USM Summer Math Institute Co-Sponsored by Institutions of Higher Learning (IHL) U.S. Department of Education (No Child Left Behind Funding) The Center for Science and Mathematics Education The Department of Mathematics College of Science and Technology College of Education and Psychology Day TwelveSpreadsheet Farmer Brown and working backwards to solution

USM Summer Math Institute Your Mathematics Instructors, Staff and Partners Ms. Michelle Green, Co-Director and Co- Instructor for (SM) 2 I –Stringer Attendance Center –National Board Certified/Early Adolescence – Phone 601- Dr. Myron Henry, Director and Co-Instructor for (SM) 2 I –Department of Mathematics and the Center for Science and Mathematics Education –Johnson Science Tower 314 – Phone or All Participants (that’s you)

3 Jobs are changing….Education must keep up. Teachers must show students through example that learning is a life long process.

4 3. Backwards to a Solution. Day Twelve of the (SM) 2 I 1. Choose the best plan for you. 2. Farmer Brown and Chickens

5 Cellular Phone Problem Plan A is $20 per month and cost $0.30 per minute with no free minutes. Plan B is $8 per month and cost $0.50 per minute with no free minutes. Joe is a traveling salesman and his income is directly effected by his contacts Sue has a full time job at home, but occasionally travels and would like a cell phone for safety reasons. Which plan should Joe choose? What about Sue? Why?

6 Lets set it up! After all, each plan is just an equation! What determines how much your bill is? Your monthly charge The number of minutes that you talk What will change each month? The number of minutes that you talk X = minutes …. So let’s set up our equations

7 Equations Plan A –Total Bill (Y) = $20 + $0.30 ·X Plan B –Total Bill (Y) = $8 + $0.50 · X Now put them in your to find the best plan. How many minutes have to be used so that both plans cost the same? Don’t forget to choose your window according to the problem!

8 Both plans are $38 if you talk for 60 minutes.

9 What does it all mean? Why should Sue choose this plan? Why should Joe choose this plan?

10 Farmer Brown and Chickens 1.Roosters cost $5. ($3) 2.Hens cost $1. ($1) 3.Chicks (Biddies) cost $.05. ($.10) 4.Farmer Brown must spend $ Farmer Brown must purchase 100 chickens. 6.Farmer Brown must purchase at least one of each type. 7.How many of each type can Farmer Brown buy?

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14 Now to another spreadsheet!

15 Backwards to a Solution! Alias Traveling on the Wabash Cannonball 7 th Grade: Writes and solves equations that represent problem solving situations. 5 th Grade: Solves multi-step word problems using four basic operations (SM) 2 I Day Twelve (continued)

16 A number of passengers board the Wabash Cannonball at its starting point P. At the first stop (S 1 ) a third of these passengers leave the train, and 40 new passengers climb aboard. At the second stop (S 2 ), a quarter of those on board get off, and 52 new passengers get on. At the third stop (S 3 ), a fifth of the passengers get off and 35 new passengers board the train. The fourth stop is the end of the line (E), and 163 passengers arrive there. How many passengers were on the Wabash Cannonball at its starting point? Did the Wabash Cannonball go through Peru, IN? What river is the Wabash Cannonball named after.

17 P S2S2 S1S1 S3S3 E

18 A number of passengers board the Wabash Cannonball at its starting point P. At the first stop (S 1 ) a third of these passengers leave the train, and 40 new passengers climb aboard. At the second stop (S 2 ), a quarter of those on board get off, and 52 new passengers get on.

19 At the third stop (S 3 ), a fifth of the passengers get off and 35 new passengers board the train. The fourth stop is the end of the line (E), and 163 passengers arrive there. How many passengers were on the Wabash Cannonball at its starting point?

passengers were on board the Wabash Cannonball initially. This is an example of solving a word problem by working backwards, an important technique for problem solving. Try number ten on the test using this approach.

21 The Wabash Cannonball Through Peru By John W. Daly and Myron S. Henry

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25 A number of passengers board the City of New Orleans passenger train at its origin, Chicago, IL. At the first stop (Centralia, IL, 30% get off the train and 26 new passengers board the train. At the second stop (Memphis, TN), 25% of the passengers leave the train and 51 new passengers board. At the third stop (Jackson, MS), 60% of the passengers get off and 10 new passengers get on. The fourth stop is New Orleans, the end of the line, and all 76 passengers disembark. How many passengers boarded the City of New Orleans at its city of origin, Chicago, IL. ityneworl htmlwww.streamlinerschedules.com/concourse/track1/c ityneworl html Backwards to a Solution? Again?

26 Backwards to a Solution? (Again) 2 ? After shopping in three Peru stores, Jane spent all but $3 of what was in her purse initially. If in each store she spent $5 more than half of what she had when she entered the store, how much money did Jane have in her purse when she started her shopping spree? (Hint: Let S 3 be the amount Jane had left in her purse when she entered store three and work backward.)

27 West Jasper implements pit crews for teachers. You think there is a grant out there for this????

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31 Backwards to a Solution! (Again) 2 !