Exploring Fraction Division: Why We Flip and Multiply
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- Annice Wiggins
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1 The Reading Club is hosting a pizza party for all students at Central Middle School who have read at least ten books this semester. Help them decide how many pizzas they should order if they are expecting 150 students to attend the party. They predict that each student will want to eat one-third of a pizza for lunch. Use your pizza pieces to complete the table. # of Pizzas Serving Size = Picture/Process # of Servings 1 How many are in 1 pizza? pizza servings
2 Use the results from your table to answer the following questions: 1) How many servings of pizza could they get from 10 pizzas? 2) How many pizzas do they need to order for 150 students if each student gets of a pizza? 3) The club president doesn t want to order that many pizzas. She suggests they limit each person to of a pizza. How many servings can they get from 1 pizza? Include a sketch in your explanation. 4) How many pizzas do they need to order for 150 students if each student gets of a pizza? 2
3 Summary: 5) The process of dividing a pizza into servings of pizza can be written symbolically as. Since there are 3 servings of pizza in one whole pizza, we know that. a) How many thirds are in 2 pizzas? So, =. b) How many thirds are in 8 pizzas? So, =. c) How many thirds are in one-third of a pizza? So, =. d) How many thirds are in one-half of a pizza, including part of a serving of size one-third? So, =. e) How many thirds are in one-fourth of a pizza? (Be sure to include partial servings). So, =. 6) Explain how to divide a number by a unit fraction like 3
4 The treasurer complains that 1/6 of a pizza is not enough, and besides, the pizzeria cuts each pizza into 8 slices and not 6. He suggests they allow each student to have 3/8 of a pizza. Use this information to complete the table. Include partial servings in your answer. # of Pizzas Serving Size = Picture/Process # of Servings 1 How many pizza servings are in 1 pizza? ) About how many pizzas should they order for all 150 students if each student is served 3/8 of a pizza? 4
5 Summary: 8) The process of dividing a pizza into servings of pizza can be written symbolically as. Since there are servings in one whole pizza, we know that. Rewriting the mixed number as an improper fraction, we see that. Use the idea that 1 pizza has of a group (serving) of to answer the following questions. Write any mixed numbers as improper fractions. a) How many are in 2 pizzas? So, =. b) How many are in 3 pizzas? So, =. c) How many are in five pizzas? So, =. d) How many would there be in one-half of a pizza, including part of a serving of size one-third? So, =. e) How many are in one-fourth of a pizza? (Be sure to include partial servings). So, =. 9) Describe how to divide a number by a non-unit fraction like 3/8. 5
6 The secretary is making bookmarks for each of the children out of lengths of ribbon donated by ClothMart. Use fraction strips to help you determine the number of bookmarks she can cut each piece of ribbon. She starts with a piece of ribbon that is If each bookmark needs to be long. long, then she can cut whole bookmarks, with of ribbon leftover. She could cut another part of a bookmark from the leftover ribbon. So would make bookmarks (including partial bookmarks). Complete the table to help her decide how many bookmarks she can cut from each piece of ribbon based on the lengths provided. Leave the last column blank for now. Length of Ribbon Length of Bookmark # of Whole Bookmarks Length of Leftover Ribbon Part of a Bookmark Division Sentence 2 bookmarks bookmark 10) Notice the secretary was able to make 2 or more bookmarks from each piece of ribbon but always had ribbon leftover (remainder) that was too short to make another whole bookmark. Therefore, the answer to each of these division problems could be written as a mixed number. Complete the last column in the table by writing the answer (# of bookmarks) as a mixed number. Does the fractional part of each mixed number answer refer to the length of leftover ribbon or to part of a bookmark? 6
7 Using a Ruler: Many word problems involving fraction division can be solved using a ruler. Try these sample problems. Start by drawing a segment that has the same length as the dividend. Then determine how many groups of the divisor are in the dividend by marking off segments that are the same length as the divisor. Be careful with the remainder! 11) I have 5 ½ s of ribbon. If each bow requires 1 ½ s of ribbon, how many bows can I make? To solve, let 1 inch represent 1 of ribbon. Draw a 5 ½ inch-long segment. Mark the segment every 1 ½ inches to determine the number of bows I can make. # of bows: (include part of a bow in your answer) Number Sentence: 5 ½ 1 ½ = 12) Ari is making root beer. His recipe makes 4 ¾ gallons of root beer. How many ½ gallon bottles can he fill? # of bottles of root beer: (include part of a bottle in your answer) Number Sentence: 7
8 13. Are these division problems for? For those that are, which interpretation of division is used (measurement or partitive division). For those that are not, determine how to solve the problem if it can be solved. a) Beth poured ¾ cup of cereal in a bowl. The cereal box says that one serving is ½ cup. How many servings are in Beth s bowl? b) Beth poured ¾ cup of cereal in a bowl. Then Beth took ½ of that cereal and put it into another bowl. How many cups of cereal are in the second bowl? c) If ¾ cup of flour makes ½ batch of cookies, then how many cups of flour are required for a full batch of cookies? d) If ½ cup of flour makes a batch of cookies, then how many batches can you make with ¾ cup of flour? e) If ¾ cup of flour makes a batch of cookies, then how much flour is in ½ of a batch of cookies? The last problem (#13) was adapted from Beckman, S. (2008). Activities to accompany mathematics for elementary teachers. Boston: Pearson. 8
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Breaking News English.com Ready-to-Use English Lessons by Sean Banville 1,000 IDEAS & ACTIVITIES FOR LANGUAGE TEACHERS breakingnewsenglish.com/book.html Thousands more free lessons from Sean's other websites
Lesson 13: Finding Equivalent Ratios Given the Total Quantity
Name: Hr: Classwork Example 1 A group of 6 hikers are preparing for a one-week trip. All of the group s supplies will be carried by the hikers in backpacks. The leader decided that it would be fair for
Did you know there are specific varieties of apples used to make applesauce?
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STACKING CUPS STEM CATEGORY Math TOPIC Linear Equations OVERVIEW Students will work in small groups to stack Solo cups vs. Styrofoam cups to see how many of each it takes for the two stacks to be equal.