Exploring Volume: It's More Than a Formula!

This week we have transitioned from area to volume. Students started the investigation using 3D boxes and centimeter cubes to estimate how many cubes would fill the space of the cube. This year, I removed the "lines" that traditionally are preprinted on the cubes. This removal of lines dramatically changed the types of estimates that were offered from students.  

Eventually, students were encouraged to fill the boxes with the cubes to determine the actual number of cubes needed to fill the space of the box. 

Our next investigation involved a book by Jo Boaler which you can find in the book Mindset Mathematics. Want to see the book? Find the link here. After our first investigation of filling the boxes, it was evident that students were still developing their ideas of volume and how the different views of each face can help us find the volume.  This task is not about "finding the volume" rather how we can rotate and turn the cube and making sense of the images. I compare this activity to solving a Rubik's cube and at the end discovering that you have one solo tile that is out of place. A bigger challenge than meets the eye!

  

Students will continue to finish the investigation as they progress through the volume unit. 

As we continue to experience volume, students were asked to build cubes and rectangular prisms with given dimensions (see below). This is reinforcing What is length? What is width? What does that number represent? An observation that became clear was many students believe that just rearranging the order of the dimensions could "change the size" of the prism. This opened up a conversation about what those numbers mean.  We rotated their prisms and showed how rearranging the dimensions does not change the shape's presentation. I noted that this is the commutative property of multiplication.  

 To help students see how they could "change" the dimensions without changing the volume, I returned to a number string that I had opened the lesson with. I asked how the part squared off in red could help them with problem number 3 on their worksheet? The conversation was productive and students were revising their dimensions with greater success.  

 

Finding Volume in Real World Settings

Students were challenged to find the volume of the Willis Tower in Chicago, Illinois. Students were estimating the volume of the 9 towers to find an approximate volume for the actual skyscraper! Such a great, thought-provoking lesson for fifth graders!

This is a lesson from our district's math materials Everyday Math. Love the series!

Learning about Area and Volume

Students have been working hard to learn concepts about area and volume.

Last week, we learned that we can find the area of a square by multiplying the length by the width. A=L * W a formula we may remember from our school days. Students are also thinking about how we may find the number of pieces that cover that "square area"--including using the fractional parts.

For example:
How many 1/2 ft squares or parts would you need to fill one square foot?
It would take four 1/2 square feet pieces to create one square foot.

We were looking for a pattern to help us solve other problems. Some noticed that if we multiply the denominators, we will get the number of pieces needed to cover the square foot.  In the second example, it would take nine 1/3 square feet pieces to cover one square foot.

This week, we transitioned to volume. Students have been working to find the volume using either of the following formulas:

V = L * W * H   or V = B * H

Students were also working to visualize the size of various cubic units. We have worked with cubic centimeters, cubic decimeters, and cubic meters. Below, you can see us building a cubic meter. 

These first few days in math have been challenging. However, it is exciting to see students think deeply about math!