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

2. OVERLAND TRAIL FAMILIES
MINIMAL FAMILY
LARGE FAMILY
NON FAMILY
CONGLOMERATE FAMILY

3. PLANNING FOR THE
LONG JOURNEY

4. SHOELACES
ADULT BOOT 48 INCHS
ADULT SHOE 32 INCHES
CHILDS BOOT 24 INCHES

5. LACED TRAVLERS
EACH MAN NEEDS 5 YDS
EACH WOMAN NEEDS 4 YDS
EACH CHILD NEEDS 3 YDS

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

7. OX EXPRESSIONS
F # OF FAMILIIES IN WAGON TRAIN
M # OF MEN IN A FAMILY 2

8. IF I COULD SEE THIS THING

9. WAGON TRAIN SKETCHES
AND SITUATIONS

10. GRAPH SKETCHES

11. IN NEED OF NUMBERS

12. THE ISSUES INVOLVED

13. SITUATIONS, GRAPHS,
TABLES, AND RULES

14. RULES, TABLES, AND GRAPHS
FIND AS MANY POINTS ON THE GRAPH AS YOU THINK YOU NEED TO GET AN IDEA OF WHAT THE WHOLE GRAPH LOOKS LIKE.

15. PREVIOUS TRAVELERS
LINE OF BEST FIT

16. SUBLETTE'S CUTOFF

17. OUT OF ACTION
MAKE A GRAPH AND WRITE A REPORT

18. GRAPHING CALCULATOR IN-OUTS

19. BIDDY MASON

20. "OUT OF ACTION" AND
"SUBLETTE'S CUTOFF"
REVISITED
BEST FIT LINE

21. FAIR SHARE ON CHORES
WRITING EQUATIONS

22. FAIR SHARE FOR HIRED HANDS
WRITING EQUATIONS

23. MORE FAIR SHARE ON CHORES
PT OF INTERSECTION

24. MORE FAIR SHARE
FOR HIRED HANDS
PT OF INTERSECTION

25. WATER CONSERVATION

26. THE BIG BUY

27. CATCHING UP
BY A SPECIFIC DATE
DISTANCE
TIME
RATE

28. CATCHING UP
BY A SPECIFIC PLACE
DISTANCE
TIME
RATE

29. WATER FOR ONE MORE

30. CATCHING UP
BY SATURDAY
NIGHT
DISTANCE
TIME
RATE

31. CATCHING UP AT AUBURN

32. PLANNING THE JOURNEY BRAINSTORM IDEAS PURCHASE FOOD AND SUPPLIES
$10 A PERSON

33. PLANNING THE JOURNEY

34. SHOELACES
HOW MANY INCHES OF SHOELACE DOES A…
WOMAN NEED?
MAN?
CHILD?

35. SHOELACES
FIND THE TOTAL LENGTH OF SHOELACES NEEDED FOR YOUR FAMILY.

36. LACED TRAVLERS
HOW MANY YARDS OF SHOELACE DID THE SETTLERS NEED ALTOGETHER?

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

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

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

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

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

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

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

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

45. WAGON TRAIN SKETCHES

46. WAGON TRAIN SKETCHES

47. WAGON TRAIN SKETCHES

48. WAGON TRAIN SKETCHES

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

50. GRAPH SKETCHES

51. GRAPH SKETCHES

52. GRAPH SKETCHES

53. GRAPH SKETCHES

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

55. IN NEED OF NUMBERS

56. IN NEED OF NUMBERS

57. IN NEED OF NUMBERS

58. IN NEED OF NUMBERS

59. IN NEED OF NUMBERS

60. THE ISSUES INVOLVED
SHOULD THE VERTICAL AXIS ALWAYS BEGIN AT ZERO? WHAT ABOUT THE HORIZONTAL?

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

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

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

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

65. RULES, TABLES, AND GRAPHS
OUT = 4*IN - 4
OUT = IN*IN
OUT = *IN

66. RULES, TABLES, AND GRAPHS
3X + 2Y = 9
Y^2 = X

67. PREVIOUS TRAVELERS HOW WOULD YOU MAKE A GRAPH FOR BEANS?
HOW WOULD YOU SCALE THE AXES?

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

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

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

71. OUT OF ACTION MARCH 20TH DAY 1 MARCH 25TH DAY 6 APRIL 1ST DAY 13
APRIL 6TH DAY 18
APRIL 18TH DAY 30

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

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

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

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

76. GRAPHING CALCULATOR IN-OUTS
Y = 3X^2 - 7X + 2

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

78. “OUT OF ACTION” AND “SUBLETTES CUT OFF” REVISITED
MARCH 20TH 55 FT LBS
MARCH 25TH 90 FT LBS
APRIL 1ST 140 FT LBS
APRIL 6TH 185 FT LBS

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

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

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

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

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

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

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

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

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

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

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

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

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

92. MORE FAIR SHARE ON CHORES
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.

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

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

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

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

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

98. WATER CONSERVATION
IN HOW MANY DAYS WOULD EACH FAMILY RUN OUT OF WATER?

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

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

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

102. 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?

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

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

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

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

107. WATER FOR ONE MORE NUMBER OF PEOPLE IN EACH FAMILY CONGLOMERATE
NON FAMILY
LARGE
MINIMAL

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

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

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

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

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

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

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

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

116. CALIFORNIA AT LAST!!!!