDS HELP TO Skip Count Backward • Have the student put 3 counters into each of 8 groups. Then have the student skip count to find the total. (3, 6, 9, 12, 15, 18, 21, 24) • Then have the student start with the total and skip count backward by 3. (24, 21, 18, 15, 12, 9, 6, 3, 0) • Repeat with other numbers of counters and groups. • How would you use repeated subtraction to solve? (Start with 24 and subtract 6 four times: 24 - 6 = 18; 18 - 6 = 12; 12 - 6 = 6; 6 - 6 = 0) Use an existing number line from 0 to 24 or draw a new one. Demonstrate skip counting backward 4 groups of 6 by drawing arrows that show the “jumps” between 24 and 18, 18 and 12, 12 and 6, and 6 and 0. Complete the Power Practice • Discuss each incorrect answer. Have the student model any exercise he or she missed using counters or a number line. • Have students complete Exercises 1 and 2 using related multiplication and division facts. Check that students understand that the same three numbers are used in each pair of related facts. Once they know one fact, they can write all four related facts. Ask: • How much is 1 × 7? (7) How much is 2 × 7? (14) How much is 3 × 7? (21) How much is 4 × 7? (28) So, what number times 4 is 28? (7) How can I use the fact 4 × 7 = 28 to find the quotient? (The numbers in the related facts are the same, so 4 × 7 = 28 and 28 ÷ 7 = 4.) • Have the students do Exercises 3 and 4 using the arrays. Check that students understand that they separate the elements of the array into equal groups. • Have the students do Exercises 5 and 6 using repeated subtraction. Check to make sure that students understand which number they begin subtracting with and that they continue subtracting the same number from the difference until they reach 0. • Have students do Exercises 7 and 8 using skip counting backward. Check that students understand where they begin counting, the number they skip count backward, and how to count the number of skips. Power Practice • Have students complete the practice items using a strategy. Then review each answer. Lesson 8-C Name Points on a Number Line Lesson 8-D Make the number line. What Can I Do? Number the line starting at 70. The marks must be the same distance apart. I want to show the location of a point on a number line. 70 71 72 73 74 75 76 77 78 79 80 Mark and label the point. Make a black circle on the point. Write a capital letter to name the point. Point H is at 73. Point M is at 79. M H 70 71 72 73 74 75 76 77 78 79 80 Write the missing numbers to complete each number line. 0 1 2 4 8 5 9 10 2. 30 32 33 35 36 55 56 37 39 3. 51 52 58 60 Make a number line. Show the numbers 20 through 30. 4. Copyright © The McGraw-Hill Companies, Inc. 1. Name Write the number that shows the location of each point. B D 60 61 A 8-D C 62 63 64 65 66 67 68 69 70 5. point A 6. point B 7. point C 8. point D 40 Lesson G E H F 41 42 43 44 45 46 47 48 49 50 9. point E 10. point F 11. point G 12. point H Copyright © The McGraw-Hill Companies, Inc. Mark a point at each location. 13. point S at the number 80 14. point T at the number 84 15. point U at the number 88 16. point V at the number 85 80 81 82 83 84 85 86 87 88 89 90 17. point W at the number 22 18. point X at the number 30 19. point Y at the number 26 20. point Z at the number 23 20 21 22 23 24 25 26 27 28 29 30 Name Points on a Number Line Lesson 8-D Lesson Goal • Identify or mark points on a number line. What the Student Needs to Know Make the number line. What Can I Do? Number the line starting at 70. The marks must be the same distance apart. I want to show the location of a point on a number line. 70 • Recognize equal intervals. • Relate number lines to familiar scales. • Count to 10. 72 73 74 75 76 77 78 79 80 Mark and label the point. Make a black circle on the point. Write a capital letter to name the point. Point H is at 73. Point M is at 79. M H Getting Started • Draw a large blank number line on the board using a ruler to make the marks 3 inches apart. Write a zero under the left-hand mark. Ask: • What is this diagram? What can you use it for? (a number line; possible uses are rounding numbers, skip counting, making a line plot) • Write the number 1 under the second mark. Point out that you have now established the meaning of each section or interval. Each interval stands for 1 unit. If you had written 2, each interval would stand for 2 units. • Have volunteers come up to the board and complete the number line by writing the numbers 2 through 10 under the appropriate marks. • Draw students’ attention to the arrowheads on the left and right sides of the number line. Ask: • What does the arrow on the right side mean? (The counting numbers continue on from 10. The next number is 11.) What does the arrow on the left side mean? (Some students may know that the negative numbers –1, –2, and so on are to the left of zero. If you wish to discuss this, a thermometer is a good model for numbers less than zero.) • Have students draw a number line from 0 to 10 on their paper. Students can use the number line on the board for help. 71 70 71 72 73 74 75 76 77 78 79 80 Write the missing numbers to complete each number line. 1. 0 1 2 3 4 5 6 7 8 36 37 38 39 40 9 10 2. 30 31 32 33 34 35 3. 50 51 52 53 54 55 56 57 58 59 60 Make a number line. Show the numbers 20 through 30. Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-D 4. 20 21 22 23 24 25 26 27 28 29 30 252_253_S_G5_C08_SI_119817.indd 252 7/12/12 5:58 PM WHAT IF THE STUDENT NEEDS HELP TO Recognize Equal Intervals • Draw two number lines on the board, one in which the intervals are equally spaced and one in which the intervals are obviously not equally spaced. Number the marks from 0 onward, counting by 1s. Have the student discuss the two lines, identifying how they are alike and how they are different. • Show the student a ruler and ask what would happen if the marks were not the same distance apart. (Possible response: The ruler would not be very useful because it wouldn’t give the same measure every time.) Relate Number Lines to Familiar Scales • Show the student a thermometer and ask how this measuring tool is like a number line. (The marks are an equal distance apart; the numbers are in order.) • Have the student describe other tools that use a scale similar to a number line. (The student may mention rulers, measuring cups, bathroom scales, odometers on cars, protractors for angles.) List his or her ideas on the board. Emphasize that the marks must always be an equal distance apart. Name Write the number that shows the location of each point. B D A Lesson 8-D What Can I Do? C Read the question and the response. Then read and discuss the example. Ask: • What is meant by a point? How do you show the location of a point on a number line? (A point is a specific location or spot; a black dot and capital letter mark the location of a point.) • Use a number line from 0 to 10. Mark the first letter of your first name at 8; mark the first letter of your last name at 0. (Check that students understand how to mark points on the number line.) 60 61 62 63 64 65 66 67 68 69 70 5. point A 67 6. point B 60 7. point C 70 8. point D 66 40 G E H F 41 42 43 44 45 46 47 48 49 50 9. point E 42 10. point F 49 11. point G 41 12. point H 45 Copyright © The McGraw-Hill Companies, Inc. Mark a point at each location. 13. point S at the number 80 14. point T at the number 84 15. point U at the number 88 16. point V at the number 85 S 80 81 T V 82 83 84 85 86 87 88 89 90 17. point W at the number 22 18. point X at the number 30 19. point Y at the number 26 W 20 21 Try It U Z 20. point Z at the number 23 Y X 22 23 24 25 26 27 28 29 30 252_253_S_G5_C08_SI_119817.indd 253 7/12/12 5:58 PM WHAT IF THE STUDENT NEEDS HELP TO Count to 10 • Count aloud with the student from 0 through 10. Ask the student to suggest ways to show in writing what you have just done. The student might make a list of the numbers separated by commas, or make a number line. Complete the Power Practice • Make sure the student understands what is meant by a point and can relate the concept of point to the black dots on the number lines. Ask questions such as: Look at the number line for Exercises 5–8, how many points are marked with letters? (four) What points are marked? (B, D, A, and C) Where are these points located? (60, 66, 67, and 70) These first exercises give students practice in completing number lines. Ask: • How do you know what numbers to write in the blank spaces on the lines in Exercise 1? (When completed, the numbers must go in order from 0 through 10.) • For Exercise 4, how will you get the marks to be an equal distance apart? (Line them up with the marks on the line in Exercise 3.) Have rulers available for those students who wish to use them. Power Practice • Review the directions with students. • When students have finished the page, the completed number lines can be used for practice in finding the distance between two points on a number line. • Check to see if the student understands the directions by asking: What were you supposed to do in this exercise? Once you have clarified the directions, the student can try again to do the exercises. Lesson 8-D Name Identify the Shaded Part Lesson 8-E Write each fraction that names each shaded part. 3. 2. ____ 8 4. ____ ____ 6 9 5. 6. ____ ____ ____ 4 5 6 7. 9. 8. ____ ____ ____ 3 8 4 Copyright © The McGraw-Hill Companies, Inc. 1. Name Identify the Shaded Part Lesson Goal • Identify part of a whole by writing a fraction. What the Student Needs to Know 8-E Write each fraction that names each shaded part. 1. 3. 2. • Identify fractions. • Model part of a whole. 3 ____ ____ 9 6 5. 4. 4 5 ____ 8 Getting Started • On the board, draw a rectangle divided into 4 equal parts. Shade 3 of the 4 parts. • How many shaded parts are in the rectangle? (3) • How many equal parts are in the rectangle? (4) • What fraction names the shaded part? __34 • Draw a hexagon with 6 different parts. Shade 5 of the 6 parts. • How many shaded parts are in the hexagon? (5) • How many equal parts are in the hexagon? (6) • What fraction names the shaded part? __56 Lesson 2 6. 4 3 ____ ____ ____ 4 5 6 () 7. 9. 8. 3 ____ 3 7 8 ____ Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-E 3 ____ 4 () Teach Read and discuss Exercise 1 at the top of the page. • How many shaded parts are in the rectangle? (3) This number will be our top number, or numerator. • How many equal parts are in the rectangle? (8) This number will be our bottom number, or denominator. • What fraction of the rectangle is shaded? __38 () Practice • Read the directions as students complete Exercises 2 through 9. • Check student work. • If students have difficulty with the activity, have them use fraction tiles or fraction circles to model the exercises. 256_S_G5_C08_SI_119817.indd 256 7/17/12 10:53 AM WHAT IF THE STUDENT NEEDS HELP TO Identify Fractions • Place students in groups. Give each group a set of recipes. Ask students to circle the fractions within the recipes. • Provide fraction tiles and fraction circles. Ask students to model the fractions that they identified in the recipes. • Create a recipe box by having students bring in recipes with fractions. Students can find and model the fractions from the recipes until they can identify fractions with ease. Model Part of a Whole • Place students in pairs. Student 1 should draw a picture of a figure divided into equal parts, and then shade some of the parts. (Ex: The student could draw a square divided into 4 equal parts with 3 parts shaded.) • Student 2 takes the drawing and writes the fraction that names the shaded part. • Together the students should count the number of shaded parts and the total number of equal parts to determine the numerator and denominator of the fraction. • If the students agree the answer is correct, they switch roles and complete the activity again as time allows. Name Multiples, Factors, and Greatest Common Factor Lesson 8-F Activate Prior Knowledge 0 5 10 15 20 25 30 1. List the factors of 30 from least to greatest. 2. List the factors of 25 from least to greatest. 3. What numbers are factors of both 30 and 25? A multiple of a number is the product of that number and any whole number. For example, 10 is a multiple of 5 because 2 × 5 = 10. A factor is a number that divides into a whole number evenly. For example, 5 is a factor of 10 because 10 ÷ 5 = 2. A greatest common factor (GCF) is the largest number that is a factor of two or more numbers. For example, the greatest common factor (GCF) of 30 and 25 is 5. 4. 5 is a of 30. 5. 25 is a of 5. 6. The of 25 and 30 is 5. List the factors of each multiple. 7. 24 8. 36 9. 9 10. 16 Find the common factors of each pair of multiples. 11. 9 and 36 12. 16 and 24 Copyright © The McGraw-Hill Companies, Inc. Complete each sentence with the term “multiple,” “factor,” or “greatest common factor.” Lesson Goal • Identify factors and multiples of numbers. Name Multiples, Factors, and Greatest Common Factor Lesson 8-F Activate Prior Knowledge 0 5 10 15 20 25 30 What the Student Needs to Know 1. List the factors of 30 from least to greatest. 1, 2, 3, 5, 6, 10, 15, 30 2. List the factors of 25 from least to greatest. 1, 5, 25 • Identify factors. 3. What numbers are factors of both 30 and 25? Getting Started A multiple of a number is the product of that number and any whole number. For example, 10 is a multiple of 5 because 2 × 5 = 10. • Draw an array of circles with 3 rows and 4 columns on the board. • How many rows are in the array? (3) How many circles are in each row? (4) How many total circles are in the array? (12) • A factor is a number that can be multiplied by another number and can be divided into a whole number evenly. The numbers 3 and 4 are factors of 12. • A multiple is the product of multiplying two whole numbers. Therefore, 12 is a multiple of 3 and 4. 1, 5 A factor is a number that divides into a whole number evenly. For example, 5 is a factor of 10 because 10 ÷ 5 = 2. A greatest common factor (GCF) is the largest number that is a factor of two or more numbers. For example, the greatest common factor (GCF) of 30 and 25 is 5. Complete each sentence with the term “multiple,” “factor,” or “greatest common factor.” 4. 5 is a factor 5. 25 is a multiple of 30. of 5. 6. The greatest common factor of 25 and 30 is 5. List the factors of each multiple. 7. 24 1, 2, 3, 4, 6, 8, 12, 24 9. 9 1, 3, 9 8. 36 1, 2, 3, 4, 6, 9, 12, 18, 36 10. 16 1, 2, 4, 8, 16 Find the common factors of each pair of multiples. Teach Read and discuss Exercise 1 at the top of the page. • Use the number line to help identify the factors of 30. Remember, factors are two numbers that are multiplied to equal the number 30. • What number can be multiplied by 1 to equal 30? (30) What number can be multiplied by 2 to equal 30? (15) What number can be multiplied by 3 to equal 30? (10) • What number can be multiplied by 4 to equal 30? (4 is not a factor of 30; a number cannot be multiplied by 4 to equal 30) • What number can be multiplied by 5 to equal 30? (6) • Put the factors in order from least to greatest. (1, 2, 3, 5, 6, 10, 15, 30) • Have students check their work by identifying factors on a multiplication table. Practice • Read the directions and complete Exercises 2 through 12. Check student work. 11. 9 and 36 1, 3, 9 12. 16 and 24 Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-F 1, 2, 4, 8 258_S_G5_C08_SI_119817.indd 258 7/12/12 6:20 PM WHAT IF THE STUDENT NEEDS HELP TO Identify Factors • One effective way for the student to learn how to find factors is to use concrete models, manipulatives, and pictorial representations. • For example: In order to find the factors of 20, give the student 20 connecting cubes. • Have the student create arrays with the connecting cubes to form equal rows and columns. • The student will find they can create an array 1 × 20, 2 × 10, and 4 × 5. • Show the student a nonexample by demonstrating how 3 rows will NOT equal an even amount of columns with 20 connecting cubes. • Encourage the student to write down the rows and columns for each array and write the numbers in order from least to greatest. Name Simplifying Fractions Lesson 8-G Use division. What Can I Do? I want to simplify a fraction. Divide both the numerator and denominator of the fraction by the same number. Divide until the numerator and denominator have only 1 as the common factor. 4 36 __ 9 ___ ÷ = ___ 36 and 72 can both be divided by 4. 3 3 9 ___ ÷ __ = __ 9 and 18 can both be divided by 3. 3 1 3 __ __ ÷ = __ 3 and 6 can both be divided by 3. 4 72 3 18 6 18 3 6 2 Since the numerator, 1, and the denominator, 2, have no common factors 1 except 1, the fraction __ is in simplest form. 2 4 4 ÷ __ 1. __ = 8 4 6 3 2. __ ÷ __ = 9 3 15 5 3. ___ ÷ __ = 25 5 3 9 4. ___ ÷ __ = 12 3 3 12 ÷ __ = 5. ___ 15 3 32 4 6. ___ ÷ __ = 36 4 3 9 7. ___ ÷ __ = 21 3 2 6 8. ___ ÷ __ = 10 2 12 24 ÷ ___ 9. ___ = 36 12 Copyright © The McGraw-Hill Companies, Inc. Use division. Simplify each fraction. Name Simplifying Fractions Lesson 8-G Lesson Goal • Simplify a fraction. What the Student Needs to Know Use division. What Can I Do? I want to simplify a fraction. • Divide whole numbers. • Find common factors of two numbers. Divide both the numerator and denominator of the fraction by the same number. Divide until the numerator and denominator have only 1 as the common factor. 4 36 __ 9 ___ ÷ = ___ 36 and 72 can both be divided by 4. 3 3 9 ___ ÷ __ = __ 9 and 18 can both be divided by 3. 3 1 3 __ __ ÷ = __ 3 and 6 can both be divided by 3. 4 72 3 18 Getting Started Ask students how to find the common factor of the numbers 18 and 27. For example, ask: • What are the factors of 18? (1, 2, 3, 6, 9, 18) • What are the factors of 27? (1, 3, 9, 27) • What are the common factors of 18 and 27? (1, 3, 9) What Can I Do? Read the question and the response. Then read and discuss the example. Ask: • What are the factors of 36? (1, 2, 3, 4, 6, 9, 12, 18, 36) • What are the factors of 72? (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) • What are the common factors of 36 and 72? (1, 2, 3, 4, 6, 9, 12, 18, 36) • In the example, which common factor are both 36 and 72 divided 9 by? (4) Is __ in simplest form? (No.) 18 • What common factor are both 9 and 18 divided by? (3) Is __36 in simplest form? (No.) • What common factor are both 3 and 6 divided by? (3) • Is __12 in simplest form? Why? (Yes. 1 and 2 have no common factors except 1.) • Would the simplest form still be __12 if you used a different common factor to divide by? (Yes.) Try It • Have students divide the numerator and denominator by the given common factor. 3 6 18 6 2 Since the numerator, 1, and the denominator, 2, have no common factors 1 except 1, the fraction __ is in simplest form. 2 Use division. Simplify each fraction. 4 4 ÷ __ 1. __ = 8 4 1 __ 2 3 9 4. ___ ÷ __ = 12 3 3 __ 3 9 7. ___ ÷ __ = 21 3 3 __ 4 7 6 3 2. __ ÷ __ = 9 3 2 __ 3 3 12 ÷ __ 5. ___ = 15 3 4 __ 2 6 8. ___ ÷ __ = 10 2 3 __ 5 5 15 5 3. ___ ÷ __ = 25 5 3 __ 32 4 6. ___ ÷ __ = 36 4 8 __ 12 24 ÷ ___ 9. ___ = 36 12 5 9 2 __ Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-G 3 260_S_G5_C08_SI_119817.indd 260 7/12/12 6:33 PM WHAT IF THE STUDENT NEEDS HELP TO Divide Whole Numbers • Practice division facts for 10 to 15 minutes daily until the student can recall the quotients automatically. • Once the division facts are mastered, have the student practice dividing by 1-digit and 2-digit divisors. Find Common Factors of Two Numbers • Have the student list all the factors of a number by having the student divide the number by each whole number that is less than the number until all the factors have been found. • Once the student has mastered finding the factors of one number, have the student find the factors of two numbers and then circle the common factors. Name Factors, Common Factors, and Greatest Common Factor What Can I Do? I want to find the greatest common factor of two numbers. Lesson 8-H What is the greatest common factor of 16 and 24? Think: I will look for pairs of numbers that can be multiplied together to make the number. 16 24 16 × 1 24 × 1 8×2 12 × 2 4×4 8×3 6×4 List the factors. The factors of 16 are 1, 2, 4, 8, 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Find the common factors. 1, 2, 4, and 8 are factors of both 16 and 24. Find the greatest common factor (GCF). 8 is the greatest factor of both 16 and 24. 1. 12 2. 8 3. 18 4. 9 Find the common factors of each pair of numbers. 5. 8 and 12 6. 9 and 18 7. 12 and 18 Name the greatest common factor of each pair of numbers. 8. 8 and 12 9. 9 and 18 10. 12 and 18 Copyright © The McGraw-Hill Companies, Inc. List the factors of each number. Name List the factors of each number. Lesson 8-H 11. 15 12. 6 13. 10 14. 20 15. 14 16. 27 Find the common factors for each pair of numbers. 17. 6 and 15 18. 10 and 20 19. 14 and 27 20. 15 and 27 21. 14 and 6 22. 15 and 14 23. 6 and 20 24. 6 and 27 25. 10 and 15 Copyright © The McGraw-Hill Companies, Inc. Name the greatest common factor for each pair of numbers. 26. 6 and 15 27. 10 and 20 28. 14 and 27 29. 15 and 27 30. 14 and 6 31. 15 and 14 32. 6 and 20 33. 6 and 27 34. 10 and 15 Lesson Goal • Find the greatest common factor (GCF) of two numbers. What the Student Needs to Know Name Factors, Common Factors, and Greatest Common Factor What Can I Do? I want to find the greatest common factor of two numbers. • Find the factors of a number. • Find the common factors of two numbers. • Find the greatest number in a set. Lesson 8-H What is the greatest common factor of 16 and 24? Think: I will look for pairs of numbers that can be multiplied together to make the number. 16 24 16 × 1 24 × 1 8×2 12 × 2 4×4 8×3 The factors of 16 are 1, 2, 4, 8, 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Find the common factors. Getting Started 1, 2, 4, and 8 are factors of both 16 and 24. Ask students to think of as many pairs of numbers as they can that have the following numbers as a product. • 8 (1 × 8, 2 × 4) • 12 (1 × 12, 2 × 6, 3 × 4) • 18 (1 × 18, 2 × 9, 3 × 6) • 19 (1 × 19) • 20 (1 × 20, 2 × 10, 4 × 5) • 25 (1 × 25, 5 × 5) Find the greatest common factor (GCF). What Can I Do? Read the question and the response. Then read and discuss the examples. Ask: • How can you find the factors of 16? (Find pairs of numbers that have 16 as their product.) • Why is it important to list the factors of the two numbers in order? (When the factors are listed in order it is easier to compare the factors of the two numbers and to locate common factors.) • How can you find the common factors of 16 and 24? (Look for numbers that are listed as factors for both 16 and 24.) • How can you tell that 4 is not the greatest common factor of 16 and 24? (There is another number, 8, that is greater than 4 and is a factor of both 16 and 24.) 6×4 List the factors. 8 is the greatest factor of both 16 and 24. List the factors of each number. 1. 12 1, 2, 3, 4, 6, 12 2. 8 1, 2, 4, 8 3. 18 1, 2, 3, 6, 9, 18 4. 9 1, 3, 9 Find the common factors of each pair of numbers. 5. 8 and 12 1, 2, 4 6. 9 and 18 1, 3, 9 7. 12 and 18 1, 2, 3, 6 Name the greatest common factor of each pair of numbers. 8. 8 and 12 4 9. 9 and 18 9 Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-H 10. 12 and 18 6 262_263_S_G5_C08_SI_119817.indd 262 7/12/12 6:44 PM WHAT IF THE STUDENT NEEDS HELP TO Find the Factors of a Number Find the Common Factors of Two Numbers • Have the student think of pairs of numbers that can be multiplied together to make a product. Explain that numbers that are multiplied together are called factors. • Tell the student to start with one and go through the numbers in order, 1, 2, 3, 4, … For each number, they should decide if it can divide evenly into the number for which they are finding factors. • Check that the student is finding all of the factors of the two numbers. • Have the student compare the factors of the two numbers one-by-one. Have him or her cross off any factors that are not common to both numbers and circle and draw lines connecting the factors that are common to both numbers. Name List the factors of each number. Lesson 8-H 11. 15 1, 3, 5, 15 12. 6 13. 10 1, 2, 5, 10 14. 20 1, 2, 4, 5, 10, 20 15. 14 1, 2, 7, 14 16. 27 1, 3, 9, 27 Try It 1, 2, 3, 6 • Tell students that each number will have at least two factors. Ask students to name the two factors that every number will have. (1 and the number itself) • Point out that 2 is listed as a factor of 12. Ask students what number times 2 equals 12. (6) Elicit from the students that 6 must also be a factor of 12. • Encourage students to share their methods for finding common factors. • Have students complete the exercises. Then have volunteers explain how they found the greatest common factor for Exercises 8–10. Find the common factors for each pair of numbers. 17. 6 and 15 1, 3 18. 10 and 20 1, 2, 5, 10 19. 14 and 27 1 20. 15 and 27 1, 3 21. 14 and 6 1, 2 22. 15 and 14 1 23. 6 and 20 1, 2 24. 6 and 27 1, 3 25. 10 and 15 1, 5 Copyright © The McGraw-Hill Companies, Inc. Name the greatest common factor for each pair of numbers. 26. 6 and 15 3 27. 10 and 20 10 28. 14 and 27 1 29. 15 and 27 3 30. 14 and 6 2 31. 15 and 14 1 32. 6 and 20 2 33. 6 and 27 3 34. 10 and 15 5 262_263_S_G5_C08_SI_119817.indd 263 Power Practice 7/12/12 6:44 PM • Ask students if every pair of numbers will have a common factor. Then have them explain their reasoning. (Each number has at least two factors, one and itself. So, each pair of numbers will have at least one common factor, 1.) • Have students complete the exercises. Then review the answers and ask volunteers to explain how they found the greatest common factors for Exercises 26–34. WHAT IF THE STUDENT NEEDS HELP TO Find the Greatest Number in a Set Complete the Power Practice • Have the student locate each number in the set on a number line. Explain that the number farthest to the right on the number line is the greatest number. Ask the student to use the number line to name the greatest number in the set. • Review comparing pairs of numbers. Name two numbers such as 15 and 21. Have the student compare the numbers saying: 21 is greater than 15 or 15 is less than 21. • Work through finding factors, common factors, and greatest common factors with the student to determine what help the student needs. Then provide reteaching and review in those areas. Lesson 8-H Name Use a Multiplication Table to Divide Lesson 8-I Use a multiplication table. What Can I Do? When you need to check a fact, use the table to find it. I want to practice the division facts. X 0 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 3 0 3 6 9 12 15 18 21 24 27 30 4 0 4 8 12 16 20 24 28 32 36 40 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 36 42 48 54 60 7 0 7 14 21 28 35 42 49 56 63 70 8 0 8 16 24 32 40 48 56 64 72 80 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 1. 25 ÷ 5 = 2. 35 ÷ 5 = 3. 27 ÷ 3 = 4. 24 ÷ 3 = Divide. 32 5. 4 6. 6 24 7. 8 16 8. 9 18 9. 8 32 9 10. 3 50 11. 5 12 12. 3 10 13. 2 16 14. 2 21 15. 3 28 16. 7 14 17. 7 6 18. 6 12 19. 6 Copyright © The McGraw-Hill Companies, Inc. Use the table to complete each fact. Name Use a Multiplication Table to Divide Lesson Goal • Complete division facts. What the Student Needs to Know 8-I Use a multiplication table. What Can I Do? When you need to check a fact, use the table to find it. I want to practice the division facts. X 0 0 1 2 3 4 5 6 7 8 9 10 • Use counters to show the meaning of division. • Read a multiplication table. • Use a multiplication fact to write two related division facts. Getting Started • Write 20 ÷ 2 on the board. Ask: What does this mean? (Divide 20 by 2; divide 20 into 2 equal groups; divide 20 into groups of 2) What is another way to write this division 20 ) problem? ( 2 • Explain your thinking when you do a problem such as 36 ÷ 6. (Possible strategies: How many times does 6 go into 36? What number times 6 equals 36? How many times can I subtract 6 from 36?) Lesson 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 3 0 3 6 9 12 15 18 21 24 27 30 4 0 4 8 12 16 20 24 28 32 36 40 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 36 42 48 54 60 7 0 7 14 21 28 35 42 49 56 63 70 8 0 8 16 24 32 40 48 56 64 72 80 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 Use the table to complete each fact. 1. 25 ÷ 5 = 5 2. 35 ÷ 5 = 7 3. 27 ÷ 3 = 9 4. 24 ÷ 3 = 8 Divide. 8 32 5. 4 4 24 6. 6 2 16 7. 8 2 18 8. 9 4 32 9. 8 3 10. 3 9 10 11. 5 50 4 12. 3 12 5 13. 2 10 8 14. 2 16 7 21 15. 3 4 28 16. 7 2 14 17. 7 1 6 18. 6 2 12 19. 6 Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-I What Can I Do? Read the question and the response. • If you have not yet memorized the division facts, what can you do? (Practice using flash cards. Some students may suggest computer software.) • Why can you use multiplication to help you do division? (Multiplication and division are opposite or inverse operations. One operation “un-does” the other.) Try It • How can you use the table for Exercise 1? (Find the row with 5 at the left. Go across this row until you get to 25. Look at the top of this column to find the quotient, 5.) Power Practice • Have the students complete the practice items. Then review each answer. 266_S_G5_C08_SI_119817.indd 266 7/12/12 7:10 PM WHAT IF THE STUDENT NEEDS HELP TO Use Counters to Show the Meaning of Division • Provide pairs of students with 50 counters. One student takes a handful of counters; the partner divides them into 2 equal groups. Students record their work using the ÷ symbol. Repeat using groups of 3 and 4. Read a Multiplication Table • Provide blank multiplication tables. Direct the student to model a fact such as 4 × 3. He or she should shade the 4 row across to the 12; shade the 3 column down to the 12. Repeat with other facts. Use a Multiplication Fact to Write Two Related Division Facts • Write 5 × 6 on the board. Have the student draw a model for the fact. Use the model to write and explain two division facts: 30 ÷ 5 = 6, 30 ÷ 6 = 5. Complete the Power Practice • Have students work in pairs using division flash cards to identify which facts they still need to memorize. Name Multiples of a Number Lesson 8-J Use models to answer. 1. There are 4 rows of 10 bees. 40 is a multiple of and . 2. There are 4 rows of 7 hammers. 28 is a multiple of and . 3. There are 4 rows of 3 clocks. 12 is a multiple of and . A multiple of a number is the product of that number and any whole number. Circle the number which is not a multiple. 4. 7 5. 4 18, 24, 28, 36, 40 6. 6 7. 8 12, 18, 22, 30, 42 16, 24, 40, 56, 62 8. Complete the graphic organizer. One example is done for you. Multiples of a Number Multiples of a Number Examples Non-Examples Examples 7: 14, 21, 28, 35 10 5: , , , 3: , , , 9: , , , Non-Examples Copyright © The McGraw-Hill Companies, Inc. 14, 21, 28, 36, 42 Name Multiples of a Number Lesson Goal 1. There are 4 rows of 10 bees. What the Student Needs to Know 2. There are 4 rows of 7 hammers. Getting Started • Write the word multiple on the board and explain the definition. A multiple of a number is the product of the number and any whole number. • Provide students with their own multiplication table. • Have students find the product of 4 × 1. What is 4 × 1? (4) The product, 4, is a multiple of 4. • What is 4 × 2? (8) The product, 8, is a multiple of 4. • What is 4 × 3? (12) The product, 12, is a multiple of 4. • What is another multiple of 4? (16, 20, 24, 28, 32, 36, 40, 44, 48…) • Practice finding the multiples of another number if needed. 8-J Use models to answer. • Find examples and non-examples of multiples of a number. • Use multiplication to find the multiple. Lesson 40 is a multiple of 28 is a multiple of 4 4 and and 10 . 7 . 3 . 3. There are 4 rows of 3 clocks. 12 is a multiple of 4 and A multiple of a number is the product of that number and any whole number. Circle the number which is not a multiple. 4. 7 5. 4 14, 21, 28, 36, 42 18, 24, 28, 36, 40 6. 6 7. 8 12, 18, 22, 30, 42 16, 24, 40, 56, 62 8. Complete the graphic organizer. One example is done for you. Multiples of a Number Multiples of a Number Examples Examples Non-Examples Non-Examples Sample answers: Sample answers: Sample answers: Sample answers: 13 7: 14, 21, 28, 35 10 3: 6 , 9 , 12 , 15 10 15 20 25 12 18 27 36 45 20 5: , , , 9: , , , Copyright © The McGraw-Hill Companies, Inc. USING LESSON 8-J Teach Read and discuss Exercise 1 at the top of the page. • Let’s use the array to find the multiple. • How many rows does the array have? (4) • How many are in each row? (10) • How many squares are in the array in all? (40) • What multiplication sentence can we use to label the array? (4 × 10 = 40) • What are the two factors? (4 and 10) • What number is the product or multiple? (40) • Write the following statement on the board: 40 is a multiple of ______ and _______. (4 and 10) Practice • Read the directions as students complete Exercises 2 through 8. • Check student work. 268_S_G5_C08_SI_119817.indd 268 7/12/12 7:17 PM WHAT IF THE STUDENT NEEDS HELP TO Use Multiplication to Find the Multiple • Have the student use arrays if they need to model multiplication number sentences. • For example, have the student model the array 5 × 2 with connecting cubes to help identify the multiple. • What is the first factor? (5) There will be 5 rows. • What is the second factor? (2) There will be 2 columns. • Have the student construct the array with connecting cubes. • Label the array 5 × 2. Count the number of connecting cubes in the array. How many connecting cubes are in the array? (10) • The total number of cubes, or the product, is a multiple. • 10 is the multiple of the number sentence 5 × 2. • What two numbers is 10 a multiple of? (5 and 2) • Continue to have the student model arrays with 5 × 3, 5 × 4, 5 × 5, etc. until the student understands the product is also the multiple of the two factors. Name Shade and Compare Fractions Lesson 8-K Compare the fractions. Write >, <, or =. 1. 2. 3. 2 __ 4 __ 2 __ 3 __ 6 6 3 3 4. 3 __ 1 __ 4 4 3 __ 3 __ 4 4 Shade and compare the fractions. Write >, <, or =. 5. 3 __ 4 __ 5 5 7. 5 __ 2 __ 8 8 4 __ 3 __ 8 8 8. 3 __ 1 __ 3 3 Copyright © The McGraw-Hill Companies, Inc. 6. USING LESSON 8-K Lesson Goal • Compare fractions with common denominators. Name Shade and Compare Fractions 8-K Compare the fractions. Write >, <, or =. 1. 2. What the Student Needs to Know • Compare whole numbers. • Use comparison symbols. Lesson 3 2 < __ __ 4 2 < __ __ 6 6 3. 3 3 4. Getting Started 3 > __ 1 __ 4 Practice • Have students read the directions and complete Exercises 2 through 8. Check their work. 4 4 Shade and compare the fractions. Write >, <, or =. 5. 6. 3 < __ 4 __ 5 2 5 > __ __ 5 7. 8 8 8. 3 > __ 1 __ 3 3 4 > __ 3 __ 8 Teach Read and discuss Exercise 1 at the top of the page. • Take a look at the two fractions in Exercise 1. What do you notice about the numbers in the numerator and denominator? (The numbers in the numerator are different and the numbers in the denominator are the same.) • Since the numbers in the denominator are the same, we need to compare the numbers in the numerator. Is 2 less than, greater than, or equal to 4? (less than) • How do you use the models to check your work? (Sample answer: The models show 2 shaded parts of the rectangle is less than 4 shaded parts of the rectangle.) 2 < __ 4. • Therefore, __ 6 6 3 3 = __ __ 4 Copyright © The McGraw-Hill Companies, Inc. • Ask students to compare whole numbers. Show students a group of 6 connecting cubes and a group of 3 connecting cubes. • Which group has more connecting cubes? (the group of 6) • Is 6 greater than, less than, or equal to 3? (greater than) • Ask for a volunteer to come to the board to use the “greater than” comparison symbol for the two numbers. (6 > 3) • Remind students to point the opening of the comparison symbol (> or <) towards the greater number. 8 270_S_G5_C08_SI_119817.indd 270 7/17/12 11:07 AM WHAT IF THE STUDENT NEEDS HELP TO Compare Whole Numbers • Give the student a pair of onedigit numbers such as 8 and 6. • Have the student make a number line and label the numbers from 0 to 10. • Be sure the student understands that the numbers increase as you move from left to right. • The student should circle the two numbers being compared on the number line. Have students circle 8 and 6. • Now, have the student identify the greater number (8) and the number that is less (6). • Have the student use comparison symbols to compare the two numbers. (8 > 6 or 6 < 8) Use Comparison Symbols • Explain that the signs (< and >) are used to compare two numbers. In a comparison like 12 > 3, the > sign means that 12 is greater than 3. • The comparison can also be written 3 < 12, where the < sign means that 3 is less than 12. • Have the student practice comparing one-digit numbers until the concept becomes clear. Name Identify Fractions and Decimals Lesson 8-L Use counting. What Can I Do? I want to name the fraction and decimal shown by the model. Each shaded part stands for a tenth of 1, or 0.1. Each shaded part also stands for one 1 ___ part of the whole. The fraction 10 represents one part shaded out of ten total parts. 0.1 Count the shaded parts. Write that number as a decimal and fraction. 6 6 parts shaded = 0.6 or ___ 10 Use counting. Write the fraction and decimal for the shaded portion. 1. 2. parts shaded 3. parts shaded parts shaded Decimal: Decimal: Decimal: Fraction: Fraction: Fraction: Copyright © The McGraw-Hill Companies, Inc. 4 4 parts shaded = 0.4 or ___ 10 USING LESSON 8-L Name Identify Fractions and Decimals Lesson 8-L Lesson Goal • Name the fraction and decimal shown by a tenths model. What the Student Needs to Know Use counting. What Can I Do? I want to name the fraction and decimal shown by the model. Each shaded part stands for a tenth of 1, or 0.1. Each shaded part also stands for one 1 ___ represents part of the whole. The fraction 10 one part shaded out of ten total parts. • Use a decimal point. • Write a fraction. 0.1 Getting Started What Can I Do? Have students read the question and the response. Then look at the example. Ask: • How many equal parts are in the square? (ten) What does each part of the square represent? (one tenth of one) • Can one square ever have more than ten tenths? (No.) • Look at the first example. How many parts of the square are shaded? (six parts) How do you write that as a decimal? (Write the number of shaded parts after the decimal point; 0.6) How do you write that as 6 a fraction? (___; six parts are shaded 10 out of a total of 10 parts.) Try It • Remind students that a zero is included as a placeholder before the decimal to show that there are no wholes. Count the shaded parts. Write that number as a decimal and fraction. 6 6 parts shaded = 0.6 or ___ 10 4 4 parts shaded = 0.4 or ___ 10 Use counting. Write the fraction and decimal for the shaded portion. 1. 2. 3. 3 parts shaded 5 parts shaded 7 parts shaded Decimal: 0.3 Decimal: 0.5 3 ___ 10 5 ___ 10 Fraction: Fraction: Decimal: 0.7 Fraction: Copyright © The McGraw-Hill Companies, Inc. Review decimals, their notation, and meaning with students. Ask: • What does a decimal and fraction represent? (It represents a part of a whole.) How can you recognize a decimal? (A decimal always has a decimal point.) • What place does the digit to the left of the decimal point hold? (ones) What place does the digit to the right of the decimal point hold? (tenths) 7 ___ 10 272_S_G5_C08_SI_119817.indd 272 7/12/12 7:27 PM WHAT IF THE STUDENT NEEDS HELP TO Use a Decimal Point Write a Fraction • Present a decimal model with five parts shaded. Have the student identify the number of parts. Have the student write a number to show each part. • Discuss how the number could be written as 0.5. Stress that the decimal point is used to separate the number of wholes from the number of parts of a whole. • Present several more models and have the student write a number to show each. • Provide manipulatives for the student if he or she needs visuals. • Remind the student that the top number in a fraction identifies the amount of shaded parts. The bottom number identifies the total amount of parts in a whole. • Have the student use fraction circles or fraction tiles to practice modeling fractions. Encourage the student to write the fraction.