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# Section 4.5 Plus Warm Ups

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October 15th, 2008 Lecture Notes on Reasoning Strategies with Word Problems.

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### Section 4.5 Plus Warm Ups

1. 1. Warm Ups: Find the GCF <ul><li>5a and 35a </li></ul><ul><li>6m 3 n and 8mn 2 </li></ul>
2. 2. Warm Ups: Simplest Form <ul><li>4bc/16b </li></ul><ul><li>12/16 </li></ul><ul><li>6m/15m </li></ul><ul><li>x 2 y/3yz </li></ul>
3. 3. Section 4.5: Reasoning Strategy Accounting for All Possibilities October 15 th , 2008 Notes There will be notes, so take them.
4. 4. Read, Plan, Solve… <ul><li>Find EVERY Possibility. </li></ul><ul><li>You need to be sure that you have found EVERY possible combination. </li></ul><ul><li>Organize lists and diagrams to help you keep track of possibilities as you find them. </li></ul>
5. 5. Example Problem: <ul><li>Mandy, Jim, Keisha, Darren, Lin, Chris, and Jen are friends. They want to take pictures of themselves with two people in each picture. How many pictures do they need to take. </li></ul>Jim Keisha Darren Lin Chris Jen Mandy Keisha Darren Lin Chris Jen Jim Darren Lin Chris Jen Keisha <ul><li>Complete the list of paired friends. </li></ul><ul><li>What pattern do we see? </li></ul>
6. 6. Friends and Pictures <ul><li>The first person, Mandy, takes a picture with the 6 other friends. </li></ul><ul><li>Jim takes a picture with 5 other friends. </li></ul><ul><li>Keisha takes a picture with 4 other friends. </li></ul><ul><li>3…2…1… </li></ul><ul><li>So: 6 + 5 + 4 + 3 + 2 + 1 = 21 pictures are taken. </li></ul><ul><li>This is the same as the Tennis Player Problem. </li></ul>
7. 7. Sandwiches… <ul><li>A sandwich shop serves turkey, ham, tuna, chicken, and egg salad sandwiches. You can have any sandwich using white, wheat, or rye bread. Suppose you eat there every day. For how many days can you order a sandwich that is different from any you have ordered before? Make a chart of all the possibilities. </li></ul>
8. 8. Sandwiches <ul><li>White Bread: Turkey, Ham, Tuna, Chicken, Egg Salad. (5 different sandwiches) </li></ul><ul><li>Wheat Bread: Turkey, Ham, Tuna, Chicken, Egg Salad. (5 different sandwiches) </li></ul><ul><li>Rye Bread: Turkey, Ham, Tuna, Chicken, Egg Salad. (5 different sandwiches) </li></ul><ul><li>5 + 5 + 5 = 15 different sandwiches. </li></ul><ul><li>15 Possibilities of sandwiches, 15 days of different sandwiches. </li></ul>
9. 9. Mystery Party… <ul><li>Eight people are at a party. Everyone shakes hands once with everyone else. How many handshakes are there all together? </li></ul><ul><li>Make a list or chart. </li></ul><ul><li>Solve…GO! </li></ul>
10. 10. Mystery Party… <ul><li>Person 1 shakes hands with 2, 3, 4, 5, 6, 7, and 8. </li></ul><ul><li>Person 2 shakes hands with 3, 4, 5, 6, 7, and 8. </li></ul><ul><li>Person 3 shakes hands with 4, 5, 6, 7, and 8. </li></ul><ul><li>Person 4 shakes hands with 5, 6, 7, and 8. </li></ul><ul><li>Person 5 shakes hands with 6, 7, and 8. </li></ul><ul><li>Person 6 shakes hands with 7 and 8. </li></ul><ul><li>Person 7 shakes hands with 8. </li></ul><ul><li>Person 8 has already shaken everyone else’s hands. </li></ul><ul><li>7+6+5+4+3+2+1+0 = 28 Handshakes. </li></ul>
11. 11. Change In Your Pocket. <ul><li>You have one penny, one nickel, one dime, and one quarter. How many different amounts of money can you make using one or more of these coins? </li></ul><ul><li>Make a list of all of the possibilities. </li></ul><ul><li>1 Penny, 1 Penny + 1 Nickel +…. </li></ul><ul><li>How many different combinations </li></ul><ul><li>of change can you have? </li></ul>
12. 12. Change In Your Pocket… <ul><li>1P , 1N , 1D , 1Q </li></ul><ul><li>1P+1N , 1P+1D , 1P+1Q , 1N+1D , 1N+1Q , 1D+1Q </li></ul><ul><li>1P+1N+1D , 1N+1D+1Q , 1P+1N+1Q , 1P+1D+1Q </li></ul><ul><li>1P+1N+1D+1Q </li></ul><ul><li>15 Total Combinations of Coins. </li></ul>
13. 13. Assignment #24 <ul><li>Page 189: Checkpoint 1 : 1-13 All. </li></ul><ul><li>Pages 192-193: 5, 7, 9 and 12. </li></ul><ul><li>Math Game! </li></ul>