Practical Application Problem

1. Practical Application Problem The Chocolate Dilemma

2. Have you ever had a problem figuring how much each person should get when you want to share things with your friends and family? • This kind of problem can be called a sharing problem. What you know about fractions can help you solve sharing problems. • Let’s try a few sharing problems. • You know that the bottom number of a fraction tells how many parts to make in each whole, and the top number tells how many parts we use. • If you want to apply what you have learned to a chocolate bar it would work like this.

3. You have one “Crunchy Delight” chocolate bar and you have 2 friends you want to share it with. • How many pieces would you cut the bar into so that you and each of your friends would get the same size of piece? • Yes, 3. So in a fraction where does the 3 go? • That’s right, the 3 goes on the bottom. 3 • How many pieces would each person get? • Yes, 1. • The 1 goes on the top. So each person would get 1 of the candy bar and 3 3 or the whole bar would be eaten by you and your friends. 3

4. But, let’s say that one of your friends says he doesn’t like chocolate so you get his piece too. You would then have 2 pieces or 2 of the bar and your 3 other friend would get 1 piece or 1 of the bar. 3

5. YOUR TURN • Draw a rectangle to represent a “Crunchy Delight” chocolate bar. • Use the rectangle to show how you would share a chocolate bar with 5 of your friends. (Don’t forget to save some for yourself.) • What size of a piece would each person get? • 1 6 1 2 3 4 5 6

6. 1 2 3 4 5 6 How much of the “Crunchy Delight” would be eaten? • Yes, 6 6 , or the whole bar.

7. Let’s try another one. • This time you get two “Crunchy Delights” so draw 2 rectangles. • Draw lines on the chocolate bars to show how you would cut the bars so you could share the 2 “Crunchy Delights” equally with 5 friends. • One possible solution is to divide each bar into thirds. • How much of the bar would each person get? • That’s right, 1 . • 3

8. By cutting each bar into 3 pieces; you get 6 pieces, 1 for you and 1 piece for each of your 5 friends. • We put a 3 on the bottom because we cut each bar into 3 parts, and we put a 6 on the top because we used 6 pieces. You and your friends ate 6 . 3 • You know that 6 is more than 1. 6 is the same as 2. 33

9. Let’s try one more. This time you only get one bar. Draw a rectangle to represent your candy bar. You are with 3 friends but you promised to save a piece of chocolate for your teacher. • Draw lines to show how you would cut the bar.

10. You should have cut the bar into 5 pieces. 1 for you, 1 for each of your 3 friends, and 1 for your teacher. • Shade in the parts of the bar that you are going to eat now with your friends. What fraction of the bar is that? • That’s right, 4 . 5 • What fraction of the bar are you saving for your teacher? • Yes, 1 . 5 1 2 3 4 5

11. In the problems we have just worked everything came out evenly just by cutting the chocolate bars into enough pieces so that each person could have an equal share. Sometimes it doesn’t work out quite that easily. • For example, what if your mother gave you and your 2 sisters 2 candy bars to share? How could you divide the 2 bars so that the 3 of you could each have an equal share? • Here is one way you could solve this problem. • Since there are 3 of you to share with, begin by cutting each bar into 3 pieces.

12. What number would go on the bottom of the fraction that represents the 2 bars? • Good, 3 because we cut each bar into 3 pieces. 3 • What number would go on the top? • Right, 6 because we have 6 pieces, so the fraction is 6 3 • Now each person can have 2 of the pieces or 2 of a bar. 3

13. Let’s try Another One • What if your mother gave you and your 4 friends 3 bars of chocolate to share? How could you cut the 3 bars so that each of you would get equal amounts? • Since there are 5 of you cut each bar into 5 pieces. • Divide the bars into 5 pieces. • In a fraction what number would go on the bottom? • Yes, 5 because we cut each bar into 5 pieces. 5

14. What number would go on the top? • Yes, 15 because we now have 15 pieces. 15 5 • How many pieces will each person get? • That’s right, each person will get 3 pieces or 3 of a bar. 5 • For now we have only looked at one way to solve these problems. Later in this program you will learn other ways to solve sharing problems.

15. Independent Practice Sally’s mom gave her a “Hunk of Chocolate” bar and told her to share it with her two brother and 2 sisters. What fraction of the bar would each child get? Answer: Divide the bar into 4 equal parts because there are four children. Each child would get 1 of the bar. 4

16. Marty has two “Creamy Chocolate” bars and wants to make them last for 4 days. What fraction of a bar could Marty eat everyday? Answer: • Divide each bar into 2 equal parts. That makes 4 . 2 Marty could eat 1 of a bar each day for 4 days. 2

17. Challenge Problem Fred bought 3 “Nutty Chocolate” bars to share with his 2 friends at a sleepover. When he got to his friends house for the sleepover there were 3 boys there. How could Fred divide the 3 bars evenly between the 4 boys at the sleepover? • What fraction of a bar would each boy get? Show Your Work Answer: 3 of a bar 4 Possible solutions: Divide each bar into 4 parts. Give each boy ¼ from each of the 3 bars so each boy would get ¾ of a bar.

18. Now you get to try your hand at writing sharing problems. • Begin by thinking of a situation where something needs to be cut-up for sharing. Write a short story giving information about what is being shared and who is sharing it. • End your story with a question that could be answered with a fraction. Write 2 sharing problems in the space below. • After writing your problems turn you paper over and write the solution to the problems on the back of this page. Be sure to show any drawings or steps that could be used to help solve your problems.