Lay the foundation for finding the area of rectilinear figures with the set of task cards, reference materials, and assessment activities. Build your students’ ability to reason about the lengths of sides on irregular figures 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 area.
• graphic reference sheet
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 4 assessment activities and key/scoring guide
The Third Grade Common Core Math Standards require students to find the area of rectilinear figures that are composed of non-overlapping rectangles. In order to do this, they need to be able to partition or decompose the figure into two rectangles, find the individual areas of those rectangles, and then recognize that the area of the entire figure is the sum of the areas 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 sides. Some students immediately pick up on the fact that two short sides are the same length as one long side that is opposite, but other students do not. This ability is crucial in being able to find the area of rectilinear figures. If a student decomposes the figure into two rectangles but can’t figure out one of the side lengths, they obviously can’t figure out the area of that section – or of the figure as a whole!
About the Cards
I designed this set to help give my students practice in using the properties of rectangles and rectilinear figures to figure out the lengths of unlabeled sides. Each of the 32 cards in this set presents the students with a figure composed of two non-overlapping rectangles. The figures have most side lengths labeled, but one or more of the sides are labeled with variables or not labeled at all. The students have to use the known side lengths to figure out the unknown side lengths or the dimensions of the rectangles into which the figure is decomposed.
The cards scale up in difficulty, as described below:
Cards 1 – 8
• all side lengths are less than 20 units
• students must identify 1 unknown side length.
Cards 9 – 12
• all side lengths are less than 40 units
• students must identify 2 unknown side lengths
Cards 13 – 20
• all side lengths are less than 200 units
• students must identify 2 unknown side lengths
Cards 21 – 28
• all side lengths are less than 60 units
• figures are partitioned into two rectangles
• two side lengths are unknown
• students must identify dimensions of given rectangles
Cards 29 – 32
• all side lengths are less than 120 units
• three side lengths are known
• figure is NOT partitioned
• dimensions of one rectangular part are identified
• students must identify dimensions of second rectangular part
Using the Cards
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 progressive nature of the cards allows for scaffolding so students can practice with rectilinear figures with numbers and in situations of gradually increasing complexity. They also allow you to differentiate for levels of need and ability in your classroom. You might have students at a beginning level of proficiency start with card 1 while students who already have demonstrated proficiency start with card 9. Some students might do all of cards 1 through 20, others might only do the odd or even cards in that set, and still others might only do the cards 21 through 32. You could also use a “gradual release model” with the cards. Do cards 1 & 2 together as a class, have students work in pairs to complete cards 3 through 8, and then your kids can complete cards 9 through 20 on their own. Then repeat the process with cards 21-28 and 29-32.
Even though the intent of the cards is simply to identify side lengths, you can re-purpose the cards once your students are done by having them find the area of each rectilinear figure after they have worked through identifying all the missing side lengths. This will give them practice with standard 3.MD.7 (“find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts”), and since the students will have already found all of the unknown side lengths, finding the areas of the figures will be easier than it would be otherwise.
Reinforcing the Concept
Included among the printables is a graphic reference sheet illustrating the relationships between side lengths on rectilinear figures. 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 area of figures composed of non-overlapping rectangles.
Assessing Student Understanding
The four provided activity sheets can be used to evaluate student understanding of determining unknown side lengths on figures composed of non-overlapping rectangules. The first two assessment activities are formatted in a similar way, as are the second two activities. In addition, the kinds of questions on the activities are similar to those on the cards. This allows the activity sheets 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 B)
World Records: Filling Foods - measurement units task cards & printables
Broken Rulers - measure to nearest inch/1/2-inch task cards + printables
I hope your students enjoy these resources and are able to build their proficiency with volume. – Dennis McDonald