Strengthen your students’ understanding of volume concepts with this set of task cards and printables, the perfect print-and-go resource for finding the volume of irregular prisms. The 32 task cards and graphic reference sheet will provide your students with practice examining irregular prisms for their volume, and the scaffolded difficulty level will allow for easy differentiation. Extend your students’ practice (or assess their level of mastery) with the eight included assessment activities. With these resources, your students will grow stronger in their understanding of key volume concepts.
Common Core State Standards for Mathematics addressed:
Measurement and Data (MD)
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
• Apply the formulas V = l x w x h and V=b x h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems. (5.MD.5b)
• Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts. (5.MD.5c)
• graphic reference sheet
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 8 assessment activities and key/scoring guide
About the Cards
This set of task cards & resources is a follow-up to earlier sets in my Turn Up the Volume!
series, which focus on the volume of figures made up of cubes and the volume of rectangular prisms. This set focuses on finding the volume of rectilinear figures
– 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.
Finding the volume of irregular figures such as the ones on these cards has always been a bit of a challenge for my students as it requires more than simple application of the volume formula. The task is often further complicated by the fact that not every edge length is always labeled, forcing students to use the properties of rectangular and rectilinear prisms (e.g., opposite edges have to be the same length) to recognize the lengths of any unlabeled edges that are needed to calculate a partial volume. Even just partitioning the figure can be difficult depending on how the figure itself is oriented. Plus, once the figure is partitioned, a given edge length might have to be ignored and replaced with two smaller lengths that the students have to figure out by reasoning through the properties of the figure. All in all, the whole prospect is rather tricky, offering many places for students to make errors!
I designed the cards to provided scaffolding for my students and so the difficulty level increases from Card 1 through Card 32. All of the cards present students with irregular figures composed of two rectangular prisms. On Cards 1 through 16, the prisms are already partitioned in two, with each section labeled as prism A or prism B. The students are asked to find the volume of either prism A or prism B, requiring them to figure out the lengths of unlabeled or partitioned edges and then apply the volume formula. On Cards 17-24, the prisms are also already partitioned, but they are not individually labeled. The students are asked to fill-in a partially completed expression (such as V = (___ x 3 x 7) + (___ x 12 x 7)) to show how the volume of the the complete prism could be calculated. The cards in the final set of 8 (cards 25 through 32) each present a non-partitioned irregular figure and ask the students to find the volume of the complete figure.
When selecting the edge lengths for the figures on the cards, I tried to limit the numbers to those that would allow for manageable computation. For the first sixteen cards, the largest number used is 30, and most of the edge lengths are less than 20. On all of the first sixteen cards, the lengths that your students will have to multiply are a one-digit number, a one-digit number, and a two-digit number, so they will never have to multiply two three-digit or four-digit numbers together to find a given volume. The numbers on cards 17 through 24 are larger, but students do not have to actually calculate volume for these cards, simply identify an expression to represent volume. The final eight cards, which present non-partitioned figures, also use mainly lengths that are less than 20, though a couple of the cards require computation that may result in students needing to multiply a three-digit number by a two-digit number.
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 organizational structure of the problems on the task cards will allow you to differentiate to meet your students’ varied needs. You might have some students complete the cards in order, beginning with the easier cards. By the time they reached the final 8 cards, their work with the earlier cards would make it more likely that they would be able to successfully find the volume of the non-partitioned figures. Any students who have already demonstrated some level of proficiency with the concept could start at a higher card, such as Card 12 or Card 16.
While the numbers used for the edge lengths on the prism are mostly less than 20, chosen to allow for more manageable computation, you may opt to have your students – or some of your students – use a calculator when they work on these cards. This would allow them to focus their attention on the target concept of finding volume and give you a better sense of whether they can find the volume of irregular figures. Since there are multiple unlabeled edge lengths on each presented figure, there is no guarantee that the students will get the correct answer even if they do
use a calculator!
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 shows how an irregular figure like the ones on the cards can be partitioned into separate prisms in order to find the volume of the complete figure. The sheet demonstrates two ways to find the volume of a given figure, making it an idea springboard for discussing how to use one method to check the answer arrived at when using the other method. [Since two of the assessment activities require students to demonstrate two ways to find the volume of a given irregular figure, the reference sheet is an ideal model for these asessment activities.] 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 eight provided assessment activities can be used to evaluate student understanding of volume of rectilinear figures. There are four full-page assessment activies and four half-page, “exit ticket”-style assessments. The activities are designed in pairs, with each pair of assessment activities are formatted in a similar way, allowing them to be easily used as pre/post assessments. [Please check out my preview to get a close look at the different activities included in theis set.] 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 –
Name That Length - analyzing irregular prisms task cards + printables (set b)
Turn Up the Volume - finding volume with cubes task cards + printables (set a)
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 volume. – Dennis McDonald