Screen 1 of 6
Hourly wage
Mary has a job where she is paid by the hour, she works a different number of hours each week, and she gets paid every week. Using a combination of phrases and mathematical operation symbols (+, -, x, /), tell me: What is the mathematical relationship between her hourly wage, the number of hours she works, and the amount she earns for the week (before taxes or other deductions are taken out)?
Isaac Newton
(hours worked) * (hourly wage) = total pay
André Weil
(hourly wage)*(hours worked)=(total earnings)
Katherine Johnson
(hours worked) * (hourly wage)= amount eared in a week
Jose Adem Chain
H x W= E W= wage H=hours E= earnings ($$)
Joseph-Louis Lagrange
(Hourly wage)*(Hours worked per week) = (The amount earned for the week)
Alan Turing
(Hourly wage) *(number of hours)= earnings for the week
George Birkhoff
(Wage)*(Hours worked)=Total Paid
Joseph Liouville
(hourly wage) * (hours worked a week) = (total earnings)
Pafnuti Chebyshev
hourly wage times hours per week equals amount per week
Niels Abel
(hourly wage)*(hours worked a week)= total earnings
Kelly Miller
(hourly wage)*(hours worked per week)=(The amount for the week)
Fan Chung
(Hourly wage) * (Hours worked) = (Total Earnings)
Mary Ellen Rudin
(hourly wage) * (x number of hours) = Earnings
Maryan Mirzakhani
(Hours work)*(wage)=total
Émile Borel
Hours worked(hourly wage) = total earnings
William Hamilton
(Hours Wage)*(number of hours)= amount earned a week
Screen 2 of 6
Thinking about your thinking
How did you come up with the mathematical relationship in the last question? What thought process did you go through?
Isaac Newton
Thinking about how I figure out my pay in my own job. Your total pay would be whatever hours you worked multiplied by your hourly wage
André Weil
To find the total weekly earnings, we multiplied the hours worked with the hourly wage.
Katherine Johnson
Thinking about how I figure out my pay at work. How ever many hours you worked times the amount that you made.
Jose Adem Chain
The result of E (earnings) is entirely dependent of the variables: H (hours worked) and W (her wage.)
Joseph-Louis Lagrange
The amount that she earns in a week is defined by the amount of hours worked multiplied by the hourly wage
Alan Turing
We know that to find her earnings for the week we need to times how much she gets paid by how many hours she has worked.
George Birkhoff
We took segments of the problem and transitioned them into variables for the equation.
Joseph Liouville
I looked at the total earnings and then looked at the factors that made it possible to get there
Pafnuti Chebyshev
wage multiplies hours equals pay per week
Niels Abel
Look at the total earnings and look at the factors that made it possible to get there.
Kelly Miller
The amount of hours that she worked is what changes the amount of income she gets each week.
Fan Chung
We multiplied the hours worked with the hourly wage to find the total earnings.
Mary Ellen Rudin
We looked at how much she was paid and then multiplied that by here hourly wage, which then gives her total earnings.
Maryan Mirzakhani
We took each one section of the problem and connect it together into variable for the equations
Émile Borel
total hours worked(hourly earnings) = her total earnings for the week
William Hamilton
We know that the amount of hours worked affects the amount earned. And thought about equations I have seen in the past.
Screen 3 of 6
Sharing housing costs
One way to save on housing costs while you’re in college is to rent a house, and share the house with several other students. If several students share a house and split the cost equally, what is the mathematical relationship between the number of students sharing the house, the total rent for the house, and each student’s share of the rent?
Isaac Newton
(Total cost of house) / (number of students sharing house) = each students share of rent
André Weil
(Total rent) / (Number of students) = (Each student's share of rent to pay)
Katherine Johnson
(total cost of the house)/ (the number of students)= each students share of rent
Jose Adem Chain
R/S=A S= number of student R= rent A= amount each student pays
Joseph-Louis Lagrange
(The total cost of the house)/(The amount of students sharing the house) = (The cost for each student for the house)
Alan Turing
(Total rent)/(number of house mates)=(each students share of the rent)
George Birkhoff
(Total Housing Rent)/(Total Number of Students)=(Individual student rent)
Joseph Liouville
(Total cost of rent) / (number of students living) = (Share of rent per student)
Pafnuti Chebyshev
total rent divided by number of students equals total amount each student owes
Niels Abel
(Total cost of rent)/(number of students living)= rent distributed
Kelly Miller
(The total cost of the house)divided by (the amount of students sharing the house)= how much each student will pay
Fan Chung
(Number of students)/(Rent)=(Cost of rent per person)
Mary Ellen Rudin
(total rent) / (the number of students) = Amount each student pays
Maryan Mirzakhani
(housing rent)/(total of #of student)= (each student individual share of rent)
Émile Borel
Student 1 + student 2 = The total cost for the rent
William Hamilton
(House cost)/(numbers of students)=each students share of rent
Screen 4 of 6
Mathematical relationships without numbers
Why were you able to describe these mathematical relationships even though you were given no numbers? (Aren't mathematical relationships all about numbers? Isn't math all about numbers?)
Isaac Newton
Based off your understanding of variables used to calculate answers
André Weil
We were given variables to describe in place of numbers.
Katherine Johnson
There are variables in place of numbers
Jose Adem Chain
When you need more than 1 variable for a result it becomes potentially mathematical, especially if each variable is subject to change.
Joseph-Louis Lagrange
Numbers aren't just symbols, they are representative of logical relationships
Alan Turing
It's about the relationship of the variables in the equation
George Birkhoff
We were able to select certain keywords from the problem and turn them into our equation.
Joseph Liouville
No it's not you can use names or letters to represent the mathematical relationship of the numbers
Pafnuti Chebyshev
it gave you the equation to find the answer if you were to need to find it
Niels Abel
No it is not you can still explain the relationship where numbers would be without actually having those numbers.
Kelly Miller
You don't need the numbers in order to create an equation to solve for when there are numbers.
Fan Chung
Because there are variables.
Mary Ellen Rudin
We used variables to understand how many students would pay
Maryan Mirzakhani
Because we can find the certain keywords in the question and put it into the equation
Émile Borel
Numbers are not need to find the answer to the equation
William Hamilton
You were using words instead of variables. When you don't now the number can still have an equation, if you use variables or words.
We updated the dashboard!Learn more.
Screen 5 of 6
Gas mileage
What is the mathematical relationship between the number of miles you drive, the number of gallons of gas you use to drive that number of miles, and the gas mileage your vehicle gets?
Isaac Newton
(number of miles you drive) * (number of gallons of gas used to drive that number of miles) = gas mileage
André Weil
(miles driven)/(gallons of gas used)=(gas mileage)
Katherine Johnson
(# of miles you drive) /( the number of gallons used)= gas mileage
Jose Adem Chain
m/g=M m= number of miles g= how many gallons M= gas mileage
Joseph-Louis Lagrange
(Miles driven)/(Gas mileage)=(The amount of gasoline used in gallons)
Alan Turing
Gallons of gas used= miles driven/gas mileage
George Birkhoff
(Miles drove)/(total number of gallons of gas used)=(Gas mileage)
Joseph Liouville
(Number of miles driven)/ (Gas used) = Gas Mileage
Pafnuti Chebyshev
total miles drove divided by gallon of gases used equals miles per gallon
Niels Abel
(Gas Mileage)+(Gallons of gas)=Number of miles able to be driven
Kelly Miller
gallons of gas used=miles driven/gas mileage
Fan Chung
(Miles Driven)/(Gallons of gas used)=(Mileage)
Mary Ellen Rudin
(miles drove) / (amount of gas it takes) = Mileage
Maryan Mirzakhani
(The number of the miles drove)/(the number of gallons of gas to get to the distance) = (gas mileage)
Émile Borel
number of miles divided by the gallons used to drive that far = the miles per gallon
William Hamilton
(miles driven)/(gallons of gas used)=gas mileage
Screen 6 of 6
Checking your thinking
How do you know whether the mathematical relationship you've written down is correct? Is there any way to check it?
Isaac Newton
Using it in a real life situation, and testing it on your own vehicles and seeing if it is accurate
André Weil
You could place numbers where the variables are to check.
Katherine Johnson
Try using the equation yourself to calculate your gas mileage
Jose Adem Chain
miles per gallon is an expression. It is common sense made into a jumbled story.
Joseph-Louis Lagrange
Yes, any equation involving variables can be checked by simply inputting numbers in place of the variables.
Alan Turing
Guess and check
George Birkhoff
A way to check our solution is to put real life numbers into our equation and test it.
Joseph Liouville
You can guess and check
Pafnuti Chebyshev
go test it out after a fill up after watching the milage
Niels Abel
You can guess and check, use more than one strategy.
Kelly Miller
Yes, we can put real numbers into the equation to see if it's correct.
Fan Chung
Try plugging in numbers to see if they seem accurate.
Mary Ellen Rudin
You could place numbers in for the variables and get the result
Maryan Mirzakhani
Calculate it yourself using your own vehicle
Émile Borel
guess and check
William Hamilton
Put in real numbers, and test.