This course is designed for students who have successfully completed the standards for Algebra I. All
students are expected to achieve the Geometry standards. The course includes, among other things,
properties of geometric figures, trigonometric relationships, and reasoning to justify conclusions.
Methods of justification will include paragraph proofs, two-column proofs, indirect proofs, coordinate
proofs, algebraic methods, and verbal arguments. A gradual development of formal proof will be
encouraged. Inductive and intuitive approaches to proof as well as deductive axiomatic methods should
be used.
This set of standards includes emphasis on two- and three-dimensional reasoning skills, coordinate and
transformational geometry, and the use of geometric models to solve problems.
A variety of applications
and some general problem-solving techniques, including algebraic skills, should be used to implement
these standards. Calculators, computers, graphing utilities (graphing calculators or computer graphing
simulators), dynamic geometry software, and other appropriate technology tools will be used to assist in
teaching and learning. Any technology that will enhance student learning should be used.
Here is a year plan, by quarter, that lays out the SOL standards for the year.
Geometry year plan.pdf
February Trigonometry
During the first few weeks of February, students will be expanding their knowledge of right triangles to include our unit on Special Right Triangles and Trigonometry.
Trigonometry is primarily a branch of mathematics that deals with triangles, mostly right triangles. In particular the ratios and relationships between the triangle's sides and angles. It has two main ways of being used:
1. In geometry
In its geometry application, it is mainly used to solve triangles, usually right triangles. That is, given some angles and side lengths, we can find some or all the others.
For example, in the figure below, knowing the height of the tree and the angle made when we look up at its top, we can calculate how far away it is (CB). (Using our full toolbox, we can actually calculate all three sides and all three angles of the right triangle ABC).
The SOL standard that relates to this unit is:
G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.
This unit is included in chapter 8 of the textbook.
Students will be required to complete Kuta software worksheets, IXL strands related to PT, and will be given an assessment with both multiple choice answers and solving for a variable. Students will also be required to take notes from Khan Academy video, as well as using Khan Academy to solve problems online.
EL strategies:
Demonstrate that vocabulary can have multiple meanings. Help students understand the different meanings of words such as "similar" and "congruent," as well as how to use them correctly in a mathematical context.
Encourage students to offer bilingual support to each other. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language. (Check the hotlinks for a list of bilingual translations of math vocabulary in multiple languages).
Provide visual cues, graphic representations, gestures, and pictures. Offer students the chance to work with objects and images in order to master vocabulary. If there aren't enough items for each student, use manipulatives on the overhead or posted throughout the classroom, and demonstrate the vocabulary in front of the students.
Identify key phrases or new vocabulary to pre-teach. This strategy will help students decide which math function they should apply. Example: "more than" means "add."
Month of January
During the month of January, students will be learning the concept of Similar Triangles and the Pythagorean Theorem with it's converse.
Students will be introduced to the 3 theorems used to prove similar triangles: AA, SAS, and SSS. Students will be able to determine triangle similarity using one of the theorems. Students will also learn to set up proportions and look for equal ratios. This unit is SOL G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs.
Students will be required to complete Kuta software worksheets, IXL strands P.1 - P.5, and will be given an assessment with both multiple choice answers and solving for a variable. Students will also be required to take notes from Khan Academy video, as well as using Khan Academy to solve problems online.
This unit is included in Chapter 7 of the textbook.
Pythagorean Theorem and it's Converse: Students will be introduced to the Pythagorean Theorem and its Converse. Students will learn how to analyze information given in a diagram or word problem in order to solve for the missing side of a right triangle. Lesson plans will include constructing a right triangle, measuring the sides, and proving a right triangle exists. This unit is SOL G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.
This unit is included in chapter 8 of the textbook.
Students will be required to complete Kuta software worksheets, IXL strands related to PT, and will be given an assessment with both multiple choice answers and solving for a variable. Students will also be required to take notes from Khan Academy video, as well as using Khan Academy to solve problems online.
EL strategies:
Demonstrate that vocabulary can have multiple meanings. Help students understand the different meanings of words such as "similar" and "congruent," as well as how to use them correctly in a mathematical context.
Encourage students to offer bilingual support to each other. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language. (Check the hotlinks for a list of bilingual translations of math vocabulary in multiple languages).
Provide visual cues, graphic representations, gestures, and pictures. Offer students the chance to work with objects and images in order to master vocabulary. If there aren't enough items for each student, use manipulatives on the overhead or posted throughout the classroom, and demonstrate the vocabulary in front of the students.
Identify key phrases or new vocabulary to pre-teach. This strategy will help students decide which math function they should apply. Example: "more than" means "add."
Weeks of October 23 - November 30th
During these weeks, students will be learning the following SOL standards:
SOL G.6
The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.
HINTS and NOTES
To prove triangles congruent:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
HL (Hypotenuse-Leg)
If two triangles share a side – Reflexive Property.
Vertical angles are always congruent.
(Look for an x)
CPCTC – Corresponding Parts of Congruent Triangles are Congruent
SOL G.5
The student, given information concerning the lengths of sides and/or measures of angles in triangles, will a) order the sides by length, given the angle measures; b) order the angles by degree measure, given the side lengths; c) determine whether a triangle exists; and d) determine the range in which the length of the third side must lie. These concepts will be considered in the context of real-world situations.
HINTS and NOTES
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
Ex:
AB + BC > AC
AC + BC > AB
AB + AC > BC
To determine whether a triangle can exist:
Add the 2 smallest sides and that must be greater than the third side
To determine the range of a third side:
The 3^{rd} side must be greater than the
2^{nd} side – 1^{st} side
OR
less than the
1^{st} side + 2^{nd} side
Weeks of October 9 - 20
During the first week, students will learn about Constructions. We will use technology in the classroom to demonstrate 5 different constructions in Geometry. Students will learn to use a tangible compass and also use a compass through an interactive website. The SOL with this unit is
G.4 -
The student will construct and justify the constructions of
a) a line segment congruent to a given line segment;
b) the perpendicular bisector of a line segment;
c) a perpendicular to a given line from a point not on the line;
d) a perpendicular to a given line at a given point on the line;
e) the bisector of a given angle,
f) an angle congruent to a given angle; and
g) a line parallel to a given line through a point not on the given line.
Students will also begin learning about the triangle-angle-sum theorem. We will do hands on activities to learn about this theorem, and how it relates to the SOL G.2, which has already been taught. We will also use this theorem to reinforce algebra skills. The lesson will be out of chapter 3.5 in our textbook. These lessons will lead us into triangle congruency. We will also use supplementary worksheets to reinforce the lesson. Here is a lesson plan we will be using. LESSON CONTENT Geometry Plan.docx
Weeks of September 18 - October 6
During these weeks, students will be working on parallel lines cut by transversals. Students will create a color coded diagram to work on distinguishing between angle relationships. We will be working from chapter 3.1, 3.2, and 3.3 in the textbook. The SOL of this unit is
G.2 - The student will use the relationships between angles formed by two lines cut by a transversal to
a) determine whether two lines are parallel;
b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and
c) solve real-world problems involving angles formed when parallel lines are cut by a transversal.
Weeks of September 4 - September 15
During these 2 weeks, students will work on the
segment addition postulate, angle addition postulate, and angle relationships. We will use Khan Academy as well as Kuta software to supplement the curriculum. Students should
ALWAYS check the basket where we put missed work whenever there is an absence. It is the STUDENT'S responsibility to make up work and return it to Ms. Eva to earn credit. Your name will be on any missed work. The SOL objective that will be addressed this week is:
*The student, given information concerning the measures of angles will solve for a variable using congruency, supplement, complement, linear pair, and vertical angle concepts.
During the first week of Geometry, students will be given an overview of the class and we will focus on basic symbols and terminology used in Geometry. Students will be given notebooks to keep all their classwork and notes organized.
Week 1: Objective - To make nets and drawings of 3-D figures and to understand basic terms and postulates in Geometry. Also, to find and compare lengths of segments.