S+Hardy,+Meng

**Office: Room 168** **Office Hours: Monday, Wednesday, Friday: 2:00-3:00pm** **Phone: 207-778-xxxx** ** E-mail: Meng.Hardy@maine.edu **
 * Teacher: Mrs. Hardy**

=Summary of Unit= Cones, cylinders, and spheres are not just mathematical figures, they are also everywhere in our daily lives. In this unit we will study the volume formulas of those 3-D shapes by first examining and comparing the similarities and differences between 2-D and 3-D shapes. Then we will learn the correlations between different attributes of 2-D and 3-D shapes. Finally we will use formulas of volumes to solve mathematical problems and apply the formulas to real life examples.

=Establish Goals=
 * Common Core State Standards**
 * Content Area:** Mathematics
 * Grade Level:** 8th Grade
 * Domain:** Geometry
 * Cluster:** Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
 * Standard:** 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

=Students will understand that= •relationships exist among two-dimensional shapes, three-dimensional figures, and between two-dimensional and three-dimensional figures. •the connections among the angles, sides, lengths, radius, perimeters, circumferences, areas, heights, volumes could be represented through mathematical formulas. •the volumes of cones, cylinders, and spheres could be applied to real-world situations.

=Essential Questions= •Why 2-D shapes and 3-D figures are related? •How are the attributes of 3-D figures connected? •How could the volumes of cones, cylinders, and spheres be applied to real world?

=Students will know= •Definitions: 2-D shapes, 3-D figures and all the attributes related to 2-D and 3-D figures •Formulas: 2-D shapes and 3-D figures •Critical details: shapes are defined by attributes, in real life volumes of cones, cylinders, spheres could be important

=Students will be able to= •describe the differences between 2-D and 3-D shapes. •compare the 2-D and 3-D shapes to see the similarities. •illustrate all the attributes of 2-D and 3-D shapes on a graph. •recognize changes in attributes leads to changes in other attributes. •solve mathematical problems using the formulas of volumes of cones, cylinders, and spheres. •imagine the real-world applications of volume formulas.

=**Performance Task Overview**=

You and a partner are two architects who are seeking job opportunities at the top rated William Rawn Associates in Boston, MA. There is a joint position opening for a design team who can produce a new office design that would appeal to the UN Building Bid Panel. You and your partner will create an iMovie to showcase your building design with related mathematical calculations to show the Panel why your design meets the criteria of (1) an innovative 21th century appeal: utilizing the shape of cones, cylinders, and spheres, (2) space efficiency: limited site area and required minimum office space. If your design is chosen by the Panel, then you and your partner will be hired by William Rawn Associates. Good luck to you all!

=Expectations= =Benchmarks= • **Microsoft Word (20 points)**: Students will create a digital brochure on their own using Microsoft Word. In the brochures, students need to describe the differences between 2-D and 3-D shapes to third graders. Students could include geometrical definitions, graphs, and/or hyperlinks to web resources. • **Comic Life (20 points)**: Students will create a comic with a partner using their flow charts to illustrate the similarities and differences between the 2-D and 3-D shapes. Students will post their comic on class wiki and share their comic with peers. • **Glogster (20 points)**: Students will illustrate all attributes of 2-D and 3-D figures in a poster to share with their parents. The poster could include class notes, geometrical definitions, and anything that helps the students to deliver their understanding. • **Google Sketchup (20 points)**: Students will use Google Sketchup to make 3-D models of cones, cylinders, or spheres to demonstrate that changes in one attribute lead to changes in other attributes through graphs and mathematical calculations. Students can choose any two or even three shapes of cones, cylinders, or spheres to show that if one attribute of the shape is fixed then, a change in the second attribute will lead to changes in other attributes. • **Prezi (20 points)**: Students will make a Prezi to exemplify how they could solve mathematical problems using formulas of volumes. Students should use sketches and mathematical calculations to show the changing factors of attributes. • **iMovie (20 points)**: Students can apply volumes of cones, cylinders, and spheres to the real world through their fictional stories. Within students' digital fictional stories, there should be shapes of cones, cylinders, and spheres present, and mathematical calculations of volumes of these shapes. • **UN Building Bid Panel Digital Presentation (30 points)**: Students will take on the role as architects working in pairs to design a new office building utilizing the shapes and volumes of cones, cylinders, or spheres for the UN in New York city. You have to create a digital presentation using Type II technology and present to the whole class, who will take on the role as the members of the UN Building Bid Panel. In your presentation, you have to demonstrate to the UN Building Bid Panel why your design of an office building that utilized the shape of cones, cylinders, or spheres is both innovative and space efficient.
 * Absences:** Attendance is vital in keeping up with new things we learn and do in this class. You are advised to attend and participate in every class. Please join the class on-time and prepared. Keep your minds open for activities and technologies we will encounter in this class. If you miss a class due to any reason, please get in contact with me via phone or email. You can also check on the class wiki for class notes, assignments, and supplemental materials. However, keep in mind there is no better way to learn than working together with your peers in class. Get in touch with your learning buddy from this class to help you stay on pace with the rest of us. There will also be a folder with handouts, assignments or any materials you missed in class due to absence.
 * Plagiarism:** Original work is required in this class. Any words, materials, or resources used should be cited. Plagiarism will not be tolerated and sanctions for academic dishonesty will be consistent with school policy.
 * Assignments:** Assignments should be reflections of what you already know and can do. They are not judgements, but useful tools for me to help you in this class. You are expected to turn your original works in on-time. Once you get feedback from me, you can make adjustments accordingly to gain more points. Late or missing assignments need to be submitted in a timely manner that you and I can both agree upon.
 * Classroom Expectations:** This class is a safe learning environment for you away from home. You are expected to treat peers, teachers, visitors, volunteers and substitute teachers, with respect and appreciation. Positive attitudes and willingness to achieve personal best are important factors for supporting this learning environment we share. You are expected to be a constructive part of this learning community.

=Grading Scale= **A** (93 -100), **A-** (90 - 92), **B+** (87 - 89), **B** (83 - 86), **B-** (80 - 82), **C+**(77 - 79), **C** (73-76), **C-** (70 - 72), **D+**(67 - 69), **D** (63 - 66), **D-** (60 - 62), **F** (0 - 59)