Grades 9–12 Expectations - The University of North Carolina · PDF file ·...

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Rachel Faruque Unit Lesson Plan MATH 410 Spring 2010

For my geometry unit on relationships within triangles, I used the 2004 Prentice Hall geometry book. I preferred this text to others because it not only covered the material in an effective, straightforward approach; but it also had problems with real world significance and a section of problems similar to what you would find on a standardized test.

As my teaching strategy, I used a combination of dialectic and exogenous in most lessons as I used PowerPoint presentations to guide my lecture, while still asking the students to explore the concepts on their own. After each example was given, I included an additional example for the students to solve by themselves and then work out on the board and explain to the class if selected. Students were also given the chance to work together on the practice at the end of each lesson, which I often tried to make a fun activity that had relevance to the real world. At the beginning of most classes, a warm-up was included on material from the previous class that was similar to a question that might possibly appear on a standardized test in order to better prepare students for a standardized test, while letting them review.

Since geometry is a subject that requires proofs, writing was involved in several of the lessons. Students were asked to write proofs, and to explain their answers to several of the problems in their homework or during the lecture. They were also asked to keep a math journal to reflect on larger tasks, such as a test, quiz, or project in order to keep them, and myself, aware of what they struggled in and why.

In order to address any special needs of students, I allotted time at the end of each class for the students to begin their homework in case anyone was confused by the lesson, and also time to go over any lingering homework questions at the beginning of every class. I also attempted to use visual aids whenever possible for students who learn better from illustrations and diagrams.

Since this unit contains a lot of vocabulary terms, misconceptions could very easily occur if a student confuses two or more definitions. Section 5.3 has an exceptionally large amount of new terms that the students have never seen before and many of the definitions are very similar. However, I scheduled an entire class period in the computer lab with guided worksheets on the material covered in 5.3 in order to help the students get a better grasp on the material. The Geometer’s Sketchpad had several applications that related directly to the material covered in this unit, so I took the opportunity to let the class explore with this program on two different occasions.

For assessments, I assigned the students homework every night we covered a new topic and collected it for either an accuracy or effort grade, but not before going over any questions or concerns the students may have had. I also scheduled a quiz on the material covered in lessons 1, 2, and 3 in order to make sure the students had a firm grasp on the material before we moved on to more difficult concepts. A final test is also included on the last day of the unit.

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NCTM objectives for this unit:

Grades 9–12 Expectations: In grades 9–12 all students should– • analyze properties and determine attributes of two- and three-dimensional

objects; • establish the validity of geometric conjectures using deduction, prove

theorems, and critique arguments made by others; • use trigonometric relationships to determine lengths and angle measures.

DPI standards for this unit: Competency Goal 2

The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

Objectives 2.01 Use logic and deductive reasoning to draw conclusions and solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs. 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs: a. Triangles. b. Quadrilaterals. c. Other polygons. d. Circles. 2.04 Develop and apply properties of solids to solve problems.

Lesson one: Parallel Lines, Perimeters, and Midpoints

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• Resources o Bass, L., Charles, R., Johnson, A., & Kennedy, D. (2004).

Midsegments of Triangles. Geometry. (pp. 243-248). Needham, MA: Prentice Hall

o White board and writing materials o Projector

• Prior knowledge o Students are expected to know how to find the perimeter of

rectangles and squares, or objects which do not requires the distance formula in order to calculate them.

• Motivation o Perimeters are used frequently in every day life in constructing

objects such as fences or swimming pools. o Parallel lines are also seen everywhere in our buildings, roads,, etc.

• Teaching style o Dialectical (lecture) o Exogenous (scaffolding)

Allow the students to do the “You Try” questions on their own and then choose students to come up to the board and work them out.

• Instructional activities o Project the PowerPoint onto the whiteboard so you and the

students can write and solve problems directly next to or under the original.

o Follow the lecture/activities on the PowerPoint. o Note: Only the teacher will be able to view “hidden” slides that may

contain extra instructions. Students will only be able to view the slideshow presentation.

• Homework o Complete the worksheet on the following page

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Lesson two: Midsegments of Triangles • Resources

o Bass, L., Charles, R., Johnson, A., & Kennedy, D. (2004). Midsegments of Triangles. Geometry. (pp. 243-248). Needham, MA: Prentice Hall

o White board and writing materials o Projector o Classroom set of rulers o Classroom set of calculators o The Midsegment Theorem worksheet on the following page

• Prior knowledge o Students must be already familiar with types of triangles and the

triangle congruence postulates. o Students must already know the definitions of a midpoint, parallel,

and perimeter. They should also know how to use a ruler properly. • Motivation

o Knowing about midsegments can be helpful in designing geometric objects such as buildings, roofs, and kites.

• Teaching style o Dialectical (lecture) o Exogenous (scaffolding)






• Homework o Page 246 #s 2, 4, 6, 7, 13, 30 o Page 247 #s 26, 34, 35 o The assignment can also be found at:

http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037878-X/Ch05/05-01/PH_Geom_ch05-01_Ex.pdf

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Lesson three: Bisectors in Triangles • Resources


o White board and writing materials o Projector o Classroom set of rulers o Classroom set of compasses o Map worksheet

• Prior knowledge o Students must be familiar with perpendicular lines and congruency. o They should also be familiar with the term equidistant. o Students should know how to use a ruler and a compass in order to

participate in the day’s activities. • Motivation

o Knowing how to find a bisector can be useful in navigating a map. • Teaching style

o Dialectical (lecture) o Exogenous (scaffolding)






• Homework o Page 251 #s 8-11, 16, 18 o Page 252 # 30 o The assignment can also be found at:


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Lesson four: Concurrent Lines, Medians, and Altitudes • Resources



• Prior knowledge o Students must have a knowledge of several properties of triangles,

including bisectors and when segments are equivalent. • Motivation

o There are many careers that involve the material covered in this section. City planning uses almost every concept understood.

o Students may also be able to better understand a map. • Teaching style







• Homework o Page 259 #s 1, 8, 9, 12, 16 o Page 260 #s 19-22, 27 o The assignment can also be found at:


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Lesson five: Quiz and The Geometer’s Sketchpad

• Resources o Altitudes and Orthocenters of a Triangle worksheet o Discovering the Incenter of a Triangle worksheet

• Teaching style o Discovery

Students take a guided note sheet and explore on their own • Instructional activities

o Answer any questions on the homework- 5 min o Hand out the quiz on the following page

Give 20 minutes to complete o Take the class to the computer lab o Hand out the following two Geometer’s Sketchpad worksheets and

instruct the students to complete as much of them as possible during the remaining class time

5.1/5

a. Fi

5.2 Quiz

ind XV

b. Find WZ

Z

NName:

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Lesson six: Inverses, Contrapositives, and Indirect Reasoning




• Prior knowledge o Students must have some basic reasoning skills in order to be

proficient in this section. o Students must also be familiar with some terms of negation.

• Motivation o Understanding conditional statements can strengthen a person’s

reasoning skills. o These concepts are also helpful when teaching English as a

second language. • Teaching style







• Homework o Page 267 #s 8, 13, 15, 16 o Page 268 #s 21, 24-27, 31 o The assignment can also be found online at:


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5.3 & 5.4 Vocabulary Crossword! ACROSS 3. A statement has the opposite meaning of the original statement� 4. Type of proof where all possibilities but one are proved false� 5. The "if" part of a conditional statement� 6. The "then" part of a conditional statement� 7. Switches both the hypothesis and conclusion of a conditional statement and negates both� 9. The point of intersection of all the lines that contain the medians of that triangle� 10. The point of concurrency of the perpendicular bisectors of a triangle� 11. The point of concurrency of the angle bisectors of the triangle DOWN 1. Negates the hypothesis and conclusion of a conditional

statement 2. A type of logical statement that has a hypothesis and conclusion� 8. Two statements that are both true or both false

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1 2 3 4

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Lesson seven: Inequalities in Triangles




• Prior knowledge o Students should be familiar with inequalities and the symbols and

terms involved.

5 6 7 8 9 10 11 12

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o Students should also understand how to calculate the value of angles in a triangle and how many degrees are in a triangle.

• Motivation • Teaching style







• Homework o Page 276 #s 1, 6, 7, 14, 17, 20, 24, 25 o Page 277 # 34 o The assignment can also be found at:


Lesson eight: Chapter 5 Test

• Resources o Chapter 5 test attached below

It is 15 questions with a bonus. Partial credit will be awarded for problems.

• Instructional activities o Go over homework from the night before and collect it for an effort

grade- 10 min. o Hand out tests and a lot the remainder of the class time for them to

complete it.

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Chapter 5 Test Name . Write the inverse and contrapositive of the following two statements:

1. If a polygon has eight sides, then it is an octagon.

2 Find 3

5.

2. If it is s

d the valu

3.

snowing,

ues of x an

then it is

nd XM in

an even-

n each fig

-numbere

gure:

4.

d year.

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6. W 7.-8thes

What can y

8. Is AB ase?

you conc

a median,

lude abou

altitude,

ut Y? Exp

perpendi

plain.

cular biseector, or n

3

none of

5

Iden 9. an 10. 11. 12. 13. ft. D

ntify each

n angle b

a median

a perpend

an altitud

The lengtDescribe a

h of the fo

isector

n

dicular bi

de

ths of twoa possible

ollowing i

isector

o sides ofe length f

in the dia

f a trianglfor the thi

agram to t

le are givrd side.

the right:

en to be 8

3

8 ft & 12

6

Bon

nus Questtion:

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Grades 9–12 Expectations - The University of North Carolina · PDF file ·...

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