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Mathematical Modeling

Mathematical Modeling . Various ways to represent the same mathematical expression or situation. Compare to Vocabulary. Cést Domage = that’s too bad cierra la boca por favor = close your mouth please a lot = plethora = myriad = surfeit. 1.

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Mathematical Modeling

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  1. Mathematical Modeling Various ways to represent the same mathematical expression or situation

  2. Compare to Vocabulary Cést Domage = that’s too bad cierra la boca por favor = close your mouth please a lot = plethora = myriad = surfeit 1

  3. Now let’s look at math terms – copy these in your notebook, please. • plus + • Is less than < • Is greater than > • two times a number 2A • The next 2 are “switcheroos” – they go at the end of the expression • less than - 7 less than 12 12-7 • more than + 4 more than 5 5+4

  4. More terms - copy these also, por favor.

  5. Take it one step at a time • 4 more than 3 times a number • 4 more than --> +4 2

  6. Keep Going4 more than 3 times a number • 4 more than +4 • 3 times a number • let A represent “a number” • 3A 3

  7. Put it all together now4 more than 3 times a number • 4 more than +4 • 3 times a number 3A • new model • 3A +4 • 4+3A this would give you the correct math answer but would NOT be written correctly. Remember more than is a switcheroo! 4

  8. Multiple ways to graph the same information 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr East 20.4 27.4 90 20.4 West 30.6 38.6 34.6 31.6 North 45.9 46.9 45 43.9 5

  9. Change a word problem to a math expression A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile. Write a math expression to indicate a taxi trip of “n”miles 6

  10. A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile. Follow the steps. a taxi trip of “n”miles = $ 7

  11. A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile, First 1/10 of a mile = 4.95 4.95 + 8

  12. A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile. .95 for each additional 1/10 of a mile How many tenths of a mile do we have? 10N = tenths of a mile 9

  13. A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile. .95 for each additional 1/10 of a mile How many additional 1/10 of miles do we have? (10n-1) --> We were charged 4.95 for the very first 1/10 of a mile. 10

  14. A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile .95 for each additional 1/10 of a mile (10n-1) .95 # of tenths of a mile times .95 11

  15. A taxi charges 4.95 for the first 1/10 of a mile and .95 for each additional 1/10 of a mile. Put it all together now. $ = 4.95 + (10n-1).95 or cost for n miles = $4.95 + .95(10n-1) 12

  16. -3 -2 -1 0 1 2 3 X < 2 13

  17. Mathematical Modeling Various ways to represent the same mathematical expression or situation 15

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