THE OVERLAND TRAIL VARIABLES, EQUATIONS, GRAPHS, AND RATES

THE OVERLAND TRAIL

VARIABLES, EQUATIONS, GRAPHS, AND RATES

MINIMAL FAMILY LARGE FAMILY NON FAMILY CONGLOMERATE FAMILY

•ADULT BOOT 48 INCHS

•ADULT SHOE 32 INCHES

•CHILDS BOOT 24 INCHES

•EACH MAN NEEDS 5 YDS

•EACH WOMAN NEEDS 4 YDS

•EACH CHILD NEEDS 3 YDS

•PROFIT = (W - .4*H) / 2

•PRICE TO CROSS=

.5*W+.25*M+.1*W+.05*C

F # OF FAMILIIES IN WAGON TRAIN 25

M # OF MEN IN A FAMILY 2

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

LINE OF BEST FIT

MAKE A GRAPH AND WRITE A REPORT

BEST FIT LINE

WRITING EQUATIONS

WRITING EQUATIONS

PT OF INTERSECTION

PT OF INTERSECTION

•DISTANCE

•TIME

•RATE

BY A SPECIFIC DATE

BY A SPECIFIC PLACE

•DISTANCE

•TIME

•RATE

•DISTANCE

•TIME

•RATE

PLANNING THE JOURNEY

BRAINSTORM IDEAS

PURCHASE FOOD AND SUPPLIES•$10 A PERSON

PLANNING THE JOURNEY

SHOELACES

HOW MANY INCHES OF SHOELACE DOES A…•WOMAN NEED?•MAN?•CHILD?

SHOELACES

FIND THE TOTAL LENGTH OF SHOELACES NEEDED FOR YOUR FAMILY.

LACED TRAVLERS

HOW MANY YARDS OF SHOELACE DID THE SETTLERS NEED ALTOGETHER?

LACED TRAVLERS

WRITE TWO MORE INTERESTING QUESTIONS AND ANSWER ONE OF THE QUESTIONS.

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

TO KEARNY...

EXPLAIN WHY THIS FORMULA MAKES SENSE.

PROFIT = (W - .4*H) / 2

TO KEARNY...

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

TO KEARNY...

USE THIS FORMULA TO EXPLAIN WHAT VIEUX CHARGED:

PRICE TO CROSS=

•.5*W+.25*M+.1*W+.05*C

TO KEARNY...

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

WRITE THE EXPRESSION EXPLAIN WHAT THE

EXPRESSION MEANS, USING A SUMMARY PHRASE

GIVE THE NUMERICAL VALUE OF THE EXPRESSION

OX EXPRESSIONS

IF I COULD SEE THIS THING

5% ADULTS WILL DIE FROM CHOLERA

10% OF THE CHILDREN WILL DIE FROM CHOLERA

WAGON TRAIN SKETCHES

WAGON TRAIN SKETCHES

WAGON TRAIN SKETCHES

WAGON TRAIN SKETCHES

GRAPH SKETCHES

EACH GRAPH ILLUSTRATES A RELATIONSHIP BETWEEN TWO QUANTITIES

DESCRIBE A SITUATION THAT IS ILLUSTRATED BY THE GRAPH

GRAPH SKETCHES

GRAPH SKETCHES

GRAPH SKETCHES

GRAPH SKETCHES

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.

IN NEED OF NUMBERS

IN NEED OF NUMBERS

IN NEED OF NUMBERS

IN NEED OF NUMBERS

IN NEED OF NUMBERS

THE ISSUES INVOLVED

SHOULD THE VERTICAL AXIS ALWAYS BEGIN AT ZERO? WHAT ABOUT THE HORIZONTAL?

THE ISSUES INVOLVED

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

THE ISSUES INVOLVED

WHY MIGHT SOMEONE MAKE THE CONCLUSION THAT BOYS GROW AT A CONSTANT RATE?

THE ISSUES INVOLVED

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

SITUATIONS, GRAPHS, TABLES, AND RULES

DISCUSS HOW THE FOLLOWING RELATE TO ONE ANOTHER:

A GRAPHIN OUT TABLERULE FOR THE TABLESITUATIONS

RULES, TABLES, AND GRAPHS

OUT = 4*IN - 4

OUT = IN*IN

OUT = 550 - 20*IN

RULES, TABLES, AND GRAPHS

3X + 2Y = 9

Y^2 = X

PREVIOUS TRAVELERS

HOW WOULD YOU MAKE A GRAPH FOR BEANS?

HOW WOULD YOU SCALE THE AXES?

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?

SUBLETTE’S CUTOFF

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

SUBLETTE’S CUTOFF

IS THERE A TIME WHEN ALL THREE FAMILIES WILL HAVE ABOUT THE SAME AMOUNT OF WATER LEFT?

OUT OF ACTION

MARCH 20TH DAY 1 MARCH 25TH DAY 6 APRIL 1ST DAY 13 APRIL 6TH DAY 18 APRIL 18TH DAY 30

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.

GRAPHING CALCULATOR IN-OUTS

IF A FAMILY BOUGHT 155 LBS OF BEANS, HOW MANY PEOPLE CAN THIS FEED?

GRAPHING CALCULATOR IN-OUTS

PROFIT = (W-4)/2

HOW MUCH PROFIT WILL THE PAPANS EACH MAKE IF 25 WAGONS USE THEIR FERRY?

GRAPHING CALCULATOR IN-OUTS

HOW MANY WAGONS WILL HAVE TO USE THE PAPANS’ FERRY BEFORE THE PAPANS MAKE $15 EACH?

GRAPHING CALCULATOR IN-OUTS

Y = 3X^2 - 7X + 2

IN OUT

1.31 ?-3.02 ?? -1.04? -2.12? -2.058.57 ?

“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

“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

“OUT OF ACTION” AND “SUBLETTES CUT OFF”

REVISITED

GUESS AND CHECK FINDING THE BEST FIT LINE

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.

BIDDY MASON

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

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?

BIDDY MASON

WHAT IF THE FAMILY HAD SIX PEOPLE?

FIND AN EQUATION THAT GIVES THE AMOUNT YOU WILL HAVE FOR EACH PERSON.

FAIR SHARE ON CHORES

HOW LONG WOULD YOU SUGGEST THAT EACH TYPE OF SHIFT BE? FIND THREE DIFFERENT PAIRS OF ANSWERS

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.

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.

FAIR SHARE ON CHORES

GRAPH THE FUNCTION ON YOUR CALCULATOR

FIND THREE MORE PAIRS OF POSSIBLE SHIFT LENGTHS FROM YOUR GRAPH

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

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

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

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

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.

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

MORE FAIR SHARE FOR HIRED HANDS

MAKE SEVERAL SUGGESTIONS OF WAYS THE FULKERTHS COULD SET UP THE TWO PAY RATES

GRAPH THIS DATA

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?

WATER CONSERVATION THE MUSTER FAMILY HAD

100 GALLONS•HOW MANY GALLONS WOULD

THEY HAVE AFTER THREE DAYS?

•EIGHT DAYS?•TWELVE DAYS?•X DAYS?

WATER CONSERVATION

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

WATER CONSERVATION

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

THE BIG BUY

WRITE TWO SEPARATE EQUATIONS FOR JILLIAN AND SEVE.

JILLIAN’S EQUATION

Y=10 + 5X

SEVE’S EQUATION

Y = 40 + 3X

THE BIG BUY

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

THE BIG BUY

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

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?

CATCHING UP...BY A SPECIFIC DATE

HOW MANY DAYS DO YOU HAVE TO CATCH UP?

HOW FAR WILL YOUR COUSIN’S FAMILY TRAVEL?

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?

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?

CATCHING UP...BY A SPECIFIC PLACE

HOW FAST WILL YOU HAVE TO GO IN ORDER TO MEET UP WITH THE WAGON TRAIN IN RENO?

WATER FOR ONE MORE

NUMBER OF PEOPLE IN EACH FAMILY•CONGLOMERATE•NON FAMILY•LARGE•MINIMAL

WATER FOR ONE MORE

IF YOU HAVE THREE GALLONS PER PERSON FOR YOUR FAMILY:• HOW MANY GALLONS DO

YOU HAVE ALTOGETHER FOR YOU FAMILY?

WATER FOR ONE MORE

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

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?

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?

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?

CATCHING UP BY SATURDAY NIGHT

POSSIBLE QUESTION TO HELP GET YOU STARTED:•HOW MANY HOURS A DAY

WILL YOU HAVE THE WAGON TRAIN TRAVEL?

CATCHING UP AT AUBURN

ROLL A DIE FOUR TIMES TO FIND THE WAGON TRAIN’S RATE

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?