More Real Number Extra Credit

Volume of a cylinder & The sum of Areas

“Why do we need to know this?” How often do we get these questions in the classroom? Sometimes in order for students to see the value in mathematics you must take it away from them.




Take for example the formula for the volume of a cylinder, V = (pi)(r^2)(h)

If you take away the (h) within the equation you are left with the equation for the area of a circle. Thus, as we know, a cylinder is simply a bunch of circles stacked over top of one another. But, do your students know this?

Here’s an exercise,

1) Bring in a printable worksheet with numerous circles of equal size

2) As your students to cut out each circle

3) Next, ask them to find the sum of all the areas of each circle they cut out

4) Next, ask them to stack all the circles and use a ruler to measure its height

5) Finally, ask them to find the volume of the cylinder using V = (pi)(r^2)(h)

6) Does it closely resemble the sum of areas they previously calculated?

7) Wasn’t it a lot faster?

Creating a Valuable Expression Game

Creating a Valuable Expression Game

You know the routine, 2x + 3z, evaluate the expression when x = 2, z =1


You see the disconnect here right? None of our students care what the solution is. Now, let’s create a new expression in which students value the solution.


You need

1) A tennis ball

2) Meter/Yard Stick

3) Stop watch

4) A football field/ or play ground

5) And an expression worth evaluating



Here’s the goal. Students will be given points based on two variables: hang time (t), distance (d).



New expression: 2t + 3d



1) Have your students line up at the goal-line of a football field

2) Designate a ball return person

3) Have each student throw the tennis ball as high and as far as they can and record the hang time and distance

4) When you return to the classroom, write the expression on the board and have each student evaluate their points to see who the winner is



Extra: Want to make it harder? Use decimals or fractions.

For example use the expression 2.1t + 3.2d or 2/3t + 3/4d