3.G.A.1*This standard is part of a supporting cluster

StandardUnderstand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Standard UnpackedStudents analyze, compare, and classify two-dimensional shapes by their properties. They explicitly relate and combine these classifications. Because they have built a firm foundation of several shape categories, these categories can be the raw material for thinking about the relationships between classes. For example, students can form larger, superordinate, categories, such as the class of all shapes with four sides, or quadrilaterals, and recognize that it includes other categories, such as squares, rectangles, rhombuses, parallelograms, and trapezoids. They also recognize that there are quadrilaterals that are not in any of those subcategories. A description of these categories of quadrilaterals is illustrated in the margin. The Standards do not require that such representations be constructed by Grade 3 students, but they should be able to draw examples of quadrilaterals that are not in the sub- categories.

Similarly, students learn to draw shapes with pre-specified attributes, without making prior assumptions regarding their classification. For example, they could solve the problem of making a shape with two long sides of the same length and two short sides of the same length that is not a rectangle.

Students investigate, describe, and reason about decomposing and composing polygons to make other polygons. Problems such as finding all the possible different compositions of a set of shapes involve geometric problem solving and notions of congruence and symmetry (MP7). They also involve the practices of making and testing conjectures (MP1), and convincing others that conjectures are correct (or not) (MP3). Such problems can be posed even for sets of simple shapes such as tetrominoes, four squares arranged to form a shape so that every square shares at least one side and sides coincide or share only a vertex.

More advanced paper-folding (origami) tasks afford the same mathematical practices of seeing and using structure, conjecturing, and justifying conjectures. Paper folding can also illustrate many geometric concepts. For example, folding a piece of paper creates a line segment. Folding a square of paper twice, horizontal edge to horizontal edge, then vertical edge to vertical edge, creates a right angle, which can be unfolded to show four right angles. Students can be challenged to find ways to fold paper into rectangles or squares and to explain why the shapes belong in those categories.

Questions/ Activities to check for understanding and increase rigor: A certain shape makes you think of a rectangle, but it is not a rectangle.

What could it be and why? You are working on a 5x5 dot grid. What polygons can you create? Show students a square and a rectangle that is not a square. Ask students to

explain how the shapes are similar and how they are different. Are they both rectangles? Are they both squares? Are they both quadrilaterals?

The shape I am thinking of has 4 equal sides and does not have any right angles. What shape(s) could I be? Am I a quadrilateral?

Draw a quadrilateral that has exactly two right angles and no sides are the same length. Compare your shape with your neighbor’s shape. Does your shape have a name? (trapezoid)

Level 1Entering

Level 2Emerging

Level 3Developing

Level 4 Expanding

Level 5Bridging

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Categorize polygons according to attributes byby working with a partner to label categories of pre-sorted shapes using a word bank.

Categorize polygons according to attributes by working with a partner to sort shapes into pre-labeled categories.

Categorize polygons according to attributes by working with a partner to label categories of pre-sorted shape names using a word bank of categories.

Categorize polygons according to attributes by working with a small group to complete an empty diagram using a word bank of shape names and categories.

Categorize polygons according to attributes by justifying their thinking orally to whole class.

Level 6 R

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ELD Standard #3: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Mathematics.