Volume: The size of a three-dimensional space
enclosed within or occupied by an object.

Area: The extent of part of a surface enclosed
within a boundary, or the extent of the surface of all or part of a solid.

Surface Area: The total area of the surface of a
three-dimensional object.

Vertex: A point where two or more straight lines meet. A corner.

Base: The surface that a solid object stands on, or the bottom
line of a shape such as a triangle or rectangle.

Face: Any of the individual surfaces of a solid object.

Edge: The line where two surfaces meet.

Regular Polygon: An enclosed shape where all angles and
sides are equal.

Cube: A box-shaped solid object that has
six identical square faces.

Cone: A three-dimensional geometric shape that
tapers smoothly from a flat base to a point called the vertex.

Sphere: A three-dimensional closed surface such
that every point on the surface is equidistant from a given point.

Rectangular Prism:  A solid (3-dimensional) object which has six faces that are rectangles.

Cylinder:  A solid object with two identical flat
ends that are circular or elliptical and one curved side.
Triangular Prism:  A prism with the cross section of a triangle.

• Students will select and categorize
       various two and three dimensional shapes found in objects located in and
       out of the classroom. 
• Students will generate a set of rules
       for classifying these selected objects.
• Students will apply the appropriate
       mathematical formulas for calculating area, surface area, and/or volume
       for each object
• Students will conclude and justify with
       evidence what he/she believe
       is the most commonly used two and three-dimensional shape in our world
       today and explain why that may be using mathematical evidence and
       calculations.

This lesson should take approximately five-six 40 minute class periods to complete.

• 
  Geometry Scavenger Hunt Work Sheet -  Geometry Scavenger Hunt.docx
• 
  Categorizing Shapes Worksheet -  Categorizing Shapes work sheet.docx
• 
  Geometry Formula Reference Page Website http://mdk12.org/share/pdf/hsa_math_reference_sheet_v2.pdf
• 
  Student and Teacher Rubric - Student and Teacher Evaluation.docx
• 
  Measuring Tape, Ruler, and/or Measuring Stick
• 
  Chart Paper, Poster Board
• 
  Optional - Digital Camera, iPad/iPod, and or computer with movie making
  or slide show ability

W: WHERE/WHY/WHAT

Because this lesson is most appropriate for students who have demonstrated mastery
of  many or all of the Fourth Grade Geometry skills for identifying and calculating shapes, students will be able
to not only extend and refine these grade-level skills, but also gain experience
and a better understanding of above grade-level skills by completing the steps
involved in this lesson.  This lesson is also infused with writing, speaking and listening, and technology skills as
well. This will provide the teacher with a means for both formative and summative assessment opportunities using observation and student/teacher rubrics (“Please Do Now”, Presentation, Final Product, and Persuasive
Essay). 

H: HOOK

Linking this lesson to real-world personal experiences allows the students to discover
how geometry skills and concepts are used in their life.  Completing a “Please Do Now” during the
introduction of this lesson provides the spark for this connection.  Integrating writing, speaking and listening,
and technology gives students who would not normally choose math as their
“favorite subject” a chance to explore the concepts in a way that they may find
more interesting.  The hands-on activity allows students to explore the concepts at their own pace using the option of
self-selection when choosing the geometric shapes.

E: EXPLORE/EXPERIENCE/EQUIP

Students will use hands-on experiences to locate, measure, and calculate the
self-selected geometric shapes.  During this exploration, students will have the opportunity to share thoughts with their
peers and listen to others’ thoughts and ideas when categorizing shapes and completing a final product to share the mathematical information.

R: RETHINK/REHEARSE/REVISE/REFINE

While categorizing shapes, students will have to reflect on what they already know
about these geometric shapes and rethink other possible properties of these
shapes.  When writing a persuasive essay, students will be required to revisit these concepts and support their thoughts
and ideas with the previously gathered data.

E: EVALUATE

Students will be formatively assessed using observation and discussion, as well as
teacher feedback of the “Geometry Scavenger Hunt” and “Categorizing Shapes”
worksheet.  Teacher will use summative assessment strategies by using a student/teacher rubric to score both the final
product/presentation and the persuasive essay.

T: TAILORED

Because this lesson is focused on differentiation for the high-ability/gifted learner,
many of the steps required in this lesson involve above-grade level concepts or
greater in-depth exploration of grade-level concepts and curriculum.  During the lesson, students will be able to
self-select the objects they are categorizing and measuring and their final
product, thus allowing them to independently increase or decrease the level of
challenge as needed.

O: ORGANIZED

Lesson and activities will be organized using a gradual release model, beginning with
whole group direct instruction (steps 1-4), and moving through guided
instruction (steps 2-3), small group/partner work (steps 5-8), and finally
individual work (step 9) involving extended thinking and real-world
application.

1. Student will complete a “Please DoNow” activity which will require him/her to write five lines reflecting on a
   time when he/she needed to calculate area, surface area, or volume outside of
   the classroom, or when he/she witnessed someone else who was calculating area
   or volume.  When complete, student will share their writing with a partner. 
   Students will then share their experience with the class. Teacher will
   document the students’ responses on chart paper.  This may lead to a class discussion of jobs
   that would require the use of geometric calculation and their importance in our
   lives.
2. Student will review geometric shapes by creating a class list of plane
   and solid geometric shapes and discussing the properties of these shapes.  Student will review formulas for area of plane geometric shapes and surface area and volume of geometric solids by
   accessing Geometry Formula Reference Page http://mdk12.org/share/pdf/hsa_math_reference_sheet_v2.pdf. 
3. Teacher will share a few selected classroom items that represent some of
   these geometric shapes. (For example: The class trash can, a calculator, the teacher’s desk, a ball, a poster,
   the door, dice, etc.) Teacher will present the students with their basic measurements and demonstrate how the area or surface area and volume of the shapes can be calculated using the formulas from the “Formula Reference Page”.  Teacher will allow for questioning and practice as needed to secure the appropriate calculation skills.
4. Teacher will explain to students that they will be challenged to go on a “Geometric
   Scavenger Hunt” in or around the classroom/school.  Working in small groups, students will search
   for a total of twelve various plane and solid geometric shapes and record them
   on their “Geometry Scavenger Hunt” worksheet. 
   When complete, each student will be required to calculate the area or
   surface area and volume of the selected objects.  They will then use their creativity to create
   a unique way to share the information they have found with the class.
5. Students will be broken into small groups and begin their scavenger hunt in a designated
   area selected by the teacher. Student will use a tape measure, ruler, or
   measuring stick to calculate the necessary dimensions to calculate the area,
   surface area or volume.  If desired, student may utilize a digital camera or iPad/iPod to take photos or video of the selected items.  Teacher may meet with small groups as needed during this time.
6. When all twelve objects are selected and calculated, student will complete the
   “Categorizing Shapes” worksheet.  This will require the student to compare the shapes, create three to four self-selected categories, and generate a set of rules for which to divide the shapes. 
7. Student will work with small group to create a final product that allows them to share
   with the class the information they have collected and the categories they have
   created.  Examples may include PowerPoint, Prezi, iMovie, poster, postcards, etc. and may utilize drawings or the pictures or videos the students collected during the scavenger hunt.
8. Groups will share their final product and calculations with the class.
9. After viewing all presentations, student will write a short persuasive essay
   identifying which plane and solid geometric shape he/she feels is most common
   or frequently used in our daily life.  Students will justify his/her conclusions with evidence, calculations and
   mathematical language learned and used throughout the lesson.

Formative Assessment will occur throughout lesson in the form of observation, "please do now" activity, at completion of "Gemetric Scavenger Hunt" worksheet, "Categorizing Shapes" worksheet, and again at completion of final product.  During evaluation of these steps in process, teacher should adjust direct instruction as needed to ensure full mastery of concept(s).

Additional Geometry
Websites

• 
  http://www.mathsisfun.com/geometry/
• 
  http://megamindacademy.com/what-is-solid-geometry/

Alternative Rubrics

• 
  http://www1.whsd.net/admin/Curriculum/files/PSSA%20Writing%20Scoring%20Guidelines.PDF 
  (Persuasive writing)