These task cards were designed to help student visualize the cubes when finding the volume of rectangular prisms with two fractional dimensions. I made these as a follow-up to another set of task cards (available in my store) that were the beginning level for this same standard.
This is a set of 28 task cards that show all of the cubes (whole and fractional) in each prism, including the edge where the two fractional dimensions overlap. I made these to use with my above level fifth grade students as they worked through this core standard. I wanted them to have a way to find the volume without resorting to a rote method of multiplying mixed numbers. We had worked on more basic fraction multiplication problems using the distributive property, and I wanted them to see how that correlated to the actual pieces of the prism.
We worked through finding the volume of the prism that was whole cubes, then finding each fractional face, and then the overlapping edge. These cards took my student 2 class periods to work through, but I felt it gave them a good understanding of where each portion of their product was in relation to the model.
Many of the problems in this set use fractional dimensions that have the same denominator. Those are definitely easier because that makes all of the "slices" of the subs the same size, except for the overlap edge. As the difficulty increases, and the denominators are different, each face needs to be counted separately. For this reason, I chose only unit fractions for the face pieces. The kids figured out how to piece those together to make wholes.
I couldn't find anything that exactly addressed what I wanted the students to be able to work through, and I feel that these helped them tremendously.
This file is a 14-page PDF. It includes 28 task cards (7 pages, 4 per page), a recording sheet, an answer key. I also made a student worksheet (and answer key), as well as 2 note pages for students. one note page focuses on problems with like denominator fractions, and the other is for unlike fractions. I also included a note page from me about how I used these cards.