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MULTIPLICATION 4.NF.4 of Whole Numbers Times Unit Fractions 01* Multiplication Purpose: Materials: To illustrate and compute products of whole numbers times unit fractions Fraction Bars and "Blank Bars Race Tracks" (attached) TEACHER MODELING/STUDENT COMMUNICATION Activity 1 Using visual fraction models 1. Give the following information: pencils and paper Fraction Bars Armari wants to make a batch of chocolate chip cookies and needs 1/3 cup of chocolate chips. a. How can the information in the problem be represented by a visual fraction model? (One possibility is to use a bar with three equal parts to represent 1/3 cup. In general, the model could be any diagram with three equal parts.) b. If Armari makes two batches of chocolate chip cookies, what fraction of a cup of chocolate chip cookies will be needed? (2/3 cup.) c. If Armari decides to make four batches of chocolate chip cookies, what amount of chocolate chips will be needed? (4/3 cups or 1 1/3 cups.) d. How can this information be represented by an addition equation? (1/3 + 1/3 + 1/3 + 1/3 = 1 1/3. By a multiplication equation? (4 × 1/3 = 1 1/3.) Discuss that repeated addition can be represented by multiplying by a whole number. e. How can your visual fraction model help to show that 4 × 1/3 = 1 1/3? ) Discuss the following two methods with the bars. Method 1: Using two blank bars with 3 equal parts, each part can be labeled with one of the numbers #1, #2, #3, and #4 for the 4 batches of cookies to show the total is 1 whole bar and 1/3 of a bar. pencils and paper Method 2: Placing the shaded amount of four copies of the 1/3 bar end-to-end shows that the total shaded amount is 1 1/3 bars. Discuss the similarity between illustrating the product of a whole number times a whole number and the product of a whole number times a fraction. In both cases we use multiplication in place of repeated addition. For example, 7 + 7 + 7 + 7 = 4 × 7; and 1/3 + 1/3 + 1/3 + 1/3 = 4 × 1/3. In both examples, the first factor 4 in the product indicates the number of times the second factor should occur. 1 whole bar 1 3 + 1 3 + 1 3 + 1 3 =1 1 3 Blank Bars Race Tracks pencils and paper 2. Distribute copies "Blank Bars Race Tracks" and ask each student to complete activity #1. Discuss results. 3. Activities 2, 3, and 4 on this sheet involve race tracks for eighths bars, fifths bars, and thirds bars. It is best if students work in pairs or small groups and each student uses their own copy of the Blank Bars Race Track. Students will need some method of randomly selecting one of the numbers from 1 through 6, and this can be done by rolling a die. Each student in turn rolls a die for a number, writes one type of letter on the parts of the bar for the number they obtained, writes the number from the die in a box beneath the bars, and then completes the equation. For each new turn, a different letter should be used in the parts of the bars as a record for checking the equations. Continue taking turns until someone reaches the End or goes beyond. After completion of each racetrack, discuss the results. You might ask questions, such as: What is the fewest number of turns for finishing the race track? (Eighths Track, 5 turns; Fifths Track, 3 turns; and Thirds Track, 2 turns.) Will a race usually be faster on the eighths track or the fifths track? (Fifths Track.) etc. Students might want to design a racetrack that uses a variety of different types of zero bars. Activity 2 Solving word problems 1. If Peyton practices on the drums for 1/5 hour each day for 4 days, what is the total amount of time spent practicing? 2. At a construction site, each hole being dug for posts requires 1/4 ton of dirt. If each hole is the same size, how much dirt is required to fill 7 holes? 3. If one-tenth of each day at a summer camp is spent in boating activities, how much time is spent in boating activities for each 7-day week? 4. Jamie runs around a racetrack, and each lap of the track is 1/8 mile. To remember how many times she has run around the track, Jamie picks up a small pebble for each lap completed. One day she picked up 25 pebbles. What was the distance Jamie ran on the track for that day? Activity 3 Computing products Here are some products for practice. If the product is greater than 1, write the answer as a mixed number. 1. 4× 5. 8 × 1 3 2. 15 × 1 12 3. 1 5 6. 11 × 1 4 7. 20 × 9× 1 2 1 14 INDEPENDENT PRACTICE and ASSESSMENT Worksheet 4.NF.4 #1 10 × 1 6 8. 12 × 1 8 4. 4.NF.4 Name: Date:____________________ Blank Bars Race Tracks 1. Leighton uses 1 4 of a pound of butter in making one batch of popcorn. Shade parts of the following bars to represent the amount of butter for making 5 batches of popcorn and write the fraction for the total amount to the right of the bars. ____ a. Complete the addition equation to show the amount of butter used for making 5 batches of popcorn. 1 4 + 1 4 + 1 4 + 1 4 + 1 4 = b. Write a multiplication equation to show the total amount of butter Leighton used for making 5 batches of popcorn. 2. Three racetracks are shown in parts a, b, and c. Roll a die, and beginning at the Start, write the letter B in each part of the bar for the number you obtained on your die. On your second turn, write the letter C in the parts of the bar, and so forth, until you reach the End of the bar. After each of your turns, complete the multiplication to show the results of your turn. a. Eighth Race Track: Start End Turn #1: × 1 8 = Turn #2: × 1 8 = Turn #3: × 1 8 = Turn #4: × 1 8 = Turn #5: × 1 8 = Turn #6: × 1 8 = b. Fifths Race Track: Start End Turn #1: × 1 5 = Turn #2: × 1 5 = Turn #3: × 1 5 = Turn #4: × 1 5 = Turn #5: × 1 5 = Turn #6: × 1 5 = c. Thirds Race Track: Start Turn #1: End × 1 3 = Turn #2: × 1 3 = Turn #3: × 1 3 = Turn #4: × 1 3 =