Area and Volume Ah-Ha Moment

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Recently, I was working with my students on both calculating the area and volume of cubes and rectangular prisms.  Most were catching on fine until the dreaded missing measure type problem reared it’s ugly head.

If you teach upper elementary math, you know the type of problem I am referring to.   It looks a little something like this:

Or like this:

My strategy has always been to have my students make a picture and fill in the known information.  Once the picture was made, they were to use what they know about rectangles and squares as well as the formula for finding the area and volume to find the missing measure.

This strategy, however, did not seem to be very effective for most of my students.  What seemed so easy for me to see, just didn’t seem to be clicking for my students.

Then it hit me!  Fifth grade students love solving one-step linear equations.  And even though it is no longer part of the 5th grade curriculum, I routinely spend time teaching the skill.  Simply because they love it so much.  Something about that type of equation, makes students feel powerful when they solve it.  Maybe it is the variable?!  Who knows.

Anyway, I tied the two together…finding a missing measure and a one-step linear equation.  And, the light bulb went on!

Here’s how:

In the case of the rectangle question above (Early Bird Task Card 6), I asked the students to write the formula for calculating area:  a = l x w.  Then we went back into the problem and supplied what we knew and wrote it into the formula.  We knew the area was 63 and that the length was 9.  We did not know what the width was.  So, our equation looked like this:  63 = 9 x w and just like that they all knew the answer was 7!  Tah-dah!

While the volume one (Goofy Gorilla: Find the Missing Measure) is a bit more sophisticated, with some modeling they caught on to it as well:  v = l x w x h…45 = 3 x w x 5.  Some divided 45 by 3 and then divided again by 5.  Others, soon realized they could multiply 3 and 5 and then divide 45 by the product.

Now to get them to label correctly…ughhhh…

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