Overview
 The topic of my unit is Basic Geometry.  This two week unit is the first of three units covering geometry designed for the seventh grade level.  In grades prior to seventh grade, mathematics content taught varies from school to school.  It is therefore important to begin with numerical prefixes and identification of polygons and quadrilaterals.  The lessons following include content such as finding perimeters, angle measures, circumference, congruency, rigid motions, and symmetry.
 I will also include some language arts by incorporating some dictionary use, note taking, and in an extension lesson, having the students explain a quilt design they designed in written as well as oral form and finally producing a class book with these products.  This final project is also relevant to real-life situations which current NCTM standards encourage teachers to do.
 Classes are made up of many mathematical skills, abilities and prior knowledge.  Since students also possess a wide range of learning styles, I use an array of teaching strategies to involve all students.  It is important for students to succeed in Basic Geology for content taught in this unit will be necessary for success in units throughout seventh grade and in school years to come.

Goals
1. Students will use a dictionary to aid them in learning numerical prefixes and apply this knowledge to learning geometric shapes.
2. Students will become familiar and comfortable with identifying different type polygons and quadrilaterals.
3. Students will succeed in finding perimeters and angle measures of polygons and circumferences, radii, or diameters of circles.
4. Students will become familiar with congruency, rigid motions, and symmetry of objects.
5. Use content learned in this unit to construct a one-patch quilt pattern.

Objectives
The students will be able to: (Bloom’s Taxonomy)
1. Locate definitions in a dictionary for words involving numerical prefixes. (Application)
2. Memorize prefixes that are associated with the numbers one through ten, one hundred, and one thousand. (Knowledge)
3. Generate new words to describe numerical phenomena and definitions of unfamiliar words without using a dictionary. (Synthesis)
4. Identify polygons and quadrilaterals and explain differences and similarities of polygons and different quadrilaterals. (Knowledge and Evaluation)
5. Solve for the perimeter of polygons and find the measure of each angle of a polygon given the total number of degrees. (Application and Analysis)
6. Solve for the circumference of a circle given the radius or the diameter; and the reverse (solve for radius or diameter).  (Application and Analysis)
7. Recognize, identify, and construct congruent relationships. (Knowledge and Synthesis)
8. Recognize the type of rigid motion illustrated and explain how a given polygon is translated, reflected and/or rotated. (Knowledge and Comprehension)
9. Identify lines and points of symmetry, construct symmetric objects and justify why they are symmetric. (Knowledge, Synthesis and Evaluation)
10. Individually create and color a one-patch quilt design based on the regular hexagon, then write and orally present a brief description of their patch and why they chose that design. (Synthesis and Evaluation)

Instructional Overview
 Mathematics is a subject that must be taught based on prior knowledge.  This is why I chose to begin this unit with an activity to introduce students to numerical prefixes.  To begin this two-day lesson, I will orally quiz the students on their knowledge of polygons such as quadrilaterals, pentagons, and so on.  Following some probing questions, each student will be given a dictionary with a worksheet of “numerical words” to look up and will write the definition of each (i.e. unique, triple, decade).  The students will then brainstorm to come up with some other words that have these same prefixes.  Students will then be given a second worksheet which asks them to, using a dictionary, write the definitions of twenty words that have numerical prefixes.  A third worksheet consists of questions the students should now be able to answer without the use of a dictionary (ex: “What is wrong with the naming of the months September, October, November, and December?”).  To tie it all together, I will draw a strange looking creature with multiple eyes, ears, legs, etc. and have the students invent a name for the creature based on number prefixes.
 My next lesson involves the students becoming acquainted with polygons and quadrilaterals.  I expect this lesson to go smoothly after the lesson on number prefixes.  The students should be ready to identify polygons according to the number of sides they have due to their knowledge of numerical prefixes.  Although quadrilaterals are polygons, students must realize there are many kinds of quadrilaterals and familiarize themselves with the differences as well as similarities.
Finding perimeters of polygons and finding the measure of angles of polygons is the next topic.  This topic could be either a one or two-day lesson depending on how well the students grasp the content.  After taking some notes, the students will work in pairs to complete a pairs-check worksheet in which partner A will complete one column and partner B will complete the second while checking each other’s work.
The next lesson includes finding circumference of a circle, the radius, or the diameter depending on the information given.  To become more competent with this material, after note taking the students will work in groups and use the Numbered-Heads Together method to answer questions from this lesson and ones prior to it.  The students’ answers will be put on slates to show to the teacher and class.  This will also serve as a review for the quiz the next day.
Having now a foundation for geometry, we can now move on to congruent relationships, rigid motions (translation, reflection, and rotation), and identifying lines and points of symmetry.  Since these topics can be learned with minimal teacher instruction, I have chosen to use the Expert-Groups Jigsaw Method for this material.  By using this method the learners are more motivated, each student is held accountable, and they will retain so much of the knowledge by teaching content to their peers.  Following this activity, each group will make a poster describing the material they learned in any way they choose.
Finally, the students will utilize the knowledge and skills they have learned and used thus far in this unit to individually design a one-patch quilt design.  The design will be based on a regular hexagon which can be “cut” into a variety of ways such as isosceles triangles, rhombii, isosceles trapezoids, equilateral triangles, and kites.  The students will be shown a few real quilts and/or books of quilts to give them some pattern ideas.  The quilt patch must be colored in to highlight the design.  The students will also write a brief description of their pattern and how they came to choose it.  Each design will then contribute into making a class quilt book ad the students will briefly orally present their design to the class.

Assessment Overview

 Throughout this course of study, formal and informal assessment will be continuous.  I will constantly be observing the students for understanding of the content.  Informal observation will go on during instruction as well as group work.  A checklist will be used during group work, which will hold students accountable for social skills used, interaction between peers and equal participation.  This will also allow me to watch the students for any problems they might be having with the material.  While watching a student’s body language, facial reactions and listening to responses to random question, I can gauge students’ understanding.  Personal conversations with the students will also allow me to get a deeper understanding of their knowledge as some students are uncomfortable with letting other students know they do not understand or “get” the material.
 While the class is involved in note taking and teacher instruction I will be asking questions, asking students to redefine terms, and explain mathematical problems and situations as I present them.  The students’ notebooks are also collected at the end of each marking period.  Math notebooks will also act as a journal as students are required to write in it at least once a week.  Students can write about their thoughts, feelings, lessons or activities they really enjoyed, things they did not understand, what I could have done to help them understand better, and just react to the week as a whole.  This will allow me to track their improvement, achievement and feelings and apprehensions about the topic at hand.
 Homework will be given nightly and will be graded according to the effort they made and the amount of work done, then we will go over the homework as a class.  Homework is important in reflection of that day’s material.  This also guides me in assessing how well students understood the content when they are out of class and must think in-depth.
 The first activity involves worksheets, which will be graded on completeness, correctness and creativity.  Participation in any group discussion during this activity will also count in the grade for this activity.  A checklist will be used during group activities to assess participation as well as a group evaluation.  Depending on the groups, class, and/or the activity these reflections may be done as a group or individually to allow me to see from their point of view what went well and what did not go well.
A Pairs-Check worksheet will be used after the lesson on finding perimeters of polygons and finding the measures of angles of polygons.  While the students complete these, in pairs, I can walk around the room to check for comprehension.  The worksheet will not be formally graded but will allow me to informally test their knowledge.
I will also use Numbered-Heads Together to assess student understanding.  By placing students in groups they can help each other and bridge off of one another’s ideas to come up with one answer.  Each student is held accountable by using this method because the students do not know which group and/or group member will be called on to answer.  For instance, I may say “All number fours write your answer on your slate” or “Group three number one write your answer”.  This method will be used to review material after the lesson on circumferences, radii and diameters of circles as well as material previous to this lesson to prepare the students for a quiz the following day.  The same will be done before the unit test.  In this way I can see if the students have grasped the material.
One quiz will be given after the lesson on circles and a unit test after the unit project.  These will include solving mathematical problems (perimeters and circumference, radius or diameter), identifying polygons and quadrilaterals, and (on the unit test only) recognizing types of rigid motions, congruency and symmetry.   True or false, multiple choice, fill-in questions and essays will appear on both the quiz and the unit test.  These will be graded on correct answers and I will have a rubric for answers that requires that all work must be shown and for the essay questions.
Since we will be using the Expert-Jigsaw Method for the lesson on rigid motions, congruent polygons and symmetry, the students will be assessed for a number of things.  I will use a checklist for this activity that will include participation, social skills, and is the material being taught to peers effectively.  The students must also construct a poster to describe any way they choose what they have learned in this lesson.  The poster and the students will be assessed on correct material being depicted on the poster, if the poster makes sense, the students can accurately explain the poster to the class, and somehow includes the material represented in the reading.
After explaining the final project to the students and handing out the student guide and the worksheet for the quilt design to the students, I will ask them to aid me in devising a rubric for the product.  Important points the students should bring up are the design originally began as a regular hexagon, the design makes one geometric shape, if continued the design would make a pattern, the product is colored, the students used colors that will enhance the design, the student’s brief essay describes and explains the design, and the students presented competently and gave sufficient information about their product and the process they went through to design their patch to the class.  I will guide the students in this discussion and will also present a rubric for the essay as well as the oral presentation when we finish our discussion.  Each quilt design will be put into a classroom book and will be used as example quilt designs for future years.  Students take pride in classroom books and like to show their contribution to friends and family no matter what the age or grade.

Table of Specifications
Category Know Reason Show Total
Prefixes 2Sr, 1Pa  1E 2Sr, 1E, 1Pa
Polygons 4Sr 1Pr 1E, 1Pr 4Sr, 1E, 1Pr
Circles 2Sr  1Pa 2Sr, 1Pa
Congruency 2Sr 2Sr  4Sr
Rigid Motions 2Sr 1E 1Pa 2Sr, 1E, 1Pa
Symmetry 2Sr 1E 1Pa 2Sr, 1E, 1Pa
Total 14 Sr, 1Pa 2 Sr, 2E, 1Pr 2E, 3Pa, 1Pr 16Sr, 2E, 4Pa, 2Pr
 

Test Items

True/ False
Circle T for true or F for false.

1.  T F      All parallelograms are rhombii.
2.  T F      All trapezoids are quadrilaterals.
3.  T F      A pentagon has seven (7) sides.
4.  T F      A scalene triangle has no congruent sides.
 

Multiple Choice
Please circle the letter of the correct answer.
1.  The sum of the measures of the angles of a regular triangle is 210 degrees.  What are
     the measures of each angle of this triangle?
a. 70,70,70
b. 60,60,60
c. 45,45,90
d.  60,60,90

2. An octagon has how many sides?
a. 5
b. 4
c. 8
d. 10

3. What is the perimeter of a regular triangle whose sides are 51m each?
a. 17m
b. 153m
c. 102m
d. 2601m
4. If a given circle has a diameter of 14mm what is its radius?
a. 28mm
b. 2.23mm
c. 3.14mm
d. 7mm
 

Fill-In
Please fill in the blank with the correct word.

1. A polygon is referred to as _______________ if all sides are congruent and all its angles are congruent.
2. Two figures are ______________ if they have the same size and shape.
3. If two figures are congruent, we can make them coincide (occupy the same space) by using one or more _________________.
4. The perimeter of a circle is called the __________________.
 

Matching
Draw a line from the polygon to the correct number of sides.

1.  decagon   a.  4
2.  hexagon   b.  7
3.  pentagon   c.  8
4.  quadrilateral  d.  10
5.  octagon   e.  5
    f.  6
 

Draw a line from the term to the definition.

1.  perimeter   a.  the distance around a circle
2.  circumference  b.  a rigid motion, “mirror”
3.  reflection   c.  the area inside a figure
4.  translation   d.  the distance around a figure
       e. a rigid motion, “slide”

Essay
Please answer the following questions using complete sentences and diagrams when necessary.

1. List three types of rigid motions including a definition and example of each.

2. Select four numerical prefixes and give a definition of each, then draw and label the polygon that goes with each prefix you chose.

Performance Assessment
 As noted in my assessment overview, for the final project of this unit the students will be instructed to design a one-patch quilt design based on a regular hexagon.  The students will be given time and materials to complete this project in class possibly with some work done at home.  Depending on the background and experience the students have thus far with individual projects, I will guide the students accordingly.  The students are also required to briefly describe their design in essay form as well as give an oral presentation to the class (minimum of five minutes).
 I will also be asking the students to help devise an assessment rubric for the quilt design.  I have found by doing this, the students have more of a feel as to what they need to get accomplished and what kind of grade they are shooting for.  As we finish I will add in the requirements for the essay and oral presentation.  The assessment scale will then be typed and given to the students the next day as they begin the project.  Depending on what the students offer during the assessment discussion, the following is an example of how I would like the assessment scale to be.
 Design Written Oral
Level 3 ? Was originally a regular hexagon
? All patterns fit neatly together
? Pattern could continue
? Design colored
? Colors enhance design, not take away from it
? Worksheet filled in ? Can explain how the regular hexagon was cut to form design
? How they decided on the design
       (drew a few designs first, first
       try, etc.)
? How they chose the colors they used
? Complete sentences
? Paragraphs
? Neatly written or typed ? Loud and clear voice
? Explains design-how regular hexagon was cut, how they chose their colors, etc.
? Makes eye contact
? Is organized and prepared
? Answers any questions
Level 2 ? Was originally a regular hexagon
? Pattern could continue
? Design colored
? Colors enhance design
? Worksheet filled in ? Complete sentences
? Paragraphs
? Neatly written or typed
? Can explain how they chose design ? Loud and clear voice
? Makes eye contact
? Answers questions
? Explain how they chose design
Level 1 ? Was originally a regular hexagon
? Design is colored
? Worksheet filled in ? Can explain how they formed the design ? Loud and clear voice
? Answers questions
? Explains how they chose their design
 

Integrity
 This unit complies with the New York State standards and is part of the mathematics curriculum.  Mathematics is a difficult subject to make fun and interesting as many abstract concepts and theories must be taught by direct instruction.  This unit, however, incorporates some group activities, allows the students to work hands-on, and use their creativity along with teacher directed instruction.  I feel that it is important that students enjoy themselves while learning new material and can apply mathematics to other content areas and to the real world.  I feel that this unit has accomplished this.