GPS Design Template
Unit Title:
M6G1 Students will further develop their
understanding of plane figures.
Subject/Course:
Math 7.6
Content Area:
GEOMETRY
Unit Designer(s):
George Maczko
Students will further develop their understanding of plane and solid geometric
figures, incorporating the use of appropriate technology and using this
knowledge to solve authentic problems.
M6G1 PLANE FIGURES
a. Determine and use lines of Symmetry.
b. Investigate rotational symmetry, including degree of rotation.
c. Use the concepts of ratio, proportion and scale factor to demonstrate the
relationships between similar plane figures.
d. Interpret and sketch simple scale drawings.
e. Solve problems involving scale drawings.
Unit Summary:
Grade Level(s):
Time Frame:
6
2 periods for a. and b.
2 periods for c., d., and e.
STAGE ONE
Desired Results Based Upon Performance Standards
Selected Standard(s) M6G1 Students will further develop their understanding of plane figures.
Enduring Understanding
1. Students will understand that plane
figures have 2 dimensions and the
properties associated with them.
2. Students will understand what is
rotational symmetry and the degrees of
rotation when turning a plane figure.
3. Students will understand how balance is
associated with linear symmetrical plane
figures.
4. Students will understand how the concepts
of ratio, proportion, and scale relate to
similar plane figures.
Essential Questions
1. How do you determine whether plane
figure is symmetrical?
2. How are linear and rotational
symmetrical plan figures similar and
different?
3. Between two similar plane figures, what is
the relationship between ratio, proportion,
and scale factors?
Knowledge and Skills
Students will know...
1. Definitions and characteristics of plane figures.
2. That similar plane figures have relationships associated with ratios, proportions and a scale factor.
3. The degrees of rotation associated with turning a plane figure.
Students will be able to do…
1. Sketch and interpret a simple scale drawing to solve problems.
2. Distinguish symmetrical verses non-symmetrical figures.
3. Determine lines of symmetry and the point of rotational symmetry in plane figures.
STAGE TWO
Evidence of Student Learning Based Upon Data
∆
Assessment through Work Product
SUMMATIVE ASSESSMENT:
SUMMATIVE FEEDBACK:
What cumulating performance task or test will be
used for students to demostrate mastery of the
content material?
1. Students will take a Saxon Generated quiz
or Class.
2. The Class will create a Venn diagram or
Double Bubble map to compare and
contrast Linear and Rotational Symmetry.
What will be the instrument for giving feedback to
students upon their performance and what criteria
will be used? How will the feedback promote
continued learning after the unit ends?
1. Mastery on Saxon generated assessment is
achieved with a score greater than 79%.
Any score below 80% will result in the
student’s need to write an essay using the
class’s graphic organizer that compares and
contrasts Rotational and Linear Symmetry.
Afterwards, the student will retake the
written assessment.
2. No grade will be given; only comments are
recorded in the student’s mark book.
FORMATIVE ASSESSMENTS:
FORMATIVE FEEDBACK:
What performance task(s) or quiz(es) will be used
for students to monitor their progress and for the
teacher to redirect the learning process?
1. Students will complete 20 problems from
lessons 180, 109, 110.
2. Students’ journal writings.
3. Students in groups will submit word maps.
What will be the instrument for giving feedback to
students upon their performance and what criteria
will be used? How will students will able to use the
feedback to increase their performance on future
assessments?
1. Students will work in collaborative pairs on
the problem set and will correct their
homework as a group. A numeric score is
given after corrections are made and the
homework grid is submitted.
2. A writing rubric will be used to score their
journal writing or students may present
their group’s activity summary, using a
presentation rubric. Comments are
recorded in the student’s mark book.
3. After class discussion, each group will
submit their word maps for review and
comments to be added. Comments may be
recorded in the student’s mark book.
∆ Assessment through Observation
∆ Assessment through Conversation
How will the teacher observations be focused,
recorded, and organized in order that they may
serve as evidence of student learning?
1. Students identify the lines of symmetry for
all letters of the alphabet.
2. Students create snowflakes.
3. Students perform Geometric Simon Says,
including degrees of rotation.
How will self-assessment and reflective dialog with
others be used as evidence of student learning?
1. Students will discuss within their groups to
determine the lines of symmetry for all letters
of the alphabet. Answer sheets may be
corrected by the students when reviewed as a
group and/or collected.
2. Students will describe to teacher how
symmetry applies to snowflakes.
STAGE THREE
Learning Experiences
Learning Activities
PROCEDURE:
1. Teacher defines transformations on white board and identifies
Simon Says gestures for Flip (reflection), Slide (translation), and
Turn (rotation). Class discusses previous Simon Says Geometric
Gestures, including degrees for angles (Acute, RIGHT, Obtuse)
to be used later with rotational symmetry. Geometric Simon Says
is used to bring students back on task or as warm up throughout
the Geometry Lessons.
2. Teacher led PowerPoint presentation describes symmetry, asking
students to use a pointer to cast a shadow on the line of symmetry
on the images displayed.
3. Box Top Activities. (Using the tops of paper boxes to organize
different activities, the teacher allows groups or pairs of students
to perform a task for 10 minutes before switching to another “box
top activity” containing a related learning activity.
a. Learning activity 1: Completing the activities and recording
in their journals, as a group, an activity summary to share
with the class, students will access the following websites:
distinguishing linear vs. rotational symmetry on
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/sym
metryrev1, and accessing the Kaleidoscopes and/or
Snowflakes projects on www.Adrianbruce.com/symmetry.
b. Learning Activity 2: Students are given a set of alphabetic
cards and a mirror. Students must categorize the letters
according to their associated number of lines of linear
symmetry. Their data should be collected, recorded, and
shared with the class at the end of the lesson.
c. Learning activity 3: Students are given instructions on how to
fold a paper into 2, 4, and 6 equal segments. Identifying the
point of rotational symmetry, students cut the paper to create
shapes, including a snowflake (H2O) six equal sides.
4. Students are to review Saxon Lessons 108 Transformations, 109
Corresponding Parts Similar Triangles, and 110 Symmetry.
5. Working in Collaborative-Pairs, students are assigned 20
problems for homework from the three lessons.
6. Homework is reviewed day 2, along with all word maps and
journal entries. Students present the information they collected
from the learning activities. A quiz may be given if students have
a clear understanding of the material or may be postponed until
after the concepts of ratio, proportion and scale factors are
demonstrated between similar plane figures (M6G1c., d., e.)
7. Students share their group’s findings, ask questions and instructed
to create a word map for the following terms: Symmetry, Similar,
Congruent, Reflection, Translation, and Rotation.
8. A Saxon generated written quiz or test is given, reviewed, and
corrected.
MATERIALS & RESOURCES:
White board and markers,
LCD projector for Symmetry
PowerPoint presentation,
pointer or meter stick, 2 PCs
with internet access to 2 to 3
website tasks, lettered cards,
mirrors, paper, scissors,
Saxon 7.6 textbook and
homework grid sheet, Saxon
generated assessment.
Comments



Previous terms included in Geometric Simon Says are from Saxon Lesson 68, including
Lines. Saxon Lessons 107 and 120 discusses the classification of Angles and Triangles,
respectively. These lessons should be reviewed and discussed prior to this unit and covering
Saxon Lessons 108, 108, and 110.
M6G1 c., d., e., in red ink, are not part of this unit plan, however, many of the concepts
should be applied and covered immediately prior to or at the conclusion of this lesson.
M6G2 Solid Figures is the second and final geometry concept to be covered in sixth grade.
Attached Files
FILE NAME WITH EXTENSION:
FILE DESCRIPTION:
Symmetry
Saxon Problem Set Grid
SYMMETRY.WS
GPS Mark Book
Symmetry PowerPoint presentation.
Homework Grid for 20 Problems
Saxon Generated written symmetry evaluation
Excel Spreadsheet for marking whether students exceed, met, or has
not yet met the GPS standard and a plan to achieve their highest level.
Unit Design template
GPS Design Template
Credits and Sources
Lynanne Betz, math teacher at Awtrey Middle School, Kennesaw, GA, LynanneBetz@cobbk12.org
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/symmetryrev1.shtml
www.Adrianbruce.com/symmetry
Saxon 7.6 An Incremental Development, third edition, Stephan Hake and John Saxon, Saxon
Publishers, Inc., 2002