advertisement

eLibrary Standards-Based Learning Activity Balance That Teacher Procedures APPROPRIATE FOR: Math, Grades 6-8 TIMELINE: Three class periods MATHEMATICS STANDARDS ADDRESSED THROUGH THIS LESSON NCTM Standard 8 | Communication In grades 5-8, the study of mathematics should include opportunities to communicate so that students can: Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods; Reflect on and clarify their own thinking about mathematical ideas and situations; Develop common understandings of mathematical ideas, including the role of definitions; Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas; Discuss mathematical ideas and make conjectures and convincing arguments; Appreciate the value of mathematical notation and its role in the development of mathematical ideas. Standard 9 | Mathematical Connections In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that students can: See mathematics as an integrated whole; Explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations; Use a mathematical idea to further their understanding of other mathematical ideas; Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business; Value the role of mathematics in our culture and society. Standard 3 | Geometry and Spatial Sense In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can: Identify, describe, compare, and classify geometric figures; Visualize and represent geometric figures with special attention to developing spatial sense; Explore transformations of geometric figures; Represent and solve problems using geometric models; Understand and apply geometric properties and relationships; Develop an appreciation of geometry as a means of describing the physical world. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. Standard 2 | Algebra In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can Understand the concepts of variable, expression, and equation; Represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the interrelationships of these representations; Analyze tables and graphs to identify properties and relationships; Develop confidence in solving linear equations using concrete, informal, and formal methods; Investigate inequalities and nonlinear equations informally; Apply algebraic methods to solve a variety of real-world and mathematical problems. Standard 4 | Measurement In grades 5-8, the mathematics curriculum should include extensive concrete experiences using measurement so that students can Extend their understanding of the process of measurement; Estimate, make, and use measurements to describe and compare phenomena; Select appropriate units and tools to measure to the degree of accuracy required in a particular situation; Understand the structure and use of systems of measurement; Extend their understanding of the concepts of perimeter, area, volume, angle measure, capacity, and weight and mass; Develop the concepts of rates and other derived and indirect measurements; Develop formulas and procedures for determining measures to solve problems. (source: http://www.standards.nctm.org) LEARNING EXPECTATIONS/OBJECTIVES Students will meet Alexander Calder via eLibrary and learn about math, art and mobiles. Students will explore techniques for constructing mobiles. Students will build a mobile, applying geometric and algebraic reasoning to achieve balance. Students will use equations to model the relationships in their mobile. Students will develop an appreciation of math is an integral part of art. MATERIALS Computer with access to eLibrary Straws Glue Variable strengths of paper Colored pens or pencils String or fishing line Wire clothes hangers ACTIVITY PROCESS: DIRECTIONS TO THE TEACHER Description of Activity In this activity, students will explore the world of Alexander Calder, a famous American sculptor. Students will also learn how to construct a mobile, applying geometric and algebraic reasoning to achieve balance. In addition, students will use equations to model the relationships in their mobile, leading to an understanding of math an integral part of art. Student mobiles will be hung around the classroom. A project folder will be kept by students to hold their notes, pictures copied and Web sites visited, activities and a sketch of their mobile. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. Background Information/Scenario Have you ever seen a large, brightly-colored geometric mobile in an office building or museum? If you have, it was most likely the work of Alexander Calder, a famous American sculptor. Mobiles are moving sculptures possessing graceful balance and are very pleasing to the eye. Viewers of these works often ponder how the artists achieved such perfect balance between the scultures’ many parts. For this project, students will learn about Calder via eLibrary, and then design, create and hang a mobile with an uneven number of objects hung at uneven distances from a main support wire. Outline of Procedures -- Day One 1. Introduce the project to the class. You might show students pictures of a Calder mobile, or even a simple mobile depicting our solar system. Ask if they have ever made a mobile. What was the hardest part of making a mobile? 2. Read over the rubric with the class. 3. Hand out Activity 1. 4. Have students individually explore eLibrary to learn more. To find information about Alexander Calder in eLibrary: Go to eLibrary. Click Topics at the top of the page. Click Arts. Click Sculptors. Click Calder, Alexander. Conduct searches within eLibrary using these keywords: wire sculpture mobiles early mobiles monumental sculpture NOTE: If it is impossible to have students using eLibrary during class due to computer availability, you can print out the relevant resources and distribute them for students to review in hard copy. 5. Students research Calder. They sketch one of his mobiles or print out pictures of at least one example. They take notes about materials and techniques he employed in creating his art. 6. Students strive to explain how balance is attained in these works during a class discussion. 7. Students complete Activity 1. 8. Students research materials and take notes on what materials other artist use to construct mobiles. Outline of Procedures -- Day Two 9. Discuss Activity 1 with students. Allow them to correct any misconceptions or errors. 10. Hand out Activities 2 and 3. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. 11. Complete Activity 2 and let students brainstorm Activity 3 before actually writing out their answers. If they do not have the math, let them write a word equation. For instance, if 2.5 small disks weigh the same as one large disk then six small disks hung higher than two large disks might balance. 12. Students should complete Activity 3 Outline of Procedures -- Day Three 13. Students should use wire, fish line, string, clothes hangers, or plastic straws to construct a mobile. Hang cardboard disks, geometric figures (2 or 3 dimensional), figures made of clay or other objects from each work of art. 14. Students should use what they have learned to design the mobile so that it balances. They should write out any equations they used to build their mobiles. 15. Students should hang mobiles in your classroom, then assemble the other parts of their project into a notebook. Students should write a summary telling what they learned about creating a mobile and how they kept it in balance. Conclusion/Finished Work Collect project notebooks and evaluate them using the rubric as a basis of expectation. ASSESSMENT Scoring Rubric 3 You designed an attractive mobile that is in perfect balance. An unequal number of objects are hung on each side, or objects are hung at different distances from the main support wire. Appropriate equations and research notes are included. 2 You designed a mobile that is slightly out of balance, and you did not make enough effort to make it attractive or original. Your equations and/or notebook may be incomplete or contain errors. 1 You designed a mobile that clearly does not balance. Your equations or notebook contains errors or omissions. 1 You left out or did not complete major elements of the project. You must have a teacher conference before you complete this project a second time. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. Research Students should be evaluated based on these criteria: Did student use eLibrary to collect information and pictures about mobiles? Did students organize information and use it in creating their mobile? Writing Students should be assessed on whether they wrote an understandable explanation of creating their mobile and used appropriate vocabulary. Each student summary should clearly communicate the process employed in completing the project. OPTIONAL EXTENDED ENRICHMENT ACTIVITIES Return to eLibrary and find other sculptors who work in other mediums. Write a paper about the artists you find most fascinating. Create a second or third mobile using mixed media, applying the principles you learned during the initial activity. ANSWER KEYS ACTIVITY 1: x + 3 = 5; 2 oz ACTIVITY 2: 2.5 in ACTIVITY 3: 3 oz; 2*6 = 4x © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. Balance That A Math Lesson Have you ever seen a large, brightly-colored geometric mobile in an office building or museum? If you have, it was most likely the work of Alexander Calder, a famous American sculptor. Mobiles are moving sculptures possessing graceful balance and are very pleasing to the eye. Viewers of these works often ponder how the artists achieved such perfect balance between the sculptures’ many parts. DURING THIS ACTIVITY YOU WILL… Meet Alexander Calder at eLibrary and learn about math and its use in constructing artistic mobiles. Keep accurate research notes as you explore techniques for construction of a mobile. Design and construct a mobile applying geometric and algebraic reasoning to achieve balance, with an uneven number of objects hung at uneven distances from the main support wire. Use equations to model the relationships within your mobile. DAY ONE 1. Read over the rubric and the activity. Focus on your end product. 2. Explore eLibrary to learn more about Calder. To find information about Alexander Calder in eLibrary: Go to eLibrary. Click Topics at the top of the page. Click Arts. Click Sculptors. Click Calder, Alexander. Conduct searches within eLibrary using these keywords: wire sculpture mobiles early mobiles monumental sculpture 3. Research Calder. Sketch one of his mobiles or print out pictures of at least one Calder work. Take notes about materials he used. Include any facts you find interesting. Keep detailed notes about the sites you visit. 4. Complete Activity 1. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. 5. Return to eLibrary and complete additional research into what materials other artists use to construct mobiles. Take detailed notes. DAY TWO 6. If needed, correct Activity 1. 7. Complete Activity 2 and brainstorm Activity 3 before actually writing out your answers. You can write a word equation. For instance: If 2.5 small disks weigh the same as one large disk then six small disks hung higher than two large disks might balance. 8. Complete Activity 3 DAY THREE 9. You are now going to create a mobile. Sketch out what you think you would like to do. Include wire/string lengths and shapes/sizes/weights. 10. Use wire, fish line, string, clothes hangers, or plastic straws to construct a mobile. Hang cardboard disks, geometric figures (2 or 3 dimensional), figures made of clay or other objects from your work of art. 11. Use what you have learned to design a mobile that balances. Write out any equations you used to build your mobile. (If you made your mobile first, create the equation that proves that it balances now.) 12. When finished, hang (display) your mobile in your classroom. 13. Assemble the other parts of your project in a notebook. Include notes, eLibrary sites you visited, sketches and all activities. You should write a summary telling what you learned about creating a mobile and how to keep it in balance. ASSESSMENT Scoring Rubric 3 You designed an attractive mobile that is in perfect balance. An unequal number of objects are hung on each side, or objects are hung at different distances from the main support wire. Appropriate equations and research notes are included. 2 You designed a mobile that is slightly out of balance, and you did not make enough effort to make it attractive or original. Your equations and/or notebook may be incomplete or contain errors. 1 You designed a mobile that clearly does not balance. Your equations or notebook contain errors or omissions. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. 0 You left out or did not complete major elements of the project. You must have a teacher conference before you complete this project a second time. Research You will be evaluated based on the following criteria: Did you use eLibrary to collect information and pictures? Did you take good notes on what you uncovered online? Writing You will be assessed on whether you used the appropriate math vocabulary as you wrote your summary. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. ACTIVITY 1 In this project you will consider mobiles on which objects hang to the left or right of a main support line/wire. Suppose you want to construct the mobile below. You want to find the weight of x that will make the mobile balance. Write and solve an equation to represent your conclusion. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. ACTIVITY 2 To construct a mobile you hang one disk five inches to the left of the main support. You want to hang two equal size disks on one string to the right of the main support. Solve the equation 2x =5(1) to find out how far away from the support wire they should be. Write a similar problem describing how to hang an unequal number of disks on each side of a mobile. Write and solve the equation you use. Experiment to test your results. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only. ACTIVITY 3 You are constructing a new mobile. You hang a 2oz. disk six inches from the main support wire. You want to hang a different sized disk four inches away from the other side of the support wire. Experiment to find out how much the disk should weigh for the mobile to balance. Write an equation to illustrate your conclusion. © 2003 ProQuest Information and Learning Company. Permission is granted to duplicate for classroom use only.