THE OVERLAND TRAIL

1
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 - .4H) / 2
• PRICE TO CROSS
• .5W.25M.1W.05C

7
OX EXPRESSIONS
F OF FAMILIIES IN WAGON TRAIN
25 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...

• EXPLAIN WHY THIS FORMULA MAKES SENSE.
• PROFIT (W - .4H) / 2

40
TO KEARNY...

• HOW MUCH MONEY WOULD EACH OF THE PAPAN BROTHERS
  MAKE FROM YOUR FAMILY?

41
TO KEARNY...

• USE THIS FORMULA TO EXPLAIN WHAT VIEUX CHARGED
• PRICE TO CROSS
• .5W.25M.1W.05C

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 SKETCHESPART 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 4IN - 4
• OUT ININ
• OUT 550 - 20IN

66
RULES, TABLES, AND GRAPHS

• 3X 2Y 9
• Y2 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
SUBLETTES CUTOFF

• BASED ON YOU GRAPH WHO DO YOU THINK WILL MAKE IT
  AND WHO WILL NOT?

70
SUBLETTES 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 3X2 - 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 BOYS.
• 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.

JILLIANS EQUATION Y10 5X
SEVES EQUATION Y 40 3X
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 COUSINS 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 TRAINS
  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!!!!