“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 size2) 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)
7) Wasn’t it a lot faster?
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 size3) 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?
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