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THE OVERLAND TRAIL VARIABLES, EQUATIONS, GRAPHS, AND RATES.

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Presentation on theme: "THE OVERLAND TRAIL VARIABLES, EQUATIONS, GRAPHS, AND RATES."— Presentation transcript:

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2 THE OVERLAND TRAIL VARIABLES, EQUATIONS, GRAPHS, AND RATES

3 w MINIMAL FAMILY w LARGE FAMILY w NON FAMILY w CONGLOMERATE FAMILY

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5 ADULT BOOT 48 INCHS ADULT SHOE 32 INCHES CHILDS BOOT 24 INCHES

6 EACH MAN NEEDS 5 YDS EACH WOMAN NEEDS 4 YDS EACH CHILD NEEDS 3 YDS

7 PROFIT = (W -.4*H) / 2 PRICE TO CROSS=.5*W+.25*M+.1*W+.05*C

8 F # OF FAMILIIES IN WAGON TRAIN 25 M # OF MEN IN A FAMILY 2

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15 FIND AS MANY POINTS ON THE GRAPH AS YOU THINK YOU NEED TO GET AN IDEA OF WHAT THE WHOLE GRAPH LOOKS LIKE.

16 LINE OF BEST FIT

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18 MAKE A GRAPH AND WRITE A REPORT

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21 BEST FIT LINE

22 WRITING EQUATIONS

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24 PT OF INTERSECTION

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28 DISTANCE TIME RATE BY A SPECIFIC DATE

29 BY A SPECIFIC PLACE DISTANCE TIME RATE

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31 DISTANCE TIME RATE

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33 PLANNING THE JOURNEY w BRAINSTORM IDEAS w PURCHASE FOOD AND SUPPLIES $10 A PERSON

34 PLANNING THE JOURNEY

35 SHOELACES w HOW MANY INCHES OF SHOELACE DOES A… WOMAN NEED? MAN? CHILD?

36 SHOELACES w FIND THE TOTAL LENGTH OF SHOELACES NEEDED FOR YOUR FAMILY.

37 LACED TRAVLERS  HOW MANY YARDS OF SHOELACE DID THE SETTLERS NEED ALTOGETHER?

38 LACED TRAVLERS  WRITE TWO MORE INTERESTING QUESTIONS AND ANSWER ONE OF THE QUESTIONS.

39 TO KEARNY BY EQUATION w FEE FOR CROSSING THE RIVER= $1 PER WAGON w FERRY CAPTAIN EARNED 40CENTS PER HOUR w A ROUND TRIP ON THE FERRY TAKES 20 MINUTES PER WAGON

40 TO KEARNY...  EXPLAIN WHY THIS FORMULA MAKES SENSE. PROFIT = (W -.4*H) / 2

41 TO KEARNY...  HOW MUCH MONEY WOULD EACH OF THE PAPAN BROTHERS MAKE FROM YOUR FAMILY?

42 TO KEARNY... w USE THIS FORMULA TO EXPLAIN WHAT VIEUX CHARGED: PRICE TO CROSS=.5*W+.25*M+.1*W+.05*C

43 TO KEARNY... w WHAT WOULD IT COST YOUR FAMILY TO CROSS THE VERMILLION RIVER?

44 w WRITE THE EXPRESSION w EXPLAIN WHAT THE EXPRESSION MEANS, USING A SUMMARY PHRASE w GIVE THE NUMERICAL VALUE OF THE EXPRESSION OX EXPRESSIONS

45 IF I COULD SEE THIS THING w 5% ADULTS WILL DIE FROM CHOLERA w 10% OF THE CHILDREN WILL DIE FROM CHOLERA

46 WAGON TRAIN SKETCHES

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50 GRAPH SKETCHES w EACH GRAPH ILLUSTRATES A RELATIONSHIP BETWEEN TWO QUANTITIES w DESCRIBE A SITUATION THAT IS ILLUSTRATED BY THE GRAPH

51 GRAPH SKETCHES

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55 GRAPH SKETCHES PART II w BEGIN WITH A SITUATION IN WHICH YOU DESCRIBE A POSSIBLE RELATIONSHIP BETWEEN TWO QUANTITIES w PUT THIS DESCRIPTION ON ONE SIDE OF A PIECE OF PAPER AND THE GRAPH ON THE OTHER.

56 IN NEED OF NUMBERS

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61 THE ISSUES INVOLVED w SHOULD THE VERTICAL AXIS ALWAYS BEGIN AT ZERO? WHAT ABOUT THE HORIZONTAL?

62 THE ISSUES INVOLVED w THE GRAPH AT THE RIGHT SHOWS THE AVERAGE HEIGHT OF BOYS IN THE US AT DIFFERENT AGES.

63 THE ISSUES INVOLVED w WHY MIGHT SOMEONE MAKE THE CONCLUSION THAT BOYS GROW AT A CONSTANT RATE?

64 THE ISSUES INVOLVED w WOULD YOU DRAW A CONTINUOUS OR A DISCRETE GRAPH TO SHOW THE # OF LIVESTOCK DEATHS DURING THE OVERLAND TRAIL TRIP?

65 SITUATIONS, GRAPHS, TABLES, AND RULES w DISCUSS HOW THE FOLLOWING RELATE TO ONE ANOTHER: A GRAPH IN OUT TABLE RULE FOR THE TABLE SITUATIONS

66 RULES, TABLES, AND GRAPHS w OUT = 4*IN - 4 w OUT = IN*IN w OUT = 550 - 20*IN

67 RULES, TABLES, AND GRAPHS w 3X + 2Y = 9 w Y^2 = X

68 PREVIOUS TRAVELERS w HOW WOULD YOU MAKE A GRAPH FOR BEANS? w HOW WOULD YOU SCALE THE AXES?

69 PREVIOUS TRAVELERS w WHERE IS THE LINE THAT COMES CLOSEST TO THE DATA? w BASED ON THE LINE OF BEST FIT, HOW MANY LBS OF BEANS WILL EACH OF YOUR OVERLAND TRAIL FAMILIES NEED?

70 SUBLETTE’S CUTOFF w BASED ON YOU GRAPH WHO DO YOU THINK WILL MAKE IT AND WHO WILL NOT?

71 SUBLETTE’S CUTOFF w IS THERE A TIME WHEN ALL THREE FAMILIES WILL HAVE ABOUT THE SAME AMOUNT OF WATER LEFT?

72 OUT OF ACTION w MARCH 20THDAY 1 w MARCH 25THDAY 6 w APRIL 1STDAY 13 w APRIL 6THDAY 18 w APRIL 18THDAY 30

73 GRAPHING CALCULATOR IN-OUTS w NUMBER OF LBS OF BEANS= 12(# OF PEOPLE) w USING YOUR GRAPHING CALCULATOR, FIND HOW MANY LBS OF BEANS 20 PEOPLE WILL EAT.

74 GRAPHING CALCULATOR IN-OUTS w IF A FAMILY BOUGHT 155 LBS OF BEANS, HOW MANY PEOPLE CAN THIS FEED?

75 GRAPHING CALCULATOR IN-OUTS w PROFIT = (W-4)/2 w HOW MUCH PROFIT WILL THE PAPANS EACH MAKE IF 25 WAGONS USE THEIR FERRY?

76 GRAPHING CALCULATOR IN-OUTS w HOW MANY WAGONS WILL HAVE TO USE THE PAPANS’ FERRY BEFORE THE PAPANS MAKE $15 EACH?

77 GRAPHING CALCULATOR IN-OUTS w Y = 3X^2 - 7X + 2

78 “OUT OF ACTION” AND “SUBLETTES CUT OFF” REVISITED w MAKE AN IN/OUT TABLE w PLOT THE DATA ON YOUR CALCULATOR w SET UP YOUR WINDOWS USING YOUR IN/OUT TABLE

79 “OUT OF ACTION” AND “SUBLETTES CUT OFF” REVISITED w MARCH 20TH55 FT LBS w MARCH 25TH90 FT LBS w APRIL 1ST140 FT LBS w APRIL 6TH185 FT LBS

80 “OUT OF ACTION” AND “SUBLETTES CUT OFF” REVISITED w GUESS AND CHECK FINDING THE BEST FIT LINE

81 BIDDY MASON w PICK OUT A SUPPLY ITEM, AND DECIDE HOW MUCH OF THAT ITEM YOU HAVE AT THE TIME YOU MEET THIS FAMILY. w PICK A REASONALBE AMOUT THAT WILL LAST 20 DAYS.

82 BIDDY MASON w FIGURE OUT HOW MUCH OF THE SUPPLY ITEM THERE IS PER PERSON FOR YOUR OVERLAND TRAIL FAMILY.

83 BIDDY MASON w YOU MEET A FAMILY THAT CONSISTS OF FOUR PEOPLE. w HOW MUCH WILL THERE BE PER PERSON IF YOU LET THIS FAMILY JOIN YOU?

84 BIDDY MASON w WHAT IF THE FAMILY HAD SIX PEOPLE? w FIND AN EQUATION THAT GIVES THE AMOUNT YOU WILL HAVE FOR EACH PERSON.

85 FAIR SHARE ON CHORES w HOW LONG WOULD YOU SUGGEST THAT EACH TYPE OF SHIFT BE? FIND THREE DIFFERENT PAIRS OF ANSWERS

86 FAIR SHARE ON CHORES w LET G REPRESENT THE LENGTH OF EACH GIRLS SHIFT AND B REPRESENT EACH BOY’S. w WRITE AN EQUATION EXPRESSING THE FACT THAT THE TOTAL OF ALL THEIR SHIFTS IS TEN HRS.

87 FAIR SHARE ON CHORES w EXPRESS B IN TERMS OF G w THAT IS WRITE AN EQUATION THAT BEGINS “B=…” AND HAS AN EXPRESSION USING G ON THE RIGHT OF THE EQUAL SIGN.

88 FAIR SHARE ON CHORES w GRAPH THE FUNCTION ON YOUR CALCULATOR w FIND THREE MORE PAIRS OF POSSIBLE SHIFT LENGTHS FROM YOUR GRAPH

89 FAIR SHARE FOR HIRED HANDS w SUGGEST THREE POSSIBLE COMBINATIONS OF WEEKLY PAY RATES. w PLOT ALL THREE COMBINATIONS USING X FOR THE PAYRATE OF AN INEXPERIENCED WORKER AND Y FOR EXPERIENCED

90 FAIR SHARE FOR HIRED HANDS w DESCRIBE IN WORDS HOW YOU COMPUTE THE EXPERIENCED PAY RATE IF YOU KNOW THE INEXPERIENCED PAY RATE w WRITE AN EQUATION GIVING Y IN TERMS OF X

91 MORE FAIR SHARE ON CHORES w WHAT ARE SOME POSSIBLE SHIFT LENGTHS IN WHICH A BOY WORKS A HALF HOUR LONGER THAN A GIRL? GIVE FOUR POSSIBILITIES

92 MORE FAIR SHARE ON CHORES w WRITE AN EQUATION IN WHICH G REPRESENTS THE EACH GIRLS SHIFT AND B REPRESENTS EACH BOYS SHIFT w GRAPH YOUR EQUATION

93 MORE FAIR SHARE ON CHORES w FIND A PAIR OF SHIFT LENGTHS THAT WOULD TOTAL TEN HOURS AND STILL HAVE THE SHIFT OF EACH BOY BE HALF AN HOUR LONGER THAN EACH GIRL.

94 MORE FAIR SHARE FOR HIRED HANDS w WRITE AN EQUATION FOR YOUR GRAPH w FIND A SET OF PAY RATES THAT WOULD MAKE THE TOTAL WEEKLY PAY FOR THE HIRED HANDS APPROXIMATELY $30

95 MORE FAIR SHARE FOR HIRED HANDS w MAKE SEVERAL SUGGESTIONS OF WAYS THE FULKERTHS COULD SET UP THE TWO PAY RATES w GRAPH THIS DATA

96 WATER CONSERVATION w THE STEVENS FAMILY STARTED WITH 50 GALLONS HOW MANY GALLONS WOULD THEY HAVE LEFT AFTER THREE DAYS? EIGHT DAYS? TWELVE DAYS X DAYS?

97 WATER CONSERVATION w THE MUSTER FAMILY HAD 100 GALLONS HOW MANY GALLONS WOULD THEY HAVE AFTER THREE DAYS? EIGHT DAYS? TWELVE DAYS? X DAYS?

98 WATER CONSERVATION w IS THERE A TIME WHEN BOTH FAMILIES WOULD HAVE THE SAME AMOUNT OF WATER LEFT?

99 WATER CONSERVATION w IN HOW MANY DAYS WOULD EACH FAMILY RUN OUT OF WATER?

100 THE BIG BUY w WRITE TWO SEPARATE EQUATIONS FOR JILLIAN AND SEVE. JILLIAN’S EQUATION Y=10 + 5X SEVE’S EQUATION Y = 40 + 3X

101 THE BIG BUY w IF THE GRAPHING CALCULATOR COSTS $72 WHO WILL BE ABLE TO BUY ONE WITH THE LEAST WORK TIME?

102 THE BIG BUY w IF THE GRAPHING CALCULATOR COSTS $100 WHO WILL BE ABLE TO BUY ONE WITH THE LEAST WORK TIME?

103 THE BIG BUY  FOR WHAT PRICE MUST THE CALCULATOR SELL IN ORDER FOR JILLIAN AND SEVE TO EARN THAT AMOUNT WITH THE SAME NUMBER OF HOURS OF WORK?

104 CATCHING UP...BY A SPECIFIC DATE w HOW MANY DAYS DO YOU HAVE TO CATCH UP? w HOW FAR WILL YOUR COUSIN’S FAMILY TRAVEL?

105 CATCHING UP...BY A SPECIFIC DATE w WHAT DISTANCE DO YOU HAVE TO TRAVEL AND IN HOW MANY DAYS WILL YOU HAVE TO TRAVEL THAT DISTANCE?

106 CATCHING UP...BY A SPECIFIC PLACE w HOW MANY HOURS WILL IT TAKE THE WAGON TRAIN TO TRAVEL 80 MILES? w HOW MANY HOURS DO YOU HAVE TO CATCH UP?

107 CATCHING UP...BY A SPECIFIC PLACE w HOW FAST WILL YOU HAVE TO GO IN ORDER TO MEET UP WITH THE WAGON TRAIN IN RENO?

108 WATER FOR ONE MORE w NUMBER OF PEOPLE IN EACH FAMILY CONGLOMERATE NON FAMILY LARGE MINIMAL

109 WATER FOR ONE MORE w IF YOU HAVE THREE GALLONS PER PERSON FOR YOUR FAMILY: HOW MANY GALLONS DO YOU HAVE ALTOGETHER FOR YOU FAMILY?

110 WATER FOR ONE MORE w HOW MUCH WATER CAN YOU ALLOW PER DAY FOR EACH PERSON WITH THE ADDITION OF ONE MORE PERSON?

111 WATER FOR ONE MORE w SUPPOSE THERE WERE 10 PEOPLE IN YOUR FAMILY, HOW MUCH WATER WOULD YOU HAVE PER PERSON IF YOU INCLUDED THE STRAGGLER?

112 WATER FOR ONE MORE w SUPPOSE THERE WERE 20 PEOPLE IN YOUR FAMILY, HOW MUCH WATER WOULD YOU HAVE PER PERSON IF YOU INCLUDED THE STRAGGLER?

113 WATER FOR ONE MORE w SUPPOSE THERE WERE X PEOPLE IN YOUR FAMILY, HOW MUCH WATER WOULD YOU HAVE PER PERSON IF YOU INCLUDED THE STRAGGLER?

114 CATCHING UP BY SATURDAY NIGHT w POSSIBLE QUESTION TO HELP GET YOU STARTED: HOW MANY HOURS A DAY WILL YOU HAVE THE WAGON TRAIN TRAVEL?

115 CATCHING UP AT AUBURN w ROLL A DIE FOUR TIMES TO FIND THE WAGON TRAIN’S RATE

116 CATCHING UP AT AUBURN w HOW MANY DAYS WILL YOU BE VISITING JAMES P. BECKWOURTH? w HOW MANY DAYS DO YOU HAVE TO CATCH UP TO THE WAGON TRAIN?

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