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.
