1. Little Big League Working with Fractions

2. Little Big League2 Please go to http://www.math.harvard.edu/~knill/mathmovies/swf/league.html to view a short clip from the 1994 movie “Little Big League”, starring Luke Edwards and featuring Jonathan Silverman.

3. Little Big League3

4. 4 The Problem Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together?

5. Little Big League5 An Estimate Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together? If they each took 3 hours to paint the house, it would take 1½ hours if they worked together. If they each took 5 hours to paint the house, it would take 2½ hours if they worked together. The correct answer must be somewhere between 1½ and 2½ hours – roughly 2 hours (give or take a bit).

6. Little Big League6 Does the answer look reasonable? Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together? If they each took 3 hours to paint the house, it would take 1½ hours if they worked together. If they each took 5 hours to paint the house, it would take 2½ hours if they worked together. The correct answer must be somewhere between 1½ and 2½ hours – roughly 2 hours (give or take a bit). Some of the answers given in the video make no sense at all! 3 x 5 = 15 hours3 + 5 = 8 hours (3 + 5) ÷ 2 = 4 hrs

7. Little Big League7 Right, now let’s work out the exact answer. Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together? Joe can paint 1 / 3 of the house in an hour. Sam can paint 1 / 5 of the house in an hour. Together, they can paint ( 1 / 3 + 1 / 5 ) of the house each hour.

8. Little Big League8 1 / 3 + 1 / 5 = ? 1 3 1 5 ? ?

9. Little Big League9 1 / 3 + 1 / 5 = ? 5 15 3 ? ?

10. Little Big League10 1 / 3 + 1 / 5 = 5 / 15 + 3 / 15 = 8 / 15 5 15 3 8

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12. Little Big League12 Right, now let’s work out the exact answer. Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together? Joe can paint 1 / 3 of the house in an hour. Sam can paint 1 / 5 of the house in an hour. Together, they can paint 8 / 15 of the house each hour.

13. Little Big League13 7½ is a half of 15; 8 is a little over ½ of 15 Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together? Together, they can paint 8 / 15 of the house each hour. They paint a little over ½ the house in an hour, so will take a little under 2 hours to paint the whole house.

14. Little Big League14 1 ÷ 8 / 15 = ? 1 8 / 15

15. Little Big League15 1 ÷ 8 / 15 = ? 1 8 / 15

16. Little Big League16 1 ÷ 8 / 15 = 1 7 / 8 1 8 / 15 1 lot of 8 / 15 7 / 8 of 8 / 15

17. Little Big League17 1 ÷ 8 / 15 = 1 / 1 x 15 / 8 = 1 7 / 8 1 8 / 15 1 lot of 8 / 15 7 / 8 of 8 / 15

18. Little Big League18 Back to finding the exact answer: Joe can paint a house in 3 hours. Sam can paint the same house in 5 hours. How long will they take to paint the house if they work together? Together, they can paint 8 / 15 of the house each hour. They paint a little over ½ the house in an hour, so will take a little under 2 hours to paint the whole house. They would take 1 7 / 8 hours to paint the house.

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20. Little Big League20 References / Sources: http://www.math.harvard.edu/~knill/mathmovies/swf/ league.html http://www.muzic.com/frames.php?target=http://mp3 4u.muzic.com/posting/5044&domain=mp34u&xmlURL= http://www.muzic.com/player/Posting/5044 http://www.youtube.com/watch?v=VnOlvFqmWEY