Build your students' ability to compose and decompose two-dimensional figures with this set of interactive task cards and printables. The 32 task cards will provide your students with practice manipulating two-dimensional shapes, combining them in different ways to compose larger figures. Extend your students’ practice (or assess their level of mastery) with the four included assessment activities. With this set of print-and-go resources, your students will grow stronger in their understanding of composing and decomposing two-dimensional figures.
Common Core State Standards for Mathematics addressed:
• Compose two-dimensional shapes or three-dimensional shapes to create a composite shape, and compose new shapes from the composite shapes (1.G.2)
• graphic reference sheet
• shape cut-out template
• shape reference sheet
• sample task card
• 32 task cards
• task card answer sheet and key
• 4 assessment activities and keys
About the Cards
This set of cards is designed to help students practice using pairs of shapes to compose larger shapes. When working with these cards, students will be presented with the outline of a figure and they can physically move around smaller shapes (provided on a resource sheet) rotating, flipping, and sliding them to try to fit perfectly in the larger shape. As your students work with the shapes, they will consider the attributes of the shapes and how the shapes' attributes compare to each other and to the larger "target shape." When your students are done working with these cards, they will have a much stronger understanding of how to compose and decompose geometric figures.
Using the Cards
You can begin by making copies of the Composing Shapes: Shape Cut-Outs resource sheet and cut out (or have your students cut out) a set of shapes for each student or pair of students. The shapes on the card are: rectangle, square, two different parallelograms/rhombi, two different trapezoids, two different triangles, and a half-circle. Let your students explore with the shapes, comparing them and combining them to build larger figures. Then, present them with a copy of the sample card and have students work to try to figure out which pair of the shape cut-outs can be combined to make the figure on the card.
Once some, most, or all of the students have found the correct pair of shapes, you can have students share about the shapes that worked and any shapes they tried that didn't work. Have your students talk about how they knew certain shapes or would not fit and why. You might then project the provided Composing Shapes: What Works? graphic and have your students talk through the hypothetical students' work on the graphic, justifying their thinking and critiquing the thinking of others.
As the students work on the cards, they record the letters of each pair of shapes on the recording sheet. There are many options for how you can vary how your students work on the cards to differentiate based on your students’ levels of proficiency with the target concept. You may:
1) have your students work in pairs on the first sixteen cards and then on their own on the second half of the set; or,
2) have some students work in pairs while other students work on their own; or,
3) have the bulk of your class work on the cards in pairs or own their own while you provide guidance to a small group.
If some of your students demonstrate a high level of proficiency with identifying the pairs of shapes that can be combined to make the target shape, you can up the rigor for those students by having them use the Composing Shapes reference sheet. This sheet has the same figures from the "shape cut-outs" sheet, and requires your students to be able to identify the correct pair of shapes on each card visually, without physically manipulating the smaller shapes.
There are lots of options for how you can have your students to work on the task cards. This set includes a four-page guide that describes multiple ways to implement the cards to differentiate for varied needs in your class.
Reinforcing and Assessing Understanding
The printables consist of a graphic reference sheet, a corresponding resource sheet, and four different one-page assessment tasks.
The graphic reference sheet defines the term "compose" and illustrates how two two-dimensional figures (a trapezoid and a quarter-circle) can be combined to compose a new, larger figure. This sheet includes an open-ended question, prompting students to consider how the original shapes' attributes compare to the attributes of the new shape, and also asks students to consider a set of composite shapes to determine which could be composed of the trapezoid and quarter-circle shown. This reference sheet can be used interactively by giving students their own trapezoids and quarter-circles (template provided) and having them manipulate the shapes to try to create the composite figures on the sheet; this will give them practice with the kind of work they will do when completing the task cards. Once done, your students can glue the sheets in their journals to be a regular reference when doing other work with geometric shapes.
The four provided assessment activities can be used to evaluate student understanding of composing figures from two or more smaller shapes. Each sheet features four composite figures and a set of labeled shapes, just like the cards do. Students have to identify the pair of lettered shapes that can be combined to compose each of the four composite figures. You may have your students work through the assessment activities as they are, or you may opt to have the students cut the lettered shapes out and physically manipulate them to identify the make-up of the composite figures.
I hope your students enjoy these resources and are able to build their proficiency with two-dimensional figures. – Dennis McDonald