Lay the foundation for finding the volume of rectilinear prisms with the set of task cards, reference materials, and assessment activities. Build your students’ ability to reason about the lengths of edges on irregular prisms with the 32 task cards in this set. Extend their practice (or assess their understanding) with the four included assessment activities. The materials in this set will strengthen your students’ reasoning skills and build a strong foundation for their later work with volume.
• graphic reference sheet
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 4 assessment activities and key/scoring guide
About the Set
The Fifth Grade Common Core Math Standards require students to find the volume of three-dimensional figures that are composed of non-overlapping rectangular prisms. They need to be able to partition or decompose the figure into two rectangular prisms, find the individual volumes of those prisms, and then recognize that the volume of the entire figure is the sum of the volumes of the individual sections.
When I have taught this concept, one of the challenges for some students is simply knowing the lengths of some of the unlabeled edges. Some students immediately pick up on the fact that opposite edges are the same length, but other students do not. Even trickier for some students is understanding that one long edge is equal to the sum of smaller edges that are opposite it. In my experience, some kids pick that up immediately, and others struggle to see it! This ability is crucial in being able to find the volume of a three-dimensional figure made up of rectangular prisms. If a student decomposes the figure into two prisms but can’t figure out one of the edge lengths, they obviously can’t figure out the volume of that section – or of the figure as a whole!
I designed this set to help give my students practice in using the properties of rectangular and rectilinear prisms to figure out the lengths of unlabeled edges. Each of the 32 cards in this set presents the students with a three-dimensional figure composed of two non-overlapping rectangular prisms. The figures have most edge lengths labeled, but two of the edges have their lengths identified with variables. The students have to use the known side lengths to figure out the unknown side lengths.
Practicing the Concept
There are lots of ways in which you can implement the task cards. You can have the students work on them independently, working through the task cards on their own. The students can work on them in pairs or small groups, completing all the task cards in one session. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. You can even use them as a variation of “problem of the day”, giving each student 1 sheet of 4 cards to glue in their journals and solve, one sheet per day for eight days.
The cards scale up in difficulty, allowing you to differentiate for diverse student needs in your class. The first twenty cards in the set primarily use lengths of less than forty units wile the final twelve cards use larger numbers for the edge lengths. You may choose to have all students work through the cards in order so they begin with cards that have smaller, more manageable numbers and then only begin working with the larger numbers once they are more proficient with the skill of reasoning unknown edge lengths. However, if you have some students that are particularly struggling with the concept on which the cards focus, you might them complete Cards 1 through 16, while the other students work on Cards 17 through 32.
Included in this set are eight “answer cards” that can serve as a resource if you use a self-paced structure for implementing the task cards. Often, I would have kids work in pairs on cards while I circulated to spot check and give feedback to pairs of students. Naturally, I would get backed up and not be able to reach as many kids until after they had already made many mistakes. I designed these answer cards so that the students could check themselves: catching errors, figuring out for themselves what they did wrong, and (hopefully) avoiding the same mistake on later cards.
Reinforcing the Concept
Included among the printables is a graphic reference sheet that illustrates the relationships between edge lengths on rectangular and rectilinear prisms. When I use reference sheets such as the one included in this set, I have my students glue it in their journals and use it as a guide when completing classwork and homework. Your students can use this reference sheet as a guide while they work on the cards, as well as when they complete other tasks that relate to finding the volume of figures composed of non-overlapping rectangular prisms.
Assessing Student Understanding
The four provided activity sheets can be used to evaluate student understanding of determining unknown edge lengths on figures composed of non-overlapping rectangular prisms. There is a pair of full-page assessment activies and a pair of half-page, “exit ticket”-style assessments. The exit tickets require students to explain their thinking in writing, making them ideal for building or assessing your students’ communication skills. Each pair of assessment activities are formatted in a similar way, allowing them to be easily used as pre/post assessments. While I designed these activities as assessments, you can use them in a variety of ways – homework, center assignments, paired practice, or any other purpose that fits your teaching style or classroom routines. Answer keys, rubrics, and scoring guides are included for all of the assessment activities.
For more practice with measurement concepts, please check out the other related resources I have available –
In and Around - area and perimeter task cards + printables (set C)
World Records: Filling Foods - measurement units task cards & printables
Area and Perimeter Puzzlers - task cards + printables
I hope your students enjoy these resources and are able to build their proficiency with reasoning about rectilinear prisms. – Dennis McDonald