Lesson Plans 1 - Zometool

1 Www Zometool com 2009 Zometool , Inc. Zometool is a registered trademark of Zometool Inc. 1-888-966-3386 US Patents RE 33,785; 6,840,699 B2. Based on the 31-zone system, discovered by Steve Baer, Zomeworks Corp., USAL esson Plans SystemBuilds Genius!1 Table of Contents 2002 by Zometool , Inc. All rights System in the ClassroomSubjects Addressed by Zome System ..5 Organization of Plans .. 5 Graphics ..5 Standards and Assessment ..6 Preparing for Class ..6 Discovery Learning with Zome System ..7 Cooperative vs Individual Learning ..7 Working with Diverse Student Groups ..7 Additional Resources ..8 Caring for your Zome System Kit ..8 Basic Concept PlansGeometric Shapes ..9 Geometry Is All Around Us ..112-D Polygons ..13 Animal Form ..15 Attention!..Angles ..17 Squares and Rectangles ..19 Try the Triangles ..21 Similar Triangles ..23 The Equilateral Triangle ..252-D and 3-D Shapes ..27 Shape and Number ..29 What Is Reflection Symmetry?

2 33 Multiple Reflection Symmetries ..35 Rotational Symmetry ..39 What is Perimeter? ..41 Perimeter Puzzles ..43 What Is Area? ..45 Volume For Beginners ..47 Beginning Bubbles ..49 Rhombi ..53 What Are Quadrilaterals? ..55 Trying Tessellations ..57 Tilings with Quadrilaterals ..59 Triangle Tiles - I ..61 Translational Symmetries in Tilings ..63 Spinners ..65 Printing with Zome System ..67 Zome SystemBuilds Genius!Printing Cubes and Pyramids ..69 Picasso and Math ..73 Speed Lines! ..75 Squashing Shapes ..77 Cubes - I ..79 Cubes - II ..83 Cubes - III ..87 Cubes - IV ..89 Even and Odd Numbers ..91 Intermediate Concept PlansDescriptive Writing ..93 Bubbles II: Surface Tension and Minimal Surfaces ..95 Tallest Tower in the World ..99 The Livable City ..103 Prime Factors ..105 Plane Patterns ..109 Triangle Tiles - II ..111 Tilings with Multiple Symmetries ..115 Spiral Symmetry ..117 Symmetries in Quadrilateral Tilings ..119 Measures of Space - I: Length and Areas.

3 121 Measures of Space - II: Volumes ..1253-D Triangles ..1293-D Triangle Tiles ..133 Finding Tau ..137 Naming 2-D and 3-D Shapes ..141 Plato s Solids - I ..145 Plato s Solids - II ..1492-D and 3-D Stars ..153 Kepler s Tilings ..155 Richert-Penrose Tilings ..157 Bridge Building Project ..159 Euler s Formula for Polyhedra ..171 Fun Fibonacci ..175 Fibonacci Numbers and the Golden Section ..179 Advanced Concept PlansArchimedian Solids ..181 Beehive City ..185 Similarity and the Golden Section ..189 Table of Contents 2002 by Zometool , Inc. All rights SystemBuilds Genius!3 Resources and Recommended ReadingsBooks Recommended for Specific Lesson Plans ..191 Suggested Extension Resources ..191 Blueprint, or Photosensitive, Paper: How to Use With Zome System ..191 Polygon Shapes for Paper Models ..193 Academic StandardsFine Art Standards ..201 Language Arts Standards ..201 Physical Science Standards ..201 Mathematics Standards for Grades K-4.

4 202 Mathematics Standards for Grades 5-8 ..202 Mathematics Standards for Grades 9-12 ..205 Zome System Glossary ..209 Table of Contents 2002 by Zometool , Inc. All rights reserved. 1526 South Pearl Street, Denver, Colorado 80210, USAP hone: 303-733-2880 Toll Free: 888-966-3386 Web site: SystemBuilds Genius!5 Subjects addressed by Zome SystemThe relationships inherent in Zome System s components make it possible to teach a vast num-ber of concepts. Teachers can apply the system to both purely mathematical pursuits, as well as a toolto explore structure and geometry as they relate technology, fine arts and the natural sciences. Whilea few of these concepts are covered by the initial Lesson Plans in this document, many more can beillustrated with Zome System. A partial list of ideas include: Art: proportions and scale, symmetry, perspective drawing, mosaics, and architectural design; Biology: symmetries in fruits and flowers, Fibonacci sequences, cell structures; honeycombs, DNAstructures; Chemistry: basic molecules, Buckyballs and other complex molecules; Civics: city planning; resource distribution, role of art and design in society; Geology: crystallography Mathematics: geometry, numbers sense, progressions, algebra, trigonometry, Fibonacci sequences,budgeting; Physics/technology: perspective drawing, architectural structures, stresses and gravity forces, of Plans The Lesson Plans are divided into three groups based on complexity level; basic concepts, inter-mediate concepts, and advanced concepts.

5 The complexity level is noted at the top of each three complexity levels are related to, but not limited to, the grade level the Plans are appropri-ate for. It is quite possible that we have miscalculated the appropriate complexity level for some of theplans. Teachers should evaluate the Plans individually before introducing the concepts to their stu-dents. The intent of the complexity classification is that first through third grade students will be ableto grasp the easier basic concept Plans . Fourth and fifth graders will be able to work with all the basic concept Plans , and in many cases move into the intermediate concepts. Middle school, andhigh school teachers should review the basic concept Plans before moving into the intermediate and advanced Plans . The lessons Shape and Number, What is Reflection Symmetry? and MultipleReflection Symmetry are particularly important for all grade levels to have covered before encourage all teachers to try concepts that they might not have attempted with their students inthe past.

6 Zome System is a very powerful system, and even very young students can use it to under-stand advanced lessons are organized in strings, where a plan may build on concepts introduced in aprevious one, and suggest continuation in more advanced ones. Here it is also important that theteacher ensures that students understand the basic ideas and how they work in Zome System, beforethey start working on the intermediate and advanced Plans . GraphicsMost of the Plans in Zome System Lesson Plans graphics of Zome System models are either required in the Plans , or are examples of structures students may build duringthe class. To contain printing costs these graphics are in black and white. However, the graphics areZome System in theClassroom 2002 by Zometool , Inc. All rights SystemBuilds Genius!6in most cases easy to interpret, as the shape of the struts is indicated. The struts can also be identifiedby their shading; red struts are depicted as dark gray/black, blue struts as light gray, and yellow strutsas white.

7 None of the graphics in this book depict the supplementary green struts that are availablefrom Zometool , Inc. Green struts are necessary to build some specific 3-D solids. blue strutsred strutsyellow strutsStandards and AssessmentTo aid teachers in states or provinces that promote uniform achievement levels, the Lesson plansmake reference to educational standards. Whenever possible we have chosen standards that are devel-oped or recognized by US national organizations in the subject area. In the case of mathematics con-cepts this means the standards adopted by the National Council of Teachers of Mathematics (NCTM).As most state and district standards in the US draw heavily on their national counterparts, Americanteachers will find that they can relatively easily convert one to the other. References to standards onthe Lesson Plans is limited to the title of each standard. More extensive text, including the variousbenchmarks the Plans address, is available as an appendix at the end of this Assessment section of each plan suggests how a teacher can evaluate students understand-ing of the concepts they are working on.

8 The assessment model is roughly in line with the one fea-tured in the NCTM Assessment Standards. The section states what the students must achieve or cre-ate in order to meet the standard, and what they must do to exceed the standard. Preparing for ClassPlay with Zome System before teaching with Zome System! The system has so many possiblecombinations and possibilities that teachers will benefit from exploring before introducing it to stu-dents. Playing with the pieces in advance will make the Lesson Plans easier to relate to. Students willinvariable ask questions about the system, and discover new relationships that can serve as a basis foradditional need to play and explore also applies to students. The first time Zome System is introduced,students should be allowed to investigate the system without having a specific task to perform. Theinitial exploration will help prepare them for the classes, and will make them excited about the con-cepts they are to pursue.

9 It is of course appropriate to discuss any features and relationships studentsobserve during the play period .Discovery Learning with Zome SystemThe lessons in Zome System Lesson Plans written in a format that promotes discoveryZome System in theClassroom 2002 by Zometool , Inc. All rights SystemBuilds Genius!7learning. In most cases the Plans are structured so the students are given tasks to complete, or prob-lems to solve using the Zome System pieces. Discussion questions are suggested in italics to promptstudent analysis of the concepts they are working on. The intention is that students will build under-standing for themselves so they can explain and replicate the knowledge. This process stimulates stu-dent curiosity and encourages them to study the subject matter further. Teacher will also find that thelessons will allow them to discover new ideas and challenge their previous understandings. The discovery learning promoted here does not replace the need for direct instruction.

10 Directinstruction is needed for clarification and guidance throughout each class. The level of instructionrequired for each group of students should be evaluated by the teacher. Cooperative vs. Individual LearningMost of the lessons in this document encourage group projects. Work in groups promotes valu-able team skills that often are difficult to apply in mathematics and science courses. By discussing thechallenges they are given in the lessons, students practice communication in mathematical language,and draw deeper understanding from the observations of their team members. A useful discussion onthe benefits of group work can be found in the discourse section of the NCTM Professional System can of course be equally useful for individual student projects. The lessons can eas-ily be modified to for individual work as deemed appropriate by the teacher. The lessons may in somecases require larger numbers of Zome System pieces when students work with Diverse Student Groups Zome System is unusual in that it can be applied with excellent results at a wide range of profi-ciency levels.