## Geo Jammin' - Day 4, Lesson 14: Give It a Whirl

### Katie KoehnemannBay District Schools

#### Description

Exploration of rotating 3-D shapes at varied speeds has students discovering, discussing, and questioning. Personal reflections move students to a hands-on activity that has them transition a two-dimensional square into a three-dimensional pinwheel.

#### Objectives

The student writes for familiar occasions, audiences and purposes (including but not limited to entertaining, informing, responding to literature).

The student uses volume, phrasing, and intonation appropriate for different situations (for example, large or small group settings, sharing oral stories, dramatic activities).

The student describes attributes of two-dimensional shapes using mathematical language (for example, curves, edges, vertices, angles).

The student describes attributes of three-dimensional shapes using mathematical language (for example, curves, vertices, edges, faces, angles).

The student sorts two- and three-dimensional figures according to their attributes.

The student knows the names of two-dimensional and three-dimensional figures presented in various orientations in the environment.

#### Materials

-A prepared 8½-inch square pinwheel pattern (See Associated File)
-One large, sturdy drinking straw (not the kind from the lunchroom) for each child
-Scissors
-Sturdy, extra long pins
-Pliers
-Computer hooked up to a television monitor
-Geo George puppet
-Copy of Give It A Whirl Geometric Word Part Meanings (See Associated File)
-An Assessment Management Tool for each student (See Associated Files in the Unit Plan)

#### Preparations

1. On the pinwheel pattern (See Associated File) line segments extend to the sides of the paper. When printed, the lines are beyond the print area so they appear to be cut off on the outer most edges. Solution: After printing, either extend each by drawing in with pencil and ruler, or be ready to have students extend the lines before they begin to cut.
2. Make sure the computer is hooked up to a large television monitor.
3. Visit the Website. Be familiar with features of the rotating polyhedra and bookmark the site.
4. Copy the pinwheel pattern for each student. (See Associated File)
5. Copy the Give It A Whirl Geometric Word Parts Meanings page. (See Associated File)
6. Gather a drinking straw for each student.
7. Gather scissors for each student.
8. Have on hand heavy-duty pins.
9. Secure a pair of pliers to use.
10. Prepare the Geo George puppet.
11. Use the Assessment Management Tool to record student formative assessment results. (See Associated Files in the Unit Plan)
12. Associated File contains:
Pinwheel Pattern
Give It a Whirl Geometric Word Part Meanings

#### Procedures

1. This lesson comes directly on the heels of Lesson 13, Where, Oh Where, Can the Geo Be?, introduced by Geo George saying he can show what all the odd named polyhedron shapes are from the story just read.

2. Geo George directs students’ attention to the television monitor. Pull up suggested Website and move students through the rotating polyhedron activity.
*NOTE: This is a fascinating site. Expect students to be enthralled by what they see and can do with the various three-dimensional shapes. If it is not possible to supply your classroom with three-dimensional manipulatives which students can hold, feel, touch, and explore, this rotating feature is about as good as it gets.

3. Facilitate student exploration of rotating shapes by allowing a free flow of questions and observations by students as they experience activities/questions 1-5 provided with the site. Allow the students themselves to answer, discuss, and explain to each other questions and observations that are forthcoming.

4. Formative assessment occurs as questions are asked and students discuss in response. Listen for feedback given by peers, guiding the instruction through further questioning by Geo George. For example, left click the F=4 button. To stop the rotating shape, left click it. By left clicking on it again and holding the button down, you can move the object very slowly and at will.
*A student may observe that this reminds them of the pyramid that was discussed, but it's not really because it's different.
*Another student may add that all the faces are triangles. There isn’t a square part to it.
*Challenge by asking, if the faces of this polyhedron are all triangles (demonstrate this by rotating slowly with the mouse) what do you think the name of this polyhedron is.
*Draw students’ attention to the top of the chart, and state it is a tetrahedron.
*Write tetrahedron on the chalkboard in two parts: tetra- and hedron.
*Ask “What does tetra mean?” (Four; having four parts)
*Ask “What does hedron mean?” (From a Greek word for seat)
*Students should come up with the idea that the word tetrahedron means “four seats.”

5. Point out that each of these three-dimensional objects is one of the polyhedrons listed in the story from Lesson 13, Where, Oh Where, Can the Geo Be? Ask why they think the code for changing to a different design is F=4, F=6, F=8, F=12, F=20? Students should break the code and respond that “F” stands for “face,” and the number equals how many faces that design has.

6. To transition from one shape to the next, spin the figure by gliding the mouse over it. The speed of your motion determines the speed of the spin. Spin horizontally and vertically.

7. Explore each polyhedron with students as explained above. Ask higher-order thinking questions, leading students to discover interesting facts about these shapes. (See Associated File for a list of word meanings. The intent is not to spend much time and tangle with big technical words and their meaning. This is only a glimpse into more technical geometry to expose student. Do not let this make the lesson become too long or detailed).

8. After all shapes have been investigated, choose one shape, set the rotation, and as one of the shapes turns very slowly, ask students to take out their Math Moments journals and write their reflections of what they think about two- and three-dimensional shapes.

9. Give students 4–5 minutes to make their journal entry. As students write, Geo George puts a question on the board, “Can a two-dimensional figure become a three-dimensional figure?” Direct student attention to the question on the board. Students are to write their response to the question in their math journals.

10. Geo George calls on a few students to read their responses to his question. Formatively assess as students share ideas on transforming from 2-D to 3-D. Accept all thoughts and possibilities, listening for misunderstanding and confusion and use this data to guide the next part of instruction.

11. Turn off the television monitor.

12. Hand out to each student a pinwheel pattern. (See Associated File) Have students identify it as a two-dimensional square.

13. Hand out a drinking straw. Have students identify it as a three-dimensional cylinder. Formatively assess individual student responses as they are called on to identify various two-dimensional features of the pinwheel pattern and three-dimensional features of the drinking straw. For the square, monitor student response for accurate and correct usage of mathematical language with regards to DIAGONAL LINE SEGMENTS, POINTS on each LINE SEGMENT, CENTER POINT, SURFACE, SIDES, and the fact that only HEIGHT and LENGTH can be measured. Follow the same procedure with the straw. Students should identify the FACES, EDGES, and the idea that height, length, and depth can be measured.

14. Directions for making the pinwheel are written using geometric language. They are located at the bottom of the pinwheel pattern. (See Associated File)

15. Guide students through the written instructions one step at a time. Guide through mathematical language, highlighted by small-scale upper case letters. After each step is read silently and orally, call on a student to put into their own words what the instructions are telling them to do. Formatively assess student interpretations for accuracy.

16. Students work on making the pinwheel. Formative assessment occurs as students demonstrate comprehension by following the directions. Monitor students as they work. Give positive and corrective feedback.
*For example, if a student is not sure where to cut the diagonal line segment, ask them to point to a side angle. Ask, “Where is the vertex of that angle?” Ask them to explain what they are to do from this vertex. Student may respond, “Cut the line.” Ask, “What about cutting the line?” Student may respond, “Cut the line segment to the point.” Ask the student to show where the point is.

17. As students complete their pinwheel, use the pliers to bend over the tip of each pin.

18. Instruct students to take out their Math Moments journals and re-address the question, “Can a two-dimensional figure become a three-dimensional figure?”

19. Allow time for various students to share how their ideas and thoughts are alike and/or different now from their ideas and thoughts before the activity.

20. Take the class for a walk around the school with their pinwheels. (Optional)

21. Set up learning centers with polyhedron patterns for students to make their own three-dimensional shapes. (See Extensions below)

22. For individual formative assessment, read students’ journal entries at the end of the day giving positive and corrective feedback on the page. Formative assessment data should drive further instruction.

#### Assessments

Student understanding of mathematical language and the ability to identify and describe two- and three-dimensional shapes and attributes is formatively assessed as oral responses and answers are given to thinking questions and as students share observations and participate in class discussions with regards to similarities and differences they notice using rotating three-dimensional polyhedrons. Students are formatively assessed on their understanding of mathematical terms through the making of a pinwheel by following directions which are written geometrically correct, and through their journal entries by which they demonstrate an understanding of the characteristics of two- and three-dimensional figures.

#### Extensions

1. Set up at learning centers three-dimensional polyhedra nets so students can create their own. The nets are at the suggested web site and can be copied. The dodecahedron and icosahedron have so many sides that it is quite complicated and it is not suggested for little second grade hands. However, the tetrahedron, cube, and octahedron should be a fun and an enjoyable challenge. Each of the nets is small. Enlarge on a copy machine to make them more of a workable size. Experimenting with enlarging them, listed below is one way to get the patterns the size of a full sheet of 8 1/2” x 11” piece of paper. Note that each needs to be enlarged differently. As you enlarge each time, be cognizant of how to place the original on the copier. Slide one way or another to cut off text and get just the net on the paper.

Tetrahedron
Print from Website
Enlarge original 142 %
Enlarge the enlargement 125%

Cube
Print from Website
Enlarge original 142%

Octahedron
Print from Website
Enlarge original 142%
Enlarge enlargement 142%
Enlarge enlargement 125%

2. Lessons may reflect modifications of, but are designed in conjunction with the Reading Framework approach to classroom instruction and may be adapted to the Four Block Classroom.
3. This is Lesson 14 – Give It a Whirl; a Math lesson
Lessons 1 – 3 are for Day 1 of the unit Geo Jammin’
Lessons 4 – 7 are for Day 2 of the unit Geo Jammin’
Lessons 8 – 11 are for Day 3 of the unit Geo Jammin’
Lessons 12 – 15 are for Day 4 of the unit Geo Jammin’
Lessons 16 – 19 are for Day 5 of the unit Geo Jammin’
Lesson 20 is for Day 6 of the unit Geo Jammin’
Lesson 21 is for Day 7 of the unit Geo Jammin’
4. The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2959. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, “Associated Files.” This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).
5. The Facts Please, Mr. Mumble is an interactive Student Web Lesson that addresses the standard: the student describes attributes of two-dimensional shapes using mathematical language (for example, curves, edges, vertices, angles). Students should visit the lesson regularly for optimal practice in describing two-dimensional attributes. The Facts Please, Mr. Mumble can be visited by clicking the link in the Weblinks section of this lesson plan or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=3161
6. Geo Cleo and the Shape Caper is an interactive Student Web Lesson that addresses the standard: the student describes attributes of three-dimensional shapes using mathematical language (for example, curves, vertices, edges, faces, angles). Students should visit the lesson regularly for optimal practice in describing three-dimensional attributes. Geo Cleo and the Shape Caper can be visited by clicking the link in the Weblinks section of this lesson plan or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=3160
7. Check the Geo Jammin’ Glossary for word definitions. The glossary is located in the Associated File of Lesson 2, Math Mouth.
8. Ask the ESE teacher for further modifications with regards to students needing extra assistance and/or learning strategies.

Math Forum Suzanne Alejandre – Polyhedra Activity
Math Forum

Web supplement for Day 4, Lesson 14 – Give It a Whirl
Polyhedra Nets

This is an interactive Student Web Lesson that addresses the standard: the student describes attributes of two-dimensional shapes using mathematical language (for example, curves, edges, vertices, angles).