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Multiplying Fractions by Whole Numbers Objective To apply and extend previous understandings of multiplication to multiply a fraction by a whole number. o www.everydaymathonline.com ePresentations eToolkit Algorithms Practice EM Facts Workshop Game™ Teaching the Lesson Key Concepts and Skills • Use a number line to represent a fraction. [Number and Numeration Goal 2] • Understand a fraction _ab as a multiple of _1b . [Number and Numeration Goal 3] • Determine between which two whole numbers a fraction lies. [Number and Numeration Goal 6] • Solve number stories involving multiplication of a fraction by a whole number. [Operations and Computation Goal 7] • Write equations to model number stories. Family Letters Assessment Management Common Core State Standards Ongoing Learning & Practice Math Boxes 7 12a Math Journal 2, p. 217F Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Operations and Computation Goal 5] Study Link 7 12a Math Masters, p. 242A Students practice and maintain skills through Study Link activities. [Patterns, Functions, and Algebra Goal 2] Key Activities Students use a number line as a visual a fraction model to represent a fraction _b multiplied by a whole number n as the (n ∗ a) a product n ∗ (_b ) or _ b . They solve number stories involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problems. Curriculum Focal Points Interactive Teacher’s Lesson Guide Differentiation Options READINESS Skip Counting to Show Multiples of Unit Fractions Math Masters, p. 242B calculator Students use calculators to skip count by unit fractions. ENRICHMENT Visual Models for Multiplying a Fraction by a Whole Number Student Reference Book, p. 58 Math Masters, pp. 242C and 242D Students explore alternative visual fraction models for multiplying a fraction by a whole number. EXTRA PRACTICE 5-Minute Math 5-Minute Math™, pp. 22 and 23 Students practice multiplying fractions by whole numbers. Ongoing Assessment: Informing Instruction See page 637D. Key Vocabulary multiple equation Materials Math Journal 2, pp. 217A–217E Study Link 7 12 half-sheets of paper calculator (optional) Advance Preparation Teacher’s Reference Manual, Grades 4–6 pp. 143, 144 637A Unit 7 Fractions and Their Uses; Chance and Probability 637A_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637A 3/3/11 2:51 PM Getting Started Mental Math and Reflexes Math Message Have students name the next three multiples in a sequence. Suggestions: Name the next three multiples in each sequence. 8, 16, 24, ... 32, 40, 48 50, 60, 70, ... 80, 90, 100 25, 50, 75, ... 100, 125, 150 82, 84, 86, ... 88, 90, 92 56, 60, 64, ... 68, 72, 76 18, 27, 36, ... 45, 54, 63 70, 140, 210, ... 280, 350, 420 3 1 __ 2 __ __ 10 , 10 , 10 , __ __ __ … 10 , 10 , 10 3 1 __ 2 __ __ 4 5 6 4, 4, 4, 4 5 6 … _4 , _4 , _4 Study Link 712 Follow-Up Have small groups compare the results of the penny toss experiment. Ask volunteers to share their answers for Problem 5. Have students indicate thumbs-up if they agree. 600; 1,200; 1,800; ... 2,400; 3,000; 3,600 125, 250, 375, ... 500, 625, 750 1 Teaching the Lesson Adjusting the Activity Math Message Follow-Up Provide students with calculators to assist with skip counting. See the Part 3 Readiness activity for additional information. WHOLE-CLASS DISCUSSION AUDITORY KINESTHETIC TACTILE VISUAL Ask students how they determined the next three multiples in each sequence. Possible strategies: NOTE In Third Grade Everyday Mathematics 1 Think of the problem as skip counting by _ s. To get the 10 1 _ next multiple, add 10 to the previous fraction. For example, 3 _ 1 + _ 1 = _ 2 _ 1 = _ 1 = _ 4 _ ; 2 +_ ; 3 +_ ; and so on. 10 10 10 10 10 10 10 10 10 children participated in skip-counting activities to help them memorize the multiplication facts. While completing these activities, they were finding multiples. A multiple of a number is the product of a counting number and the number itself. Think in terms of equal groups. For example, 1 group of _14 is _14 ; 2 groups of _14 is __24 ; 3 groups of _14 is _34 ; 4 groups of _14 is _44 ; and so on. Tell students that in this lesson they will use their understanding of multiples to multiply fractions by whole numbers. Student Page Date Time LESSON 7 12a Multiples of Unit Fractions 58 For Problems 1–3, fill in the blanks to complete an equation describing the number line. Using a Visual Fraction Model to PARTNER ACTIVITY Multiply a Unit Fraction by a Whole Number 1. 1 8 0 2 8 _1 8 Equation: 5 ∗ 3 8 4 8 _5 5 8 6 8 7 8 1 8 = 2. 1 6 0 3 Equation: (Math Journal 2, pp. 217A) 2 6 _3 or _1 6, 2 1 ∗_ 6 = 3 6 4 6 5 6 1 3 3 4 3 5 3 6 3 3. 1 3 0 Draw the number line below on the board or overhead. 2 3 Equation: _4 _1 4 3 ∗ = 3, or 1_13 For Problems 4–6, use the number line to help you multiply the fraction by the whole number. 0 1 2 2 2 3 2 4 2 5 2 6 2 Have volunteers explain how they could use the number line and their understanding of multiples to help them solve the problem 3 ∗ __12 . 4. 1 4 0 _2 4, 1 Equation: 2 ∗ _ 4 = 5. 0 1 10 or 2 10 1 Equation: 6 ∗ _ 10 = 2 4 3 4 1 _1 2 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 4 5 5 5 6 5 7 5 8 5 9 5 10 5 6 __ _3 10 , or 5 6. 0 1 5 1 Equation: 7 ∗ _ 5 = 2 5 _7 5, 3 5 _2 or 15 Math Journal 2, p. 217A 185-218_EMCS_S_MJ2_G4_U07_576426.indd 217A 3/24/11 9:28 AM Lesson 7 12a 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637B 637B 3/24/11 2:40 PM Student Page Date Time LESSON One way is to visualize jumps or hops on the number line, starting at 0. The fraction tells the size of the jump; the whole number tells the number of jumps. Thus, 3 ∗ _12 is 3 jumps, each _12 unit long. You end up at _32 . So, 3 ∗ _12 = _32 , or 1_12 . An Algorithm for Multiplying a Fraction by a Whole Number 7 12a 6 1 _ Example 1: Equation: 6 ∗ _ 5 = 5 1 5 1 5 1 5 1 5 1 5 1 5 58 5 5 0 2 _ 5 Example 2: Equation: 3 ∗ = 2 5 10 5 6 _ 5 2 5 2 5 5 5 0 1 2 10 5 1 2 1 2 Write an equation to describe each number line. 1 4 1 4 1 4 1 4 1 4 1 4 1. a. _1 0 6 4 4 _6 4 ∗ 8 4 0 4 = 3 4 3 4 1 2 2 2 3 2 4 2 5 2 6 2 b. _3 0 2 _6 4 ∗ 1 3 1 3 4 4 4 = 1 3 1 3 8 4 1 3 1 3 1 3 Partners complete journal page 217A. Tell students that an equation is a number sentence with an equals sign, such as 3 ∗ _12 = _32 . As you circulate and assist, pose questions such as the following: 1 3 2. a. 3 3 _1 0 8 3 ∗ 2 3 6 3 _8 9 3 3 = 2 3 2 3 2 3 b. 4 3. 3 3 _2 0 3 ∗ 6 3 _8 9 3 3 = ● Which number in the equation tells you the size of the jump? The first fraction ● Which number in the equation tells you the number of jumps? The whole number ● Can you name the products in Problems 3 and 6 as mixed numbers? _43 = 1_13 ; _75 = 1_25 Study the pairs of number lines above. Use the patterns you see to describe a way to multiply a fraction by a whole number. Sample answer: If I take the whole number, multiply it by the numerator of the fraction and then write the product over the denominator, that is my answer. 217B Math Journal 2, p. 217B 185-218_EMCS_S_MJ2_G4_U07_576426.indd 217B 3/3/11 12:39 PM Using a Visual Fraction Model WHOLE-CLASS ACTIVITY to Multiply Any Fraction by a Whole Number (Math Journal 2, pp. 217B and 217C) Have partners study the examples at the top of journal page 217B. On a half-sheet of paper, students should record any similarities and differences they see between the equations modeled on the number lines. Student Page Date Time LESSON 7 12a Multiplying Fractions by Whole Numbers Expect students to share observations such as the following: 58 Both equations involve multiplication of a fraction by a whole number. Use number lines to help you solve the problems. _5 1 _ 1. 5 ∗ 6 = 6 1 6 1 6 1 3 1 3 0 1 3 1 8 1 8 0 _8 3, 1 8 3 8 6. 217C 6 3 _3 10 , or 5 2 10 0 9 3 It takes more jumps of _15 to get to _65 than it does jumps of _25 because the jumps of _15 are smaller than the jumps of _25 . Sample answer: 4 8 8 8 The whole number factor in 6 ∗ _15 = _65 is twice as much as the whole number factor in 3 ∗ _25 = _65 . The fraction factor in 6 ∗ _15 = _65 is half as much as the fraction factor in 3 ∗ _25 = _65 . 4 3 , or 1_48, or 1_12 6 __ The factors in the equations are different, but _25 is a multiple of _15 and 6 is a multiple of 3. 1 3 4 3 0 0 Both equations have the same product. 1 =3∗_ 8 or 2_23 12 __ 8 1 3 3 3 _3 4 _ 4. 2 ∗ 3 = 5. 1 6 6 6 1 3 8 3. 1 6 6 _ 3 , or 2 0 1 _ 2. 6 ∗ 3 = 1 6 3 3 3 8 6 3 3 =4∗_ 8 4 8 3 8 3 8 8 8 2 10 2 =3∗_ 10 9 3 2 10 12 8 16 8 Sample answer: 5 10 10 10 Math Journal 2, p. 217C 185-218_EMCS_S_MJ2_G4_U07_576426.indd 217C 3/3/11 12:39 PM 637C Unit 7 Fractions and Their Uses; Chance and Probability 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637C 3/3/11 2:51 PM Student Page Have partners complete Problems 1 and 2 on journal page 217B by writing a multiplication equation to describe each number line. When students have completed Problem 3, bring the class together to discuss the algorithm for multiplication of a fraction by a whole (n ∗ a) a = _ number. The pattern can be expressed as: n ∗ __ . b b Have students complete journal page 217C for additional practice multiplying fractions by whole numbers. Encourage students to use the pattern they discovered on journal page 217B to check their answers. Date Time LESSON Solving Number Stories 7 12a 1 cup flour 1 _ 2 cup whole-wheat flour 1. The sisters decided to double the recipe. a. How many cups of whole-wheat flour do they need now? _2 2, c. cup(s) Equation: _6 or 1_24, or 1_12 cup(s) Equation: How many cups of honey do they need now? _4 or 1_13 cup(s) Equation: 2 ∗ _12 = _22 2 ∗ _34 = _64 2 ∗ _23 = _43 Suma and Puja decide to make 48 muffins instead of 12. a. How many teaspoons of salt do they need now? _4 4, b. When Carlos goes to the gym, he exercises for of an hour and burns about 200 calories. Last week he went to the gym 5 times. How many hours did Carlos spend at the gym last week? or 1 How many cups of blueberries do they need now? 3, 2. 3 _ 4 8 Use the list of recipe ingredients to help you solve the number stories below. For each problem, write an equation to show what you did. PARTNER ACTIVITY Pose the following number story: 3 1 _ 4 cup cooking oil 3 _ teaspoon cinnamon 4 1 _ 4 teaspoon salt 4, (Math Journal 2, pp. 217D and 217E) 1 egg 1 _ 2 cup skim milk 2 _ cup honey 2 teaspoons baking powder 3 _ cup blueberries b. Solving Number Stories 58 Suma and her sister Puja are making 12 blueberry-wheat muffins for breakfast. The recipe lists the following ingredients: teaspoon(s) Equation: How many teaspoons of cinnamon do they need now? 12 __ 8 c. or 1 , or 1_48, or 1_12 teaspoon(s) Equation: 4 ∗ _14 = _44 12 4 ∗ _38 = __ 8 How many cups of skim milk do they need now? _4 2, or 2 cup(s) Equation: 4 ∗ _12 = _42 Math Journal 2, p. 217D 185-218_EMCS_S_MJ2_G4_U07_576426.indd 217D 3/3/11 12:39 PM Ongoing Assessment: Informing Instruction Watch for students who are distracted by the “extra” 200 in the number story. Encourage them to eliminate irrelevant information by determining exactly what they want to find out, what information they already know, and what they might need to know in order to solve the problem. On a half-sheet of paper, have students draw a visual fraction model to represent the number story. Expect drawings such as the following: 3 4 0 3 4 3 4 4 4 3 4 8 4 3 4 12 4 16 4 20 4 Then have students write a multiplication equation to represent 15 the problem. 5 ∗ _34 = __ 4 Ask students to determine between which two whole numbers of hours the product lies. 3 and 4 hours Have them explain their strategy for finding the answer. Possible strategies: Use the number line drawn to represent the number story. Note 16 12 that the product lies between _ , or 3, and _ , or 4. 4 4 15 The fraction _ can be renamed as the mixed number 3_34 by 4 dividing the numerator, 15, by the denominator, 4: 15 4 → 3 R3. The quotient, 3, is the whole number part of the mixed number. The remainder, 3, is the numerator of the fraction part of the mixed number. It tells how many fourths are left over after making as many wholes as possible. NOTE In Lesson 3-8, students used number models to model number stories. A number model is a number sentence or part of a number sentence. A number model can include an equal sign, but it is not required. An equation is a number sentence with an equal sign. See Section 10.2 in the Teacher’s Reference Manual for more information. Lesson 7 12a 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637D 637D 3/3/11 2:52 PM Have partners complete journal pages 217D and 217E. Encourage students to use visual fraction models, such as number lines, to help them solve the problems. When reviewing answers, pose questions such as the following: ● Which of the products on journal page 217D can you rename as whole numbers? Problem 1a: _22 = 1; Problem 2a: _44 = 1; Problem 2c: _42 = 2 ● Between which two whole numbers does the product in Problem 2b lie? 1 and 2 ● In Problem 2, how did you decide which whole number you would multiply the recipe ingredients by? Sample answer: The recipe makes 12 muffins. If the sisters want 48 muffins they will need to quadruple the recipe because 12 ∗ 4 = 48. ● How did you solve Problem 6? Sample answer: Let the letter a stand for the number of meetings Cole would need to attend 15 and write the equation a ∗ _52 = _ . Use the algorithm for 2 multiplying a fraction by a whole number and think: What 15 number times 5 will give me 15? 3 ∗ 5 = 15, so 3 ∗ _52 = _ . Cole 2 will need to attend 3 meetings. ● In Problem 6, between which two whole-number distances does 15 the distance _ miles lie? Between 7 and 8 miles 2 Allow time for students to share and solve the number stories they wrote for Problem 7. For each problem, pose questions such as the following: ● Between which two whole numbers does the answer lie? ● Can you use a visual fraction model or an equation to represent the problem? Student Page Date Time LESSON Solving Number Stories 7 12a continued The Hillside Elementary School walking club meets every Monday after school. The table below shows how far some students walked at their last meeting. Student Miles Katie Mahpara Nikhil Cole Maria Jack 1 _ 9 _ 5 _ 5 _ 4 _ 5 _ 3 10 4 2 3 6 Use the information in the table to solve the number stories. 3. a. _2 If Katie walks the same distance at every meeting, how far will she walk after 2 meetings? _7 3, 3 _1 or 23 b. After 7 meetings? c. After 7 meetings, Katie will have walked between Circle the best answer. 1 and 2 miles 4. a. 2 and 3 miles . 3 and 4 miles 15 __ , or 2_36, or 2_12 If Jack walks the same distance at every 6 meeting, how far will he walk after 3 meetings? b. After 3 meetings, Jack will have walked between Circle the best answer. 5. a. If Mahpara walks the same distance at every 10 meeting, how far will she walk after 4 meetings? 1 and 2 miles b. miles miles miles . 2 and 3 miles 3 and 4 miles 36 __ 6 _3 , or 3__ 10 , or 3 5 miles . After 4 meetings, Mahpara will have walked between Circle the best answer. 1 and 2 miles 2 and 3 miles 3 and 4 miles Try This 6. If Cole walks the same distance at every meeting and wants to 15 walk a total of _ 2 miles, how many meetings will he need to attend? 7. Make up your own multiplication number story about Nikhil or Maria. 3 meetings Answers vary. Math Journal 2, p. 217E 185-218_EMCS_S_MJ2_G4_U07_576426.indd 217E 637E 3/24/11 9:28 AM Unit 7 Fractions and Their Uses; Chance and Probability 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637E 3/24/11 2:40 PM Student Page 2 Ongoing Learning & Practice Math Boxes 7 12a Date Math Boxes 7 12a 1. INDEPENDENT ACTIVITY Time LESSON Karen used 60 square feet of her back 3 yard for a garden. Vegetables fill _ 5 of 1 her garden space. Tomato plants fill _ 6 of the space taken up by vegetables. How many square feet are used for tomatoes? 6 2. Multiply. Use a paper-and-pencil algorithm. 3,741 = 87 ∗ 43 square feet (Math Journal 2, p. 217F) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lessons 7-9 and 7-11. The skill in Problem 6 previews Unit 8 content. b. Ongoing Assessment: Recognizing Student Achievement Lukasz drew a line segment that was 2 2_ 8 inches long. Then he extended it 3 another 2_ 8 inches. How long is the line segment now? 4_58 [Operations and Computation Goal 5] Write an equivalent fraction, decimal, or whole number. Decimal a. inches 1 Sybil drew a line segment 3_ 8 inches 3 long. Then she extended it another 2_ 4 inches. How long is the line segment now? 58 5. inches -3.49 in 104.16 100.67 83.86 45.72 55.41 42.23 51.92 77.69 74.20 60 ___ 100 d. 0.9 _ 65 100 _ 50 50 9 __ 10 61 62 6. Complete. a. b. out 87.35 c. 0.65 1.0 b. Fraction 0.60 55–57 Complete the table and write the rule. Rule: Use Math Boxes, Problem 3 to assess students’ ability to solve mixed-number addition problems. Students are making adequate progress if they are able to solve Problem 3a, which involves mixed numbers with like denominators. Some students may be able to solve Problem 3b, which involves mixed numbers with unlike denominators, by using equivalent mixed numbers with like denominators, using manipulatives, or drawing pictures. 4. _7 Math Boxes Problem 3 18 19 59 3. a. c. d. e. 3 192 5 67 in. = 7 22 ft = 1 4 1_ yd = 2 42 in.= ft 16 ft = in. ft yd ft 162–166 7 1 6 in. in. ft in. 129 Math Journal 2, p. 217F 185-218_EMCS_S_MJ2_G4_U07_576426.indd 217F Study Link 7 12a 6 3/3/11 12:39 PM INDEPENDENT ACTIVITY (Math Masters, p. 242A) Home Connection Students use number lines to multiply fractions by whole numbers. Study Link Master Name Date Time LESSON 7 12a Multiplying Fractions by Whole Numbers Use the number lines to help you solve the problems. 5 _1 1. 5 ∗ = 5 _, or 1 5 1 5 1 5 1 5 0 2. 1 5 2 5 1 5 3 5 4 5 12 _ _3 _1 3 ∗ _ = 9 , or 1 9 , or 1 3 4 9 0 4 9 3 6 5 5 4 9 6 5 3 6 8 5 9 5 10 5 4 9 18 9 3 6 3 6 6 6 0 7 5 9 9 18 _ , or 3 _3 3. 6 ∗ 6 = 6 58 1 5 3 6 3 6 12 6 18 6 Write a multiplication equation to represent the problem and then solve. _1 4. Rahsaan needs to make 5 batches of granola bars. A batch calls for 2 cup of honey. How much honey does he need? Equation: 5 ∗ _12 = _52 , or 2_12 cups 6 _ 5. Joe swims 10 of a mile 5 days a week. How far does he swim every week? Equation: 6 30 _ 5∗_ 10 = 10 , or 3 miles How far would he swim if he swam every day of the week? 6 42 2 1 5 10 10 10 Equation: 7 ∗ _ = _, or 4_, or 4_ miles Practice 1 and 5 b. Is 5 a prime number? 1 and 21; 3 and 7 no b. Is 21 a prime number? 6. a. List the factor pairs of 5. yes 7. a. List the factor pairs of 21. 242A Math Masters, p. 242A 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242A 3/23/11 12:43 PM Lesson 7 12a 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637F 637F 3/24/11 2:40 PM Teaching Master Name Date Time 3 Differentiation Options LESSON 7 12a Skip Counting by a Unit Fraction 1 1. Use your calculator to count by _2 s. Complete the table below. One _1 2. 2 Two _1 s 2 Three _1 s 2 Four _1 s 2 Five _1 s 2 Six _1 s 2 Seven _1 s 2 Eight _1 s 2 Nine _1 s 2 Ten _1 s 2 _1 _2 _3 _4 2 2 2 2 5 _ 2 6 _ 2 7 _ 2 8 _ 2 9 _ 2 10 _ 2 One _1 3. 3 Two _1 s 3 Three _1 s 3 Four _1 s 3 Five _1 s 3 Six _1 s 3 Seven _1 s 3 Eight _1 s 3 Nine _1 s 3 Ten _1 s 3 _1 _2 _3 _4 3 3 3 3 5 _ 3 6 _ 3 7 _ 3 8 _ 3 9 _ 3 10 _ 3 5 Two _1 s 5 Three _1 s 5 Four _1 s 5 Five _1 s 5 Six _1 s 5 Seven _1 s 5 Eight _1 s 5 Nine _1 s 5 Ten _1 s 5 _1 _2 5 5 3 _ 5 4 _ 5 5 _ 5 6 _ 5 7 _ 5 8 _ 5 9 _ 5 10 _ 5 8 _1 8 Three _1 s 8 Four _1 s 8 Five _1 s 8 Six _1 s 8 Seven _1 s 8 Eight _1 s 8 Nine _1 s 8 Ten _1 s 8 2 _ 8 3 _ 8 4 _ 8 5 _ 8 6 _ 8 7 _ 8 8 _ 8 9 _ 8 10 _ 8 10 Two 1 _ 10 s Three 1 _ 10 s Four 1 _ 10 s Five 1 _ 10 s Six 1 _ 10 s Seven 1 _ 10 s Eight 1 _ 10 s Nine 1 _ 10 s Ten 1 _ 10 s 1 _ 10 2 _ 10 3 _ 10 4 _ 10 5 _ 10 6 _ 10 7 _ 10 8 _ 10 9 _ 10 10 _ 10 To explore multiples of unit fractions, have students skip count on the calculator. Remind students that when you skip count by a number, your counts are the multiples of that number. Review the steps for counting by 5s on the calculator. Students can program their calculator using the following steps: 1 1 How is skip counting by _3 s on your calculator from 0 to nine _3 s the same as 1 finding the product 9 ∗ _? TI-15: 3 Sample answer: When you skip count by _13 from 0 nine times, you are finding nine groups of _1 . This is the same as 9 ∗ _31 . 1. Press On/Off and Clear simultaneously. This clears your calculator display and memory. 3 Math Masters, p. 242B 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242B 15–30 Min (Math Masters, p. 242B) 1 Use your calculator to count by _ 10 s. Complete the table below. One 1 _ 6. Two _1 s 8 SMALL-GROUP ACTIVITY Multiples of Unit Fractions 1 Use your calculator to count by _8 s. Complete the table below. One _1 5. Skip Counting to Show 1 Use your calculator to count by _5 s. Complete the table below. One _1 4. READINESS 1 Use your calculator to count by _3 s. Complete the table below. 2. Press Op1 + 5 Op1 . This tells the calculator to count up by 5s. 3/3/11 10:44 AM 3. Press 0. This is the starting number. Casio fx-55: 1. Press . This clears your calculator display and memory. 2. Press 5. This tells the calculator to count by 5s. 3. Press . This tells the calculator to count up. 4. Press 0. This is the starting number. Now the calculator is ready to count by 5s. Without clearing their calculators, have students press the Op1 key or the key. Press the Op1 key or the key repeatedly as the students count together by 5s. Next have students skip count by the unit fraction _14 . You may first need to remind students of the steps to enter a fraction on their calculators. To enter _14 : On a TI-15: 1 n 4 On a Casio fx-55: 1 d . 4. Have students skip count by unit fractions to complete the tables on Math Masters, page 242B. Afterward, discuss how Problem 6 highlights the concept that a fraction such as _93 means the same thing as 9 ∗ (_13 ). In general, _ab = a ∗ (_1b ). 637G Unit 7 Fractions and Their Uses; Chance and Probability 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637G 3/28/11 4:34 PM Teaching Master ENRICHMENT Visual Models for Multiplying SMALL-GROUP ACTIVITY Name Date Time LESSON 7 12a Addition Model for Multiplying Draw models for each product. Then add the fractions to find the product. 15–30 Min _1 + _1 = _2 3 3 3 1. 1 2 ∗ _3 = 2. 1 3 ∗ _2 = _1 + _1 + _1 = _3 2 2 2 2 3. 2 2 ∗ _5 = _2 + _2 = _4 5 5 5 4. 2 4 ∗ _3 = Sample shading is given in models. 58 a Fraction by a Whole Number (Student Reference Book, p. 58; Math Masters, pp. 242C and 242D) To extend students’ understanding of fraction multiplication, have them explore two different models: addition and area. Begin by having students read Student Reference Book, page 58. Discuss the example provided for each model as a group. Have students complete Math Masters, pages 242C and 242D. For page 242C, encourage the groups to discuss how each number in the problem was represented in the model. The whole number is the number of rectangles drawn. The denominator of the fraction is the number of equal parts each rectangle is divided into. The numerator of the fraction is the number of parts of each rectangle that are shaded. _2 + _2 + _2 + _2 = _8 3 3 3 3 3 Math Masters, p. 242C EXTRA PRACTICE ▶ 5-Minute Math SMALL-GROUP ACTIVITY 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242C 3/23/11 12:43 PM 5–15 Min To offer students more experience with multiplying fractions by whole numbers, see 5-Minute Math, pages 22 and 23. Teaching Master Name Date Time LESSON 7 12a Area Model for Multiplying For each problem, divide the model into strips, and then shade a fraction of the area to find the product. _2 _1 1. 3 of 2 square units = 1 So, _3 ∗ 2 = _1 2. 4 square unit(s) . _4 4 _4 4 square unit(s) . _6 3 of 3 square units = 2 So, _3 ∗ 3 = _3 4. 4 3 of 4 square units = 1 So, _4 ∗ 4 = _2 3. 3 3 _2 58 Sample shading is given in models. _6 3 square unit(s) . 15 _ 4 of 5 square units = 3 So, _4 ∗ 5 = 15 _ 4 square unit(s) . Math Masters, p. 242D 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242D 3/3/11 10:44 AM Lesson 7 12a 637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637H 637H 3/28/11 4:34 PM Name Date Time LESSON 7 12a Multiplying Fractions by Whole Numbers Use the number lines to help you solve the problems. 58 1. 5∗ _1 5 = 0 2. 1 5 2 5 3 5 4 5 6 5 7 5 8 5 9 5 10 5 4 3 ∗ _9 = 9 9 0 3. 5 5 18 9 3 6 ∗ _6 = 0 6 6 12 6 18 6 Write a multiplication equation to represent the problem and then solve. Copyright © Wright Group/McGraw-Hill 4. 1 Rahsaan needs to make 5 batches of granola bars. A batch calls for _2 cup of honey. How much honey does he need? Equation: 5. 6 Joe swims _ 10 of a mile 5 days a week. How far does he swim every week? Equation: How far would he swim if he swam every day of the week? Equation: Practice 6. a. List the factor pairs of 5. 7. a. List the factor pairs of 21. b. Is 21 a prime number? 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242A b. Is 5 a prime number? 242A 3/23/11 12:43 PM Name Date Time LESSON 7 12a Skip Counting by a Unit Fraction 1 1. Use your calculator to count by _2 s. Complete the table below. One _1 2. 2 Two _1 s 2 Three _1 s 2 Four _1 s 2 _1 _2 _3 _4 2 2 2 2 3 Two _1 s 3 Three _1 s 3 Four _1 s 3 _1 _2 _3 _4 3 3 3 3 Seven _1 s 2 Eight _1 s 2 Nine _1 s 2 Ten _1 s 2 Five _1 s 3 Six _1 s 3 Seven _1 s 3 Eight _1 s 3 Nine _1 s 3 Ten _1 s 3 Eight _1 s 5 Nine _1 s 5 Ten _1 s 5 Eight _1 s 8 Nine _1 s 8 Ten _1 s 8 Eight 1 _ 10 s Nine 1 _ 10 s Ten 1 _ 10 s 1 Use your calculator to count by _5 s. Complete the table below. One _1 4. Six _1 s 2 1 Use your calculator to count by _3 s. Complete the table below. One _1 3. Five _1 s 2 5 Two _1 s 5 _1 _2 5 5 Three _1 s 5 Four _1 s 5 Five _1 s 5 Six _1 s 5 Seven _1 s 5 1 Use your calculator to count by _8 s. Complete the table below. One _1 8 Two _1 s 8 Three _1 s 8 Four _1 s 8 Five _1 s 8 Six _1 s 8 Seven _1 s 8 _1 8 1 Use your calculator to count by _ 10 s. Complete the table below. One 1 _ 10 6. Two 1 _ 10 s Three 1 _ 10 s Four 1 _ 10 s Five 1 _ 10 s Six 1 _ 10 s Seven 1 _ 10 s 1 1 How is skip counting by _3 s on your calculator from 0 to nine _3 s the same as 1 finding the product 9 ∗ _? 3 Copyright © Wright Group/McGraw-Hill 5. 242B 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242B 3/3/11 10:44 AM Name Date Time LESSON 7 12a Addition Model for Multiplying Draw models for each product. Then add the fractions to find the product. Copyright © Wright Group/McGraw-Hill 58 _1 3 1. 2∗ 2. 1 3 ∗ _2 = 3. 2 2 ∗ _5 = 4. 2 4 ∗ _3 = = 242C 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242C 3/23/11 12:43 PM Name Date Time LESSON 7 12a Area Model for Multiplying For each problem, divide the model into strips, and then shade a fraction of the area to find the product. _1 1. 3 of 2 square units = 1 So, _3 ∗ 2 = _1 2. 4 _2 3. 3 . square unit(s) . of 3 square units = 2 So, _3 ∗ 3 = square unit(s) . of 5 square units = 3 So, _4 ∗ 5 = square unit(s) . Copyright © Wright Group/McGraw-Hill _3 4. 4 square unit(s) of 4 square units = 1 So, _4 ∗ 4 = 58 242D 242A-242D_EMCS_B_MM_G4_U07_576965.indd 242D 3/3/11 10:44 AM