The Locker Experiment

During one of our professional development days, our history teacher made a plea to the principal to perform a prank on one of the students.  He wanted to fill up their locker with “fun balls,” the balls usually used for a ball pit at Chucky Cheez.’   He was only allowed to do this as long as  there was some type of lesson build around it so I felt obliged to write one based on what we were learning lately.  Here is that lesson!

As seen this morning, fun balls aren’t just for little kids anymore.  It really makes people laugh early in the morning and it is fun to pull pranks on each other.  The team that finishes the most work on these experiments will get to pick a person to pull the same prank on, with the correct amount of balls to fill the locker!  There are a couple assignments, the more you do, the better your chances are to pick the next victim!  All teams must at least complete Exercise #1.

 


Exercise #1 Measurement of the ball diameter

The circumference (distance around) of a ball is .  Use a piece of string to wrap around the ball then measure the length of the string.

You will want to get a few different measurements on this to be able to complete this whole assignment so have at least 3 people in your group measure the string and perform all the calculations.

 

  1. The string measures ­___ ___.___ =

(find  on the calculator and use it in your calculations for the most accurate this way.  If you can’t use it, use the value of 3.14)

  1. The radius is then: = ____.___ ___ cm  (round to hundredths place)
  2. The diameter is twice the radius (d=2r).  Calculate this and write it here:  d= ___.___ ___
  3. Round your number to the tenths place correctly:

D = ___.___ cm

  1. Change your number to millimeters:

 

(Cross out units that appear in both the numerator and denominator)

 

 

Show your work to the teacher, the teacher will give you the specifications written on the package of the balls, this will be your “actual” value that you will use in the % error calculations.

 

Exercise #2  % Error Calculations

 

 

% Error is calculated by this equation:

 

 

 

Calculate % Error using three different values that you found:

Measured Value % Error % Error rounded to   tenths place

 

 

Exercise #3 Percentage (%) of Color

This activity is to find the correct % of each color at your table.  Fill in the table below to help you with your calculations.  Please round to the thousands place on your decimal and to the tenths place on your percent.

Color Amount(count) Fractional amount  Amount as a decimal 

 

Amount as a percent % 

Decimal*100

Blue
Green
Red
Yellow
Totaleach column

 

Question:  If your table’s balls represented of the colors found in a large container of these balls, how many of each color would you expect have if the bag contained 1,200 balls?

 

Exercise #4 Volumetric calculations

 

How many of these balls could fit into a locker?

The volume of a ball is calculated to be .  Use the actual measurement of the ball to calculate the volume of the ball.  Remember that radius (r) is ½ the diameter (d).

 

USE THE cm VALUE FOR THE RADIUS!!!

 

 

The volume calculation tells you how much space one ball will take up.  Calculate the volume of a locker and try to figure out how many balls can fit into the locker:

 

Calculate the volume of the locker by measuring the following with a piece of string:

 

Depth (how far in):  ___ ___.___ cm

Width (how wide):  ___ ___.___ cm

Height (how tall):  ___ ___.___ cm

 

Use this formula to figure out the total volume of the locker (the shape is a rectangular prism):

V= ­___ ___ ___ ,___ ___ ___.___

With these two formulas for volume, how would you calculate how many balls would fit into one locker?  Do you feel this would be completely accurate?  Why or why not?

Excuse me Miss, I think I found a pattern…

One of my 7th graders stopped me while I was going over squares and square roots.   We have just finished up some work on the distributive property using the area model and were about to get into a little geometry.  Anyhow, he said that he noticed when he was squaring numbers that if he took the number that he just squared and added it to the number squared, then added the next number, it came out to be the next number squared.  What a gem!  I was pretty excited.  I said, “That is super!  You have just found a wonderful link between algebra and geometry.”

I used the area model to show him why this worked.  I let “n” be the original number and n+1 be the next number.  Using an area model made it clearer to the students in 7th grade.  We had seen this done before with the distribution property in the CMP book.  I reminded the class of this before we started and created a model first with numbers then with “n” and “n+1.”  They wanted to know if it also worked with other values, such as “n+5.”  We used the same area model and showed that it would work with those values too.  It was one of the best classes we had all year, in my book.