# Shape Hunting This problem gives you the chance to: identify and describe solid shapes

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1 Shape Hunting This problem gives you the chance to: identify and describe solid shapes Detective Sherlock Shapehunter tracks down solid shapes using clues provided by eyewitnesses. Here are some eyewitness reports. Which shapes do they describe? 1. This shape has 6 square faces. It does not roll. It is a regular prism. It has 8 vertices and 12 edges. This shape is a. 2. This shape has one curved surface that meets at a point. Its base is one flat circular surface. This shape is a. 3. This shape has one curved surface. It has 2 flat ends that are congruent circles. This shape is a. 4. An eyewitness saw this shape. Write three clues that describe it. The name of this shape is. Copyright 2007 by Mathematics Assessment Page 95 Shape Hunting Test 5

2 5. Write three clues that would help Detective Sherlock Shapehunter to track down a pyramid on a square base. 6. Detective Sherlock Shapehunter says that a sphere is different from all other solid shapes. Write two clues that describe how it is different from other shapes. 8 Copyright 2007 by Mathematics Assessment Page 96 Shape Hunting Test 5

3 Task 5: Shape Hunting Rubric The core elements of performance required by this task are: identify and describe solid shapes Based on these, credit for specific aspects of performance should be assigned as follows points section points 1. Gives correct answer: cube 1 2. Gives correct answer: cone 1 3. Gives correct answer: cylinder Writes three correct clues such as: It has 6 vertices. It has 9 edges. It has 5 faces. 3 faces are rectangular. 2 faces are triangular. Gives a correct name: Triangular prism All four items correct. Partial credit 1 point for 2 or 3 correct items 2 (1) 2 5. Writes three correct clues such as: It has 5 faces. Four faces are congruent triangles. It has 5 vertices. It has 8 edges. It doesn t roll Partial credit 1 point for 2 correct clues. 2 (1) 2 6. Writes two correct clues such as: It has no flat surfaces. It has no edges. It has no vertices. It rolls in all directions. 1 1 Total Points 8 Copyright 2007 by Mathematics Assessment Page 97 Shape Hunting Test 5

5 Looking at Student Work on Shape Hunting Student A is an example of a student with full marks, whose clues show a high level of sophistication in geometric language and the attributes noticed. The student talks about parallel sides and uses words like congruent. Student A 5 th grade

6 Student A, part 2 Student B also has a well-developed geometric vocabulary and awareness of important geometric attributes to notice and quantify. Note the high-level explanation of the sphere in part 6. Student B 5 th grade

7 Student B, part 2 Many successful students made visual representations of the shapes to help them think about the properties being described. Student C also has a nice description for the sphere. Student D has full marks, but talks about the triangles as ends rather than parallel faces or bases. Student C 5 th grade

8 Student C, part 2 5 th grade

9 Student D Student E clearly thinks that the base is always the side on the bottom, rather than understanding that the shape can be rotated in space. What is a reasonable expectation for students at this grade level about this idea of base? How do you want to develop that idea over time to expand and deepen the understanding? Student E 5 th grade

10 Student F is able to name the shapes in on parts1-3. The students has 3 acceptable clues in part 4, but it would have been nice to describe what the congruent shapes looked like. How could you use this work to pose a question to the class that might make them see a need for given more details? In part 5 the student describes the pyramid as point on top? Is this a good geometric description? How is this vertex different? Why not 5 vertices? The student has a common misconception about the number of faces in the pyramid. Can you think of two or more reasons why students might give this answer? Student F As students start to get lower scores, they give 2-dimensional names to some of shapes. They also use more informal language to describe the attributes and don t give the level of detail. In part 5, Student G doesn t describe the shape of the sides or bottom, which are critical in order to identify the shape. Student G received 5 points on the task. 5 th grade

11 Student G Student H has a score of 2. The student is using some informal language, such as box and points. The student is unclear about critical attributes to describe, so instead talks about long without a reference. Notice that sides and bottom are different, as opposed to 5 faces. The student thinks the sphere has a base. What might the student be thinking? 5 th grade

12 Student H 5 th grade

13 At the lower end students have trouble drawing the geometric representations. Notice how Student I draws a curved surface with a point. 3 of the names used by Student I on page 1 of the task are of 2- dimensional shapes. Also the student incorrectly uses the word edge in part 5. What kinds of activities help students develop academic language? What opportunities have your students had that help them develop their ability to make better geometric representations? Student I 5 th grade

14 Student I, part 2 Student J also has difficulty with drawing the cube. Notice how the student describes the triangular prism. What van Hiele level is this student operating on? What is your evidence? Student J 5 th grade

15 Again, Student K has two points on this task. Look at how the representations. While the description for the sphere seems o.k. without the pictures, do you think the student really knows what a sphere is? Student K 5 th grade

16 The next set of work illustrates some of the difficulties students had with parts 5. 5 th grade

18 5 th Grade Task 5 Shape Hunting Student Task Core Idea 4 Geometry and Measurement Identify and describe solid shapes. Use geometrical attributes to describe a solid figure. Analyze characteristics and properties of two- and threedimensional geometric shapes, understand attributes, and apply appropriate techniques, tools, and formulas to determine measurements. Identify, compare, and analyze attributes of two- and threedimensional shapes, and develop vocabulary to describe the attributes. Based on teacher observation, this is what fifth graders knew and were able to do: Describe something about a sphere Identify a cube and a cylinder from clues Write two or three clues about a triangular prism Write two clues about a pyramid Areas of difficulty for fifth graders: Making representations of 3-dimensional shapes Using academic language to describe geometric attributes Recognizing a cone from clues Counting faces and vertices for 3-dimensional shapes Understanding the base of a prism as one of the parallel sides 5 th grade

20 Points Understandings Misunderstandings 0 70% of the students with this score attempted the task. Students used everyday language or incorrect language to describe the sphere: e.g. It looks like a ball. It s a circle. They also chose attributes that could be used for other shapes: 2 Students with this score could usually write two clues about a sphere and identify a cube from clues or write two or three clues about a triangular prism from looking at a diagram. 4 Students with this score could describe the sphere, recognize one or two shapes from descriptions, and write clues for either the triangular prism or the pyramid. Its round. 12% of the students thought the cube was a square. 10% thought the cube was a rectangle. 6% thought the cube was an octagon. 9% of the students described the overall shape for triangular prism, e.g. It looks like a roof or a box. 4% of the students said the triangular prism had a rectangular base. 3% said that it had 6 faces and another 3% thought it had 3 faces. 6% of the students only gave two clues for the triangular prism. 5% of the students did not attempt to write clues for the triangular prism. 7.6% of the students thought the cone was a sphere. 8% thought the cone was a circle. 6% did not attempt to identify the shape described in part 2. 8% thought the cylinder was a sphere. 6% thought the cylinder was a circle. 7% did not attempt to name the cylinder from the clues. Students couldn t name the triangular prism. 12% left the name blank. 5% called it a triangle. 6 Students with this score generally could not write clues for the pyramid. 10% said it looks like a triangle. 12% used nonmathematical clues: Its found on money. Bring a flashlight. 12% said it had 4 sides or faces. 4% thought it had 3 faces. 8% said there were 3 triangles. 10% said its pointy. 8 Students could name 3-dimensional shapes from clues. They could write clues for a triangular prism given a diagram. They could write clues for a sphere and square pyramid without drawings. They new important attributes for describing 3-dimensional shapes. 5 th grade

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