high school geometry days 09024

8/12/2019 High School Geometry Days 09024

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STRUCTURED CURRICULUM LESSON PLAN

Day: 009 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 6C1; 8D2; 9B

TAP:

Perform arithmetic operations involving

integers, fractions, decimals, and percents,

explicitly stated or within context

Choose and apply appropriate operational

procedures and problem-solving strategies to

real-world situations

Understand number systems

Use variables, number sentences, and equations

to represent solutions and solve problems

Analyze and interpret data presented in charts,graphs, tables, and other displays

Demonstrate understanding of measurement

concepts and apply measurement skills

ISAT:

Solve problems requiring computations with

whole numbers, fractions, decimals, ratios,

percents, and proportions

Understand and apply geometric concepts and

relationships

Use mathematical skills to estimate,

approximate, and predict outcomes and to

judge reasonableness of results

Identify, analyze, and solve problems using

equations, inequalities, functions, and theirgraphs

Unit Focus/Foci

Critical Thinking

Instructional Focus/Foci

Developing Critical Thinking Skills and Cooperative Learning Skills

Materials

Logic Puzzle from Die Hard 3

Teacher Observation Form

Educational Strategies/Instructional Procedures

Give students a copy of the logic puzzles from Die Hard 3. Have the students work in

cooperative groups of four. Give two puzzles to each group. Allow students three minutes to

read the puzzle. (You may want someone to read it aloud to the class.)

Allow the students 20 minutes to solve the puzzle. Afterward, encourage the groups to come up

and share their solutions with the class. Give each group no more than five minutes to present

their solutions. (You may not want to do all groups.) Give each student in the class the

following questions: 1) How well did your group work together? 2) Did anyone take over the

group? 3) Did everyone in your group help to find the solution? Make observations noting the


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following skills: a) listening, b) paraphrasing, c) asking questions, and d) giving complete

answers. Check to make sure that each student participates. Share observations with the class

for future presentations.

Integration with Core Subject(s)

SC: Analyze and interpret data

Apply scientific method to solve problems

SS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment:

Fine Arts:

Home: Have parents or family members solve the logic puzzles from Die Hard 3. Parents willsign teacher syllabus stating the class procedures, homework policy, and grading scale.

Remediation: Teachers Half Dozen

Technology:

Assessment

Teacher observation

Homework

Parents will sign teacher syllabus stating the class procedures and homework policy.

Teacher Notes

Solutions to Die Hard 3:

1. One2. Fill the 3-gallon bucket and empty it into the 5-gallon bucket.

Fill the 3-gallon bucket and pour it into the 5-gallon bucket. (0nly 2-gallons will fit)

The 3-gallon bucket contains 1-gallon and the 5-gallon bucket is full.

Empty the 5-gallon bucket.

Pour the 1-gallon from the 3-gallon bucket into the 5-gallon bucket.

Fill the 3-gallon bucket and empty it into the 5-gallon bucket.

The 5-gallon bucket now contains 4-gallons.


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Die Hard 3

Samuel Jackson and Bruce Willis are given the logic puzzles with only minutes to

solve each.

1. To keep a store in downtown New York from exploding, solve in 2 minutes:2. On the road to St. Vies, I met a man with seven wives. Each wife had seven

sacks. Each sack had seven cats. Each cat had seven rats. How many were

going to St. Vies?

To disarm the bomb in Central Park, solve in 5 minutes:

3. Using 3-and 5-gallon unmarked containers, place exactly 4 gallons of water onthe scale to disarm the bomb.


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Correlations (SG,CAS,CFS): 6A2; 7A2; 9A3

TAP:













ISAT:





relationships






Unit Focus/Foci

Discovering Basic Geometric Concepts


Using Graphs as Visual Representations of Geometric Concepts

Materials

Maps of Chicago (1 for each student)

Two sample problems

Colored pencils, crayons, or markers


Have students work in pairs. Have one student describe his/her trip from home to school so

precisely that the other student could use the directions to go from school to the student's home.

All directions should be written down and shared with the class. Give each student a map of the

city of Chicago.


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Have students locate the following ordered pairs on the map: (600 W., 200 S.), (1600 W., 400

N.), and (1400 E., 5300 S.). Have the students share their results.


SS: Read and interpret maps, charts, and graphs

Connection(s)

Enrichment: Have students find a picture of their favorite cartoon character and complete a

coordinate picture.

Fine Arts: See Enrichment.

Home:


Technology: Have the students find a map of Washington, D.C. on the Internet and compare it

to a map of Chicago.

Assessment

Teacher observations

Homework

Have students find the locations at least five places of interest. Have them write the addresses

and graph the five points on a city map using a different color for each.

Teacher Notes


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TAP:













ISAT:





relationships






Unit Focus/Foci



Graphing Ordered Pairs on a Coordinate Plane

Materials

Graph paper transparency

Map of Chicago

Student spiral notebook

Three-ring binder

Graph paper

Straightedge


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Opener: Solve each of the following:

1. Ifx= 4 andy= 6, find the values of 2x- 4y.

2. Solve foryiny= 6x 3, ifa. x= -2

b. x= -4

3. Determine whether or not (3, -2) is a solution of:

2x+ 3y= 18

4. What is the value of 2x2

+ 3xyifx= -1,y= 6?

Solutions: 1) -16 2) a. -15 b. -27 3) Not a solution 4) -16

Review the coordinate plane with the students.

Remind students that for the city of Chicago:

1. State Street acts as they-axis2. Madison Street acts as thex-axis3. The intersection of State and Madison acts as the origin.Have students work independently to graph (on graph paper) and give directions to locate the

following points and tell in which quadrant or axis each point is located.

1. A (3, -2 ) 2. B (5, 4) 3. C (-3, -6) 4. D (0, 3)

5. E (-1, 0)

Solutions: 1. Quadrant IV 2. Quadrant I 3. Quadrant III 4. y-axis

5.x-axis

Quadrant II

(-,+)Quadrant I

(+,+)

Quadrant III

(-,-)Quadrant IV

(+,-)


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Present the correct solutions and allow the students to check their work. Discuss any questions

that students may have.

Continue the lesson with the following points, allowing students to work in pairs to graph the

following points.

D (4, -7) E (4, 0) F (3, 5) G(-3, -3) H (-1, 1)

I (3, 2) J (0, -5) K (-2, -6) L (-6, 4) M (-5, 0)


LA: Understand explicit, factual information

SS: Read and interpret maps, charts, and graphs


Connection(s)

Enrichment: Graphing Activities: A) Complete a complex coordinate picture and/or B) design

a coordinate picture.

Fine Arts: See Enrichment.

Home: Haveparent sign student's homework assignment sheet.

Remediation: Review the coordinate plane, coordinates of points, and graphing points on a

coordinate plane. The game Battleship may be played to reinforce graphing skills.

Technology: Have the students play the computer game of Battleship.

Assessment

Teacher observation

Homework

Assign from your text appropriate problems on graphing ordered pairs.

Teacher Notes


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TAP:













ISAT:





relationships






Unit Focus/Foci



Slope Intercept Form of a Linear Equation

Materials

Geoboards

Rubber bands


Definition of Slope: The slope (m) of a line is the ratio of the vertical distance to the horizontal

distance. ( )slope mrise

runb g=Guidelines: Have students work in pairs to complete this activity. Tell students they should be

prepared to share their results with the class.


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Directions: Model the line segment AB whose endpoints are:

1. A(1, 1),B(4,4) 2. A(1, 1),B(2, 3) 3. A(4, 1),B(3, 3)

Locate the ordered pairsA(1, 1) andB(4, 4) on the geoboard. Place a rubber band around the

pegs to model AB .

Use another rubber band to show vertical distance from they-value ofAto they-value ofB. Use

another rubber band to show the horizontal distances from thex-value ofAto thex-value ofB.

In example 1, to move from pointAtoB,you can go up 3 units and right 3 units.

slope= =3

31

In example 2, to move from pointAtoB,you can go up 2 units and right 1 unit.

slope=

=2

1

2

Use your geoboard to find the slope of four different line segments. Two of the segments should

have positive slopes, and two should have negative slopes.

From the examples, you can also calculate the slopes mathematically:

Example 1: A(4, 1),B(3, 3)

slopevertical dis ce

horizontal dis ce=

tan

tanm=

=

=

3 1

3 4

2

12

Example 2: A(1, 1),B(4, 4)


horizontal dis ce=

tan

tanm=

= =

4 1

4 1

3

31

Example 3: A(1, 1),B(2, 3)


horizontal dis ce=

tan

tanm=

= =

3 1

2 1

2

12

*Write a rule for finding the slope of a line segment given any two points: A x y B x y1 1 2 2, ,b g b gand

You should allow several pairs to present their results to the class.

Review the activity with the class. In the equation y mx b= + , point out the slope (m) andy-

intercept (b). Identify the slope and y-intercept from the following equations:


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1 6 2 3 2

3 4 3 4 23

34

. .

. .

y x y x

y x y x

= + =

= + =

Have the students graph each line on a coordinate plane. Utilizing the graph of y x= 3 2 , have

the students determine whether the following points are on the line: A(0,-2),B(1,1),C(4,8),

andD(2,4). Students should observe that pointsA,B, andDare on the line. Have the class

formulate a definition for collinear pointsusing the different definitions derived by each group.

Solutions: 1. m =3

4, b = 6 2. m = 3, b = -2

3. m = -4, b = 3 4. m = 23

, b = 0



Understand the meaning of words in context



Connection(s)

Enrichment: Have the students define and illustrate a pencil of lines.

Fine Arts:

Home: Have the students measure the rise and run of 3 staircases at home or in their

neighborhood.


Technology: Have the students draw three lines using a computer drawing program and list

three collinear points from each line.

Assessment

Teacher observation


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Homework

Assign appropriate problems from your text.

Teacher Notes

Prepare copies of undefined terms.

All of the lines that pass through a single point in the same plane are called apencil of lines(see

example below).


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p - peas c - carrots b - beans g - grapes s - strawberries a apples; f - French bread w -

white bread r - rye bread. Have the students list all possible combinations after you get them

started by listing at least the first three.

Solution:

pgf psf paf cgf csf caf bgf bsf bafpgw psw paw cgw csw caw bgw bsw baw

pgr psr par cgr csr car bgr bsr bar

Have the students notepoint, line,andplaneare referred to as undefined terms. They can be

described but not defined.

1. A point has no size (dimension); represented by a small dot and labeled with one capitalletter.

2. A line has one dimension (length); extends into infinity in two directions and labeled by twopoints on the line or a single lowercase letter.

3. A plane has two dimensions (length and width); extends infinity in both directions, andlabeled by one capital letter or three non-collinear points in the plane.

Have the students describepoint, line, andplanein their own words. Have them include a

drawing or picture of each. Allow 10 minutes for the students to complete this activity. Ask

three or four students to share their responses with the class.

Have the students use the following diagram to find as many line segments as possible:

---------------------------------------------------------------------------------------

Monitor student progress and assist when needed.

Solution:

AB AC AD AE BC BD BE CD CE DE

Have the students work in pairs to complete the Undefined Terms Worksheet.






A B C D E


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Connection(s)

Enrichment: Have the studentsfind three optical illusions involving points, lines, or planes and

share their observation.

Fine Arts: Have the students research op art and bring examples to class.

Home: See Enrichment.


Technology: Have the students use the Internet to assist in their research.

Assessment

Homework


Teacher Notes

Solutions to Undefined Terms:

1. Point2. Line3. Plane4. Plane5. Line6. Point7. Point8. Plane9. Line10.Line11.a. AFD

b. BFE

12.a. See student work Possible solutions: AD, AF, BF, BE, CEb. See student work

13.a. See student work Possible solutions: AFE, CFA, BFD, BFC, DFE,b. See student work BFA, CFD,


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Undefined Terms

Each of the following is best represented by which undefined term:

1. A grain of sand. 1.

2. The edge of the desk. 2.

3. The chalkboard. 3.

4. A sheet of paper. 4.

5. The corner of the room. 5.

6. A light on a Christmas tree. 6.

7. A pencil point. 7.

8. The surface of the desk. 8.

9. The electrical wires. 9.10. A piece of string 10._______________

11. Name 3 collinear points. 11a.

11b.

12. Name 2 lines. 12a.

12b.

13. Name 2 planes. 13a.

13b.

C

D

EA

F

B


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Correlations (SG,CAS,CFS): 7A1; 8A3

TAP:













ISAT:





relationships






Demonstrate an understanding of measurement

concepts and skills

Unit Focus/Foci



Using Formulas: Area and Perimeter of Rectangles

Materials

Graph paper

Rulers

Square tiles


Review last nights homework. Answer any questions. Have the students form several

rectangles of different dimensions by using square tiles or graph paper, finding the perimeter and

area of each, and then write a general formula.


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Draw a rectangle having l= 4 and w= 5.

!!!! !!!!!! !""""! !""""

! !""""

Answer: Area = length x width Perimeter = 2 length + 2 width

Find the area: Ask the students to count the number of squares contained in the rectangle. (20

sq. cm) Draw another rectangle having l= 6cm and w= 7 cm.

!!!!!!! !!!!!!!! !""""""! !""""""! !""""""

! !""""""! !""""""

Find the perimeter and area. Have the students work independently to find the perimeter and

area of rectangles having the following dimensions: 4 x 4, 5 x 7, 4 x 8, 8 x 9, 3 x 3 and 15 x 16.

Have students find the perimeter and area of a 50 x 48 rectangle without drawing the rectangle,

then make a conjecture about the perimeter and area of the rectangle.

The formula for finding the area of a triangle is A1

2bh. Have the students explain how to find

the height when the area and base are known. Students responses should be:

a) Solve for hand substitute the values forAand binto the equation orb) Substitute the values ofAand binto the equation and solve for h.

Have the students note that this procedure will work with any formula.

Have students complete Exploring Formulas.



Understand the meaning of words in contextSC: Apply scientific method to solve problems


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Connection(s)

Enrichment: Have the students compute the perimeter and area of irregular shapes. Have

students make a conjecture about finding the perimeter and area of irregular shapes.

Fine Arts:

Home: Haveparents sign assignment sheet.

Remediation: Demonstrate how to compute the perimeter and area of several rectangles (using

square cubes). Review algebraic concepts of using formulas.

Technology:

Assessment

Teacher observation

Homework


Teacher Notes

Prepare copies of Measurement Worksheet.


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Correlations (SG,CAS,CFS): 6A1; 7B1; 9A3

TAP:





Understand geometric properties and

relationships; apply geometric concepts and

formulas

Apply a variety of estimation strategies:

standard rounding, order of magnitude, front-

ending, compatible numbers, andcompensation

Analyze and interpret data presented in charts,

graphs, tables, and other displays



ISAT:





relationships





concepts and skills

Unit Focus/Foci



Finding the Distance Between Two Points on a Number Line and the Coordinate Plane

Materials

Copies of Measurement Worksheet

Transparency of a Ruler


Review last nights homework and answer students questions. Discuss the different aspects of

measurement with the students such as: how to read a ruler, when it is necessary to round, and

the degree of accuracy desired.


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Have students measure five objects in their possession such as: 1) pencil, 2) textbook, 3) CTA

card, 4) comb, and 5) money. Discuss units of measurement and rounding. (Answers will vary.)

Discuss with the students collinearand betweeness:

Collinear: Points that lie on the same line

Betweeness: Betweeness of points only exists if the points are collinear. A point is between two

other points on the same line if its coordinate is between their coordinate.

Have the students note that the distance between any two points on a number line is the absolute

value of the coordinates of the segment.

A - B

Discuss the distance formula: d x x y y= + ( ) ( )1 22

1 2

2d x x y y= + ( ) ( )1 2

2

1 2

2 Remind

the students that all (x1,y1) and (x2,y2) are coordinates of points in the coordinate plane, and that

all measurements must be positive.

A B C

Example 1:

a) Is point CbetweenAandB?b) IsBbetweenA and C?c) Are the three points collinear?

Solutions: a) no b) yes c) yes

Example 2:

Find AB

|-4 5| = |-9| = 9

-3 -2 -1 0 1 2

-6 -5 4 3 2 1 0 1 2 3

BA


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Example 3:

Find the distance from pointAto pointB.

A(4,8) andB(-1,-4)

d x x y y= +

= +

= + + +

= +

= +

=

=

( ) ( )

( ) ( )

( ) (8 )

1 2

2

1 2

2

2 2

2 2

2 2

4 1 8 4

4 1 4

5 12

25 144

169

13

Have students complete the Measurement Worksheet.




SC: Apply scientific method to solve problems

Connection(s)

Enrichment: See Home

Fine Arts:

Home: Havestudents describe five objects in their homes that required measurement for

purchase and list the degree of accuracy needed. Instruct students to write a paragraph explaining

what effect the degree of accuracy has on two of the objects.

Remediation: Review fractions generally associated with rulers. Review using a ruler with

students. Measuresmall items and round the answers.

Technology: Demonstrate one of the electronic measuring devices and explain how they work.

B

(-1, -4)

(4, 8)

A


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Assessment

Evaluate the Measurement Worksheet using the Structured Curriculum Scoring Rubric.

Homework


Teacher Notes

Solutions to Measurement Worksheet:

1. a. AC = 9b. BD = 7c. CD = 2d. AD = 11

2. a. 14 unitsb. A = 12 sq. units

3. a. AD = 20 4 47= .b. EB = 41 6 40= .

4. a. AC = 5 unitsb. BC = 3.61 unitsc. AB = 6 unitsd.

Perimeter = 14.61 units, Area = 9 sq. units

5. See student work.

T(2,6

P(-2,

O(-

-10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

6

5

4

3

2

1

-1

-2

-3

-4

-5

S(2,3


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Measurement Worksheet

1. Find each measure:

a) AC b) BD c) CD d) AD

2. Graph the vertices of STOP.S(2, 3), T(2, 6), O(-2, 6), and P(-2, 3)

a) Find the perimeter of STOP?b) What is the area of STOP?

3. Find each measure and round your answer to the nearest tenth.

a) ADb)

EB

A B

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

C D

-5 -4 -3 -2 -1 1 2 3 4 5

5

4

3

2

1

-1

-2

-3

-4

-5

A

B

CD

E


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4. a) Find ACb) Find BC

c) Find AB

d) What is the perimeter and area of ABC?

5. Draw a line segment with length:a) 4cmb) 2 1

4in.

-5 -4 -3 -2 -1 1 2 3 4 5

5

4

3

2

1

-1

-2

-3

-4

-5

B

C

A


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Share with students some facts about Pythagoras (570 - 500 BC) and the origins of the theorem

that bears his name.

Have students complete the Pythagorean Activity #1.

Have students restate the Pythagorean Theorem and discuss how the early Egyptians used the

special triangles to determine the areas of their property. Draw a right triangle on the overhead

or chalkboard and have the students state the Pythagorean Theorem in terms of the legs and the

hypotenuse.

Have the students complete the following:

Find the missing side of each right triangle to the nearest tenth.

Solutions:1. 5 in. 2. 19.2m 3. 29.4cm 4. 12.7ft

Discuss the solutions with the students.



SS: Demonstrate an understanding of time and chronology


1. 4in.

3in. ?

2.

12m ?

15m

3. 17cm

? 24cm

4.

9ft 9ft

?


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Connection(s)

Enrichment: Have students derive the Pythagorean Theorem using the distance formula.

Fine Arts:

Home: Have parents sign assignment sheet.

Remediation: Review what is meant by the square root of a number.

Technology: Have students investigate right triangles using a computer drawing program such

as Geometers Sketchpad or Capri Geometry.

Assessment

Have the students present the even-numbered problems to the class and discuss the various

methods of solution.

Homework

Assign from your text appropriate problems.

Teacher Notes

Check to see that students can find the square root of a number on a calculator.


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6. Make a sketch showing how the pieces fit together to form one square.

7. See if you can make a two-square/one-square puzzle with two squares, a2and b

2, that are

exactly the same size. How many pieces are there? Make a sketch showing how the pieces fit

together to make one square.

8. Repeat steps 1 through 6 with two squares, a2and b

2,, and bis exactly twice as long as a.

How many pieces are there? Make sketches showing how they fit together.

Questions:

1. Explain why, in each case, the sides of the pieces are the right lengths to fit together to make

c2.

2. How well did you and your partner work together?

3. Did the other pair in your group come up with the same puzzle as you did for #8?

4. Did one person do all the work? If so, why?

5. Did all of you ever work together in the past as a group?


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Correlations (SG,CAS,CFS): 6A1; 6B2

TAP:







formulas








ISAT:





relationships





concepts and skills

Unit Focus/Foci



Locating Midpoints and Segment Congruence

Materials

Midpoint Activity

Patty paper

Ruler

Compass

Round objects (such as a can)


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Review last nights homework and answer any questions.

Have students complete the Midpoint Activity.

Have at least one student model the activity for the class. Explain to the students that the

midpoint of a segment is the point that is half-way from both endpoints. For this activity, the

students locate the midpoint of the diameters or the center of the circle.

Discuss the terms midpointandsegment bisectorwith the class and derive a class definition for

each term.

Locate the midpoint of line segments using the Midpoint Formula.

1 211 3 3 7

10 6 5 7

. ., ,

, ,

MH STM S

H T

b g b gb g b g

Solutions:

1. (10.5, 4.5) 2. (4, 7)

Have the students draw a segment and locate the midpoint using patty paper and use a ruler to

verify.




Connection(s)

Enrichment: Have studentsdraw a rectangle or a square, and then locate the midpoint of each

side using only a ruler and a compass.

Fine Arts: Have students create a picture using only points, lines, and angles. Shade them in

using three shades--dark, medium and light of the same color.

Home: See Enrichment and Fine Arts.



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Technology: Have the students find the midpoint of various line segments using a geometric

drawing program such as Geometers Sketchpad or Capri Geometry.

Assessment

Teacher observation

Homework


Teacher Notes

Demonstrate how to use a compass correctly and have the students practice drawing circles and

arcs.

Demonstrate how to use a ruler and a compass to bisect a line segment. Have each student drawtwo line segments of different lengths and construct the bisector.


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MIDPOINT ACTIVITY

Guidelines

1. For this activity, the students should work in pairs.

2. Each student should complete the activity.

3. Students should agree on the final solution.

Activity

1. Draw at least two large circles (different sizes) on sheets of patty paper, using the round

objects provided.

2. Without measuring or using a compass, find the center of each circle.

3. Discuss with your partner how you found the center of each circle.

4. Using a ruler, check to see if your point is truly the midpoint.

5. Note that the midpoint of a segment can be found if you know the endpoint of the segment.

Introduce the Midpoint Formula.x x y y1 2 1 22 2+ +

,e j

Example:

Find the midpoint of AB A B3 6 4 0, ; ,b g b g + 3 4

26 0

2

12

62

12

3

,

,

,

e j

e j

e j


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TAP:







formulas








ISAT:





relationships





concepts and skills

Unit Focus/Foci



Exploring Angles-Identifying and Classifying Angles

Materials

Copies of Measuring Angles and Segments

Protractors

Student notebooks


Discuss the following terms with the students to derive a class definition for each: angle, acute

angle, obtuse angle, right angle, andstraight angle. Have students write the terms and

definitions in their notebooks.


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Demonstrate on the overhead how to use a protractor.

Instruct students to work in groups of four or less to complete the Measuring Angles and

Segments Worksheet. Explain that each group will be asked to answer one question from the

activity.





Connection(s)

Enrichment: Have students research how the ancient Babylonians measured angles.

Fine Arts:

Home: Parents will sign students homework.

Remediation: Have students draw angles of various measures. Review how to name an angle

using three capital letters, one small letter, or a numeral. Demonstrate how to extend the sides of

an angle to make reading the protractor easier.

Technology: Have students explore angle measure using a computer drawing program.

Experiment with the lengths of the sides and angles greater than 180.

Assessment

Teacher observation and student homework

Homework

Draw four acute angles, two right angles, four obtuse angles, and two straight angles. Give the

measure of each.


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Teacher Notes

Solutions to Measuring Angles and Segments:

1. See student work 2. See student work

3. See student work

Possible solutions: AOB, AOC,AOD, AOEEOB, EOC, EOD, DOB

4. AOB = 180, AOC = 154,AOD = 62, AOE = 43, EOB = 137,EOC = 115, EOD = 20, DOB = 120,DOC = 93, COB = 26


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Measuring Angles and Segments

1. Draw each of the following angles:

a. acute b. obtuse c. right

2. Use a protractor to draw angles having the following measures:

a. 450

b. 600

c. 300

d. 900 e. 120

0 f. 135

0

Refer to the drawing given to answer the remaining questions.

D

EC

A O B

3. Name all of the angles in the drawing above.

4. Measure each of the angles with your protractor.


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TAP:







formulas








ISAT:





relationships





concepts and skills

Unit Focus/Foci



Using the Angle Addition Postulate

Materials

Compasses

Protractors

Rulers

Geomirrors or Miras


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Demonstrate on the overhead how to construct an angle congruent to a given angle (angle

duplication) and how to construct the bisector of a given angle using a protractor and ruler.

Have the students draw an acute, right, and obtuse angle on plain paper and give the measures.After completing this task, students are to construct an angle congruent to the angles drawn and

construct their bisectors using a compass and protractor.

Demonstrate on the overhead how to construct an angle congruent to a given angle (angle

duplication) and how to construct the bisector of a given angle using a Geomirror or Mira.

Have the students draw an acute, right, and obtuse angle on plain paper and give the measures.

After completing this task, the students will construct an angle congruent to the angles drawn and

construct their bisectors using a Geomirror or Mira.





Connection(s)

Enrichment: Have the students find pictures of optical illusions.

Fine Arts: Have students create an optical illusion.

Home: Have students share their pictures of optical illusions with parents.


Technology: Have the students explore optical illusions on the Internet.

Assessment

Teacher observation


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Homework


Teacher Notes

The steps given below detail the steps to follow to construct congruent angles.

1. Draw angle B.

B

2. Use your straightedge to draw a ray with endpoint E.

3. Place your compass point at vertex B and construct an arc passing through each side of B .4. Label the point of intersectionsAand C.

5. Using the same setting, place your compass at point E and construct an arc. Label the pointof intersectionF.

6. Place your compass on point C and change the setting so that it passes through A. Construct

an arc.

7. Using the same setting, place your compass at point F. Construct an arc intersecting your

previous arc. Label the pointD. Using your straightedge, draw ray ED.

Check: Measure each angle with a protractor.

The steps given below explain the steps to follow to construct an angle bisector.

1. Draw an angle. Label it A .2. Place your compass on the vertex of A and construct an arc passing through both sides.

Label the points of intersectionRand T.

3. Place your compass at point R; construct an arc on the interior of the angle.

4. Keeping the same compass setting, place your compass at point T. Construct an arc that

intersects the 1stinterior arc. Label the point of intersection S.

5. Draw AS.


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Draw two pairs of intersecting lines on the chalkboard or overhead projector. Label each

diagram as follows:

5 6

4 1 2 8 7 3

Instruct students to work individually to answer the following questions:

1. What is the relationship between the following pairs of angles?

a) 1 and 3 b) 2 and 4 c) 5 and 7 d) 8 and 6

2. What is the name of the pairs of angles from problem 1?

3. Make a conjecture about these angles.

4. List all possible linear pairs from the diagram.

5. How are the pairs related?

6. Make a conjecture about the angles that form a linear pair.

Review the answers to the above questions with the class. Draw the following examples on the

chalkboard or overhead projector:

Example 1:

1

2

450 3

Find the measure of the following angles:

m1=___, m2=____, m3=____


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Example 2:

1200

3 1

2

Find the measure of the following angles:

m1=___, m2=____, m3=____

The question for discussion is: Given two intersecting lines where angles are formed, if you are

given the measure of one angle, can you always find the measure of the remaining angles?

Definesupplementaryand complementaryangles. Have the students give five pairs of angles

that are complementary and 5 pairs of angles that are supplementary. Review with the students

the symbol and definition for perpendicular lines.





SS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment: Have students locate vertical adjacent, right, complementary, and supplementary

angles in the school and cite their location.

Fine Arts: Have students create a village using pictures from newspapers and magazines that

show vertical, adjacent, complementary, or supplementary angles.

Home: See Fine Arts.


Technology:

Assessment



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Homework


Teacher Notes

Tell students to find a novel by Agatha Christie or Sir Arthur Conan Doyle to read for Unit Two.


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Correlations (SG,CAS,CFS): 6A1; 6B1-3; 6C1; 7A1,6; 8B2; 9A3

TAP:







formulas








ISAT:





relationships





concepts and skills

Unit Focus/Foci



Reviewing Definitions, Measurement, Relationships, and Basic Constructions

Materials

Geometry Vocabulary Review #1

Compasses

Protractors

Rulers

Overhead projector


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Review the following basic constructions using student volunteers to demonstrate each one on

the overhead projector or chalkboard.

Basic Constructions:-Duplicate a segment or angle

-Bisect a segment

-Bisect an angle

-Perpendicular bisector of a segment

Have the students work in pairs. Instruct each student to draw a right, acute, and obtuse angle,

then exchange papers and measure the angles with their protractors.

Have the students complete the Geometry Vocabulary Review #1.





Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

Assessment



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Homework

Assign from your text appropriate problems to review.

Teacher Notes

Remind students to find a novel by Agatha Christie or Sir Arthur Conan Doyle for Unit Two.


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Day: 023 Subject:Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 6A1; 6B1-3; 6C1; 7A1,6; 8B2; 9A3

TAP:







formulas








ISAT:





relationships





concepts and skills

Unit Focus/Foci



Reviewing Definitions, Measurement, Relationships, and Basic Constructions

Materials

Jeopardy Review Game

Timer or watch with a second hand

Overhead projector


Review answers to the homework with the students.

Answer any questions the students may have about the unit.


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Have students divide into three groups and play the Jeopardy Review Game.



Understand the meaning of words in contextSC: Apply scientific method to solve problems

Connection(s)

Enrichment:

Fine Arts:

Home: Have family members quiz students on material covered in Unit One.


Technology:

Assessment


Homework

Review class notes, homework, and quizzes.

Teacher Notes

Prepare Unit One Assessment.

Remind students to find a novel; their selections will be due in two days.


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JEOPARDY REVIEW #1

POINTS

100 A boundless three-dimensional set of points Space

200 Each point has zero___________________________.Dimensions

300 Points that lie on the same line are___________________. Collinear

400 The midpointMofPQis the point betweenPand Qsuch that_______________________________.PM = MQ

500 For the equationy = -3x + 2, the coordinates

for thex intercept are____________________________. ( 2/3 , 0 )

Extra questions that may be substituted:

All points in a plane are__________________________. Coplanar

The intersection of thex-axis and they-axis is

called the_______________________________________. Origin

( x,y, ) is called an _________________________. Ordered Pair

ANGLES

100 The common endpoint of intersecting rays is____________ .Vertex

200 The instrument used to measure angles is called a_______.Protractor

300 One-ninetieth of a right angle is called a_________________ .Degree


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400 Nonadjacent angles formed by two intersectinglines are____________________________________. Vertical

500

Adjacent angles whose non-common sidesare opposite rays_____________________________.Linear Pair


Every linear pair of angles is also_______________.Supplementary

POTPOURRI

100 The distance around a figure is the______________.Perimeter

200 The technique of painting that uses dotsto form a picture is called __________________.Pointillism

300 A statement to be proven is called a ____________. Theorem

400 The number of units a number is fromzero on the number line is its_____________. Absolute Value

500 One of the major sources that shows theknowledge of mathematics attained by

the ancient Egyptians is called Rhind Papyrus or

___________________________. Moscow Papyrus


The formula for finding the distancebetween any two points in the co-

ordinate plane is_______________. ( ) ( )x x y y1 22

1 22+ + +


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LINES

100 Lines that intersect to form four right anglesare . Perpendicular

200 Lines that lie in the same plane and donot intersect are . Parallel

300 Two planes ____ in a line. Intersect

400 Rays that form a straight line are . Opposite

500 A line has only one . Dimension


The axes in a coordinate plane divide

the plane into four . Quadrants

ALGEBRA CONNECTION

100 If angle one has measure 32 40, whatis the measure of its vertical angle? 32 40

200 If angleAis twice its complement, how

large is angleA? 60

300 If angleBis 2 less than twice itssupplement, how large is the supplement? 119

1

3


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*Cis the midpoint ofAB. IfAC = 3X 1

andBC= 14 X, what is the value ofXand

the measure ofAB? X = 3.75

AB = 20.5

500 AngleAand angleBare vertical.

If angleA= 3x+ 4 and angle 71.5

B= 5x 41, what is the measure of

angleA?

* Double Jeopardy


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Correlations (SG,CAS,CFS):6A1; 6B1-3; 6C1; 7A1,6; 8B2; 9A3

TAP:







formulas








ISAT:





relationships





concepts and skills

Unit Focus/Foci



Understanding Basic Definitions, Measurement, Relationships, and Basic Constructions

Materials

Unit One Assessment


Have students complete the Unit One Assessment.


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Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Unit One Assessment

Homework

Select an Agatha Christie or Sir Arthur Conan Doyle novel to read. Bring the title or the book to

the next class meeting.

Teacher Notes

Solutions to Unit One Assessment:

1. F 2. F

3. F 4. F

5. T 6. F

7. F 8. T

9. F 10. T


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11.

12. AB= =33 5 74. 13. ABC and CBE ABD and DBE

14. ABC or ABD 15. CBD = 40

16. DBE = (75 3x) 17. ABC = 95 CBD = 50 DBE = 35

18. See students work 19. See students work

20. See students work

(3,1)

-2,4


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Unit One Assessment

Answer TrueorFalse.

1. Thexandyaxis divide the coordinate plane into two equal parts.2. One-ninth of a right angle is a degree.3. Supplementary angles are congruent.4. Adjacent angles are vertical.5. Postulates are statements that are assumed to be true.6. An acute angle is greater than 90.7. A point has one dimension.8. Collinear points lie on the same line.9. Two angles whose sum is 180are complementary.10.If AB BC AC+ = ,Blies betweenAand C.

For Questions 11 and 12

11. Graph the points A(3,1) and B(-2,4).

12. Find the distance betweenAandB

to the nearest hundredth.


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18. Construct a 50angle with sides 3 cm in length.

19. Draw ABC with sides AB = 3 cm, BC = 4 cm, and AC = 5 cm.

20. Construct a line perpendicular to AB through C.

A C B

high school geometry days 09024

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