1. Topic-
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| Introduction to Postulates and Paragraph Proofs |
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2. Content-
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Postulates:
2.1 Through any two points there is exactly one line.
2.2 Through any three points not on the same line, there is exactly
one plane.
2.3 A line contains at least two points.
2.4 A plane contains at least three points not on the same line.
2.5 If two points lie in a plane, then the entire line containing
those points lies in that plane.
2.6 If two lines intersect, then their intersection is exactly one
point.
2.7 If two planes intersect, then their intersection is a line.
Theorem 2.8 Midpoint Theorem: If M is the midpoint of segment AB,
then segment AM is congruent to segment MB.
Key Concept: Five Essential parts of a good proof:
1. State the theorem or conjecture to be proven.
2. List the given information.
3. Draw a diagram to illustrate the given information, if possible.
4. State what is to be proved.
5. Develop a system of deductive reasoning.
Vocabulary:
Postulate
Axiom
Proof
Paragraph Proof
Informal Proof |
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3. Goals: Aims/Outcomes-
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1. Students will understand and apply basic postulates about points,
lines, and planes.
2. Students will be able to write and understand a paragraph proof.
3. Students will understand and know the Midpoint Theorem |
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4. Objectives-
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1.Students will identify and use basic postulates about points,
lines, and planes.
2. Students will write paragraph proofs.
3. Students will identify and use the Midpoint Theorem. |
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5. Materials and Aids-
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| Materials used will include: Discovery Assessment Education website;
Dry Erase Markers and wipe-off boards; Glencoe Geometry Interactive
Chalkboard Software; Smartboard; Projector; Document Camera; paper;
pencil. Optional materials for activity if time permits: straws, glitter
sticks, construction paper. |
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6. Procedures/Methods-
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A. Introduction-
1. Say to students, "Today we will be learning about Postulates
and Paragraph Proofs.
2. As you are finding out, as we learn information information in
Geometry, we must retain it as we will apply it throughout the course.
3. We are going to review some of the things we have learned utilizing
Discovery Education before we move into using our knowledge to prove
statements and conjectures."
4. (Students in groups with wipe-offs. Go through DEA probe tallying
the group for answers) |
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B. Development-
1. Post DEA - Students add Postulates and Midpoint Theorem to Journals.
2. Use Interactive Chalkboard for examples.
3. Intro Paragraph Proofs - students add 5 parts of good proof to
journals. Examples on SmartBoard.
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C. Practice-
1. Guided Practice - utilize problems on page 91.
2. Guided Practice - Proof pg 91 #10. |
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D. Independent Practice-
Skills Practice Worksheet
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E. Accommodations (Differentiated Instruction)-
1. Individual attention is given when needed.
2. I utilize a variety of strategies in order to reach students with
various learning styles. Students work in small groups (Interpersonal),
alone (Intrapersonal), and I often use manipulatives and models for
Kinesthetic Learners. |
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F. Checking for understanding-
Homework assignment: page 92 12-30 even; 34-48 even
Optional Activity - #29 & 31 - Modeling. |
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G. Closure-
| "Today we have learned about postulates and paragraph proofs. You
now know how to use prior knowledge to 'prove' a conjecture in paragraph
form. You will use this throughout the rest of this course. Tomorrow
we will learn how to write an Algebraic Proof." |
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7. Evaluation-
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1. Students daily work and homework will be reviewed and graded
to determine level of student understanding and possible need for
reteaching.
2. Students will be tested on this concept to determine mastery.
3. Retention will be monitored throughout the course, as concepts
learned today will be applied in future lessons. |
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