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3 11. Explain to students that by sorting shapes additional comparisons can be made and relationships among the shapes can be revealed. 12. Have the class sort the shapes into two categories, shapes with parallel sides and shapes without parallel sides. 13. Observe students as they sort the shapes and assist as necessary. Reinforce the concept of parallel lines. 14. Select students to present the sorting and allow other students to provide feedback. 15. Direct the students to the pile of shapes with parallel sides. Have pairs sort the shapes into two piles, shapes with one set of parallel sides and shapes with two sets of parallel sides. Observe students as they sort and provide assistance as necessary. 16. Select students to present the sorted shapes. Have students identify the names of the shapes in each pile. 17. Explain to the students that trapezoids have at least one set of parallel sides and that parallelograms have two sets of parallel sides. Ask students to identify the shapes in the parallelogram pile. Tell students that squares, rect and rhombi are special parallelograms. 18. Have partners sort the parallelograms by angle measure, shapes with right and shapes without right. Observe how pairs sort the shapes and provide assistance as needed. 19. Have students identify the shapes in each pile. Ask students questions about the relationships. What do squares and rect have in common? (four right ) How are the rect and squares on the cards different? (lengths of sides) Can a square be described as a rectangle? Why? (A square is a special rectangle with four sides.) 20. Have students compare a rhombus and a square. Ask questions and allow pairs to discuss before selecting students to respond. Questions for discussion include: How are the square and rhombus alike? How are the rhombi and squares on the cards different? Can a square be described as a rhombus? Why? (A square is a special rhombus with four right.) 21. Summarize the relationships visually using a graphic organizer. Quadrilateral Relationships, Attachment D is an example of an appropriate organizer. Distribute to the students and complete the organizer together. Encourage students to use the shape cards to re-sort the shapes with the attributes used during the lesson. Instructional Tips: In the following days, have students share the graphic organizer and write comparisons of the quadrilaterals. For morning work or problem of the day, present prompts for students to respond, about quadrilateral relationships. Prompts may include: 1. All squares are rect, but not all rect are squares. Why? 2. All squares are rhombi, but not all rhombi are squares. Why? 3. Squares, rect and rhombi are parallelograms. Why? 3

5 Vocabulary: parallel lines parallelogram quadrilateral rhombus trapezoid Technology Connection: Use geometry software to draw and explore characteristics of quadrilaterals. Research Connections: Almy, M., E. Chittenden, & P. Miller. Young Children s Thinking: Studies of Some Aspects of Piaget s Theory. New York: Teachers College Press, National Research Council. Adding It Up: Helping Children Learn Mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, D.C.: National Academy Press, Attachments: Attachment A, Quadrilateral Post-Assessment Attachment B, Attributes of Quadrilaterals Attachment C, Quadrilateral Shapes 5

6 Attachment A Quadrilateral Post-Assessment Name Date Word Bank Parallelogram Rectangle Rhombus Square Trapezoid Directions: From the list of quadrilaterals, select two. Use the Venn Diagram to compare and contrast them. List at least two similarities and two differences for each. Name of Quadrilateral 1 Name of Quadrilateral 2 Directions: Complete this activity again using two different quadrilaterals. Use the table to compare and contrast them. List at least two similarities and two differences for each. Name of Quadrilateral 3 Name of Quadrilateral 4 Common Characteristics Different Characteristics 6

7 Attributes of Shapes Number of sides Number of Congruent sides Congruent Right Parallel sides Symmetry Congruent Investigating Quadrilaterals Grade Four Attachment B Attributes of Quadrilaterals Quadrilateral Square Rectangle Rhombus Trapezoid Parallelogram 7

8 Attributes of Shapes Number of sides Attachment B (continued) Attributes of Quadrilaterals Quadrilateral Square Rectangle Rhombus Trapezoid Parallelogram Number of Congruent sides have sides Congruent have Right have a right angle Parallel sides have parallel sides Symmetry have symmetry Congruent have All sides are All are All are right Opposite sides are parallel Has four lines of symmetry All are Opposite sides are All are All are right Opposite sides are parallel Has at least two lines of symmetry All are All sides are Opposite are Does not have to have right Opposite sides are parallel Has at least two lines of symmetry Opposite are have sides have have right At least one set of opposite sides are parallel have a line of symmetry have Opposite sides are Opposite are have right Opposite sides are parallel have symmetry Opposite are 8

9 Attachment C Quadrilateral Shapes 9

10 Attachment C (continued) Quadrilateral Cards 10

11 Attachment D Quadrilateral Relationships 11

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