In this activity you will be asked pour water into a cup using a dropper while gathering data on a t-table. The idea is that you'll be able to better understand how our y-intercept relates to you pouring water. In addition you will be asked to find the rate of change of your graph.
Objective:
At the end of this lesson you should be able to determine the rate of change of the water level as time goes on. In addition, you should be able to write an equation and graph it properly.
Materials needed:
math notebook/paper
pencil
beaker
olive oil droppers
water
stop-watch
Task 1: Setting up for the Activity
1) Working with your table, make sure you each have your notebook/paper and a pencil on your desks.
2) Make sure you have a stopwatch. If you don't have a stopwatch, find one.
3) On each of your papers create a t-table making sure to label your x/y axes
4) Before moving on check your entire table to make sure their papers are labeled properly, then show your teacher. After your teacher has approved of your labeling they will give you your beaker and dropper.
Task 2: Collecting Data
1) Before pouring any water, make sure you take your first piece of data. How many seconds has it been? How much water is in the cup? Label this on your x/y axes.
2) Have one person get their stopwatch ready and be ready to time for fifteen seconds.
3) Have one person get the dropper ready to be poured. When both the person with the stopwatch and dropper are ready. Start pouring water and timing it for fifteen seconds.
4) After the fifteen seconds is up record your next piece of data. How many total seconds have passed? How much water is in the cup?
5) Repeat steps 2-4, collecting a total of four pieces of data or until your cup is near the top, whichever comes first.
6) Find the slope of the line using the table of values in front of you. Remember you are trying to find the change in y divided by the change in x or rather the rise over run. Show your teacher before moving forward.
Task 3: Graphing Your Data
1) Now that your t-table has been filled out, create an x/y axes and label the points. Where should the time in seconds go? On the x or y axis? What about the amount of water?
2) Plot your points on the graph
3) Draw a line connecting your dots as best as you can making sure to add the arrowheads at the end.
Task 4: Debriefing the Activity
1) What is the slope of the line?
2) What is the y-interept of the line?
3) Write the equation of the line in slope intercept form (y=mx+b)
4) Why does the y-intercept start where it does?
5) How would the y-intercept be different if all of your beakers started with 5 mL already?
6) How much water would be in your beakers after one and a half minutes?
7) What does the slope of the line mean as it pertains to pouring water?