high school geometry days 041053

5/27/2018 High School Geometry Days 041053

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STRUCTURED CURRICULUM LESSON PLAN

Day: 041 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 9A3, 4; 9B2

TAP:

Understand geometric properties and

relationships

ISAT:

Understand and apply geometric concepts and

relationships

Unit Focus/Foci

Using Perpendicular and Parallel Lines

Instructional Focus/Foci

Identifying Parallel Lines and Transversals

Materials

Copies of Rectangular Prisms

Plain paper

Straight edge

Colored pencils

At least 6 rectangular boxes (1 per group)

Graphing calculator (optional)

Educational Strategies/Instructional Procedures

Review points, lines, and planes. Identify the three categories of lines.

- Intersecting - lines that lie in the same plane and have a common point.

- Parallel - lines that lie in the same plane and do not intersect.

- Skew - lines that do not lie in the same plane.


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Utilizing the classroom as a model, point out examples of each category.

Have students complete the Rectangular Prism activity and discuss their observations.

Integration with Core Subject(s)

LA: Understand explicit, factual information

Understand the meaning of words in context

SC: Apply scientific method to solve problems

SS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment: See Fine Arts.

Fine Arts: Have students research which artists were among the first to use perspective drawing

and the title of their work(s).

Home: Look for parallel lines at home.

Remediation: Draw several pairs of lines cut by a transversal and identify the special names for

the pairs of angles formed.

Technology: Have students use a graphing calculator to graph the following lines to show lines

cut by a transversal: y=x, y=x- 2, andy = 4x + 3.

Assessment

Teacher observation

Homework

Identify at least 10 pairs of parallel lines that you see around you. Assign from your text

appropriate problems identifying parallel lines and transversals.

Teacher Notes

Review the symbol for parallel lines ( ||). When defining transversal, note that the two lines thatare intersected by a transversal do not need to be parallel. For additional points or extra credit,

you may want students to make corrections on the Chapter Two Assessment.


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RECTANGULAR PRISM

1. Students should work in groups of four.

2. One person should be assigned to take notes.

3. Students should agree on the final answer.

4. Each group should be prepared to present their observations to the class.

ACTIVITY

Materials: plain paper, color pencils, and at least 6 rectangular boxes

1. Have each group label all corners of the box.

2. Have groups list the following:

a. planes

b. segments

c. vertices

3. Solution: Do any of the planes intersect? If so, name them.

4. Solution: What can we say about the intersection of two planes?

5. Solution: What can we say about the intersection of three planes?

6. Solution: Are any of the planes parallel? If so, name them.

A

H

E

BF

G

D


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Correlations (SG,CAS,CFS): 9A4; 9B1

TAP:

Understand number systems


relationships; apply geometric concepts and

formulas

Demonstrate understanding of measurement

concepts and apply measurement skills

ISAT:


relationships

Demonstrate an understanding of measurement

concepts and skills

Unit Focus/Foci



Identifying Angles Formed by Two Lines and a Transversal

Materials

Ruler

Plain paper


Each of the Sanders women purchased a pair of shoes. The salesman sold seven pairs of shoes to

the three women, each with two daughters. Explain how this sale is possible.

Solution:

Grandmother, 2 daughters, and 4 granddaughters.


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Have the students complete the following:

1. Draw two lines on a sheet of paper and label them land m.2. Draw a third line and label it t.3. Number the angles formed.

The line that intersects two lines is called a transversal. When this occurs, there are eight anglesformed. There are several names to identify the pairs and their relationships.

Corresponding angles:

a) they lie on the same side of the transversalb)one angle is interior; one angle is exteriorc) they are nonadjacent 1 5 2 6 3 7 4 8and and and and and, , ,

Alternate interior angles:

a) they lie on opposite sides of the transversal

b) they are both interiorc) they are nonadjacent

3 6 4 5and and and

12

5

84

73

6

t

l

m

12

5

84

73

6

t

l

1

2

5

84

73

6

Interior

Exterior

Exteriort

l

m

Transversal


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Alternate exterior angles:

a) they lie on opposite sides of the transversalb) they are both exteriorc) they are both nonadjacent

1 8 2 7and and and

Same side interior angles:

a) they lie on the same side of the transveralb) they are both interiorc) they are both adjacent

3 5 4 6and and and

Have students list any additional angle relationships observed in the diagram.

Student observations:

Vertical Angles Linear Pairs

1 4and 1 2 5 6and and




Have the students identify the following pairs of angles:

1.

1 6and

2. 2 3and3. 2 4and4. 5 7and

1

2

5

84

73

6

t

l

m

12

5

84

73

6

t

l

m

1 2

58

4

7

3

6

t

l

m

r


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Solution:

1. Alternate interior2. Corresponding3. Corresponding


LA:Understand explicit, factual information



Connection(s)

Enrichment: Have the students take pictures of everyday objects that illustrate two lines cut by

a transversal, and point out any angle relationships that exist.

Fine Arts: Have the students find pictures in newspapers or magazines showing angle

relationships.

Home: See Enrichment and Fine Arts.

Remediation: Teachers Half-Dozen

Technology: Have the students explore two lines cut by a transversal, using a computer drawing

program.

Assessment

Teacher observation

Homework

Assign from your text appropriate problems.

Teacher Notes


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Correlations (SG,CAS,CFS): 9A4

TAP:


relationships

Apply geometric concepts and formulas



ISAT:


relationships


concepts and skills

Unit Focus/Foci



Identifying Angles and Parallel Lines

Materials

Protractors

Colored pencils

Rulers

Copies of Angles and Parallel Lines Activity

Plain paper


Arrange the first 9 counting numbers in the squares so that each row, column and diagonal total

15.


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Solution:

2 9 4

7 5 3

6 1 8

Have students complete the Angels and Parallel Lines Activity. Invite the students to share their

observations with the class.

At the end of the discussion, remind students that if the lines are parallel, the angles will be

congruent or supplementary.

Have students complete the following example and review the solution.

Find the measure of each numbered angle.

l||m with transversals tand d.






t d

60 1 2 3 l

7 6 4 5

9

10 11 12 13 m

14 15 16 17

508


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Connection(s)

Enrichment: See Fine Arts.

Fine Arts: Have students create an optical illusion to share with the class.

Home: Have parents sign assignment sheet.

Remediation: Using a geoboard and rubber bands, make parallel lines cut by a transversal,

number all of the angles formed, and list pairs of angles that are congruent or supplementary.

Technology: Have the students find examples of optimal illusions on the Internet to share with

the class.

Assessment

Evaluate the Angles and Parallel Lines Activity using the Structured Curriculum Scoring Rubric.

Homework

Assign appropriate problems from your text.

Teacher Notes

Remind students to review their notes for a quiz tomorrow.

Solutions to in-class assignment:

1 = 120 2 = 110 3 = 70

4 = 70 5 = 110 6 = 60

7 = 120 8 = 130 9 = 50

10 = 110 11 = 70 12 = 60

13 = 120 14 = 70 15 = 110

16 = 120 17 = 60


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ANGLES AND PARALLEL LINES

1. Students should work in pairs.

2. One student should measure and the other check the results.

3. Students should agree on the final solution.

4. Students should be prepared to present their findings to the class.

ACTIVITY

Have students draw two parallel lines and cut them by a transversal. Number each angle.

Identify the following:

a. Exterior angles

b. Interior angles

c. Consecutive interior angles

d. Alternate exterior angles

e. Alternate interior angles

f. Corresponding angles

After completing a-f, measure each of your angles with a protractor.

g. Consecutive interior angles

h. Alternate exterior anglesi. Alternate interior angles

j. Corresponding angles

1. Make a conjecture about the corresponding angles formed by two parallel lines cut by a

transversal.

2. Make a conjecture about alternate interior s, consecutive interior s, and alternate

exterior s.

Have students discuss their observations.


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TAP:


relationships


ISAT:


relationships

Unit Focus/Foci



Proving Lines Parallel

Materials

Copies of Proving Lines Parallel


Return Mid-Chapter Tests.

Discuss and illustrate the five methods of proving lines parallel:

1. If two lines in a plane are cut by a transversal so that corresponding angles are

congruent, then the lines are parallel.

l

m


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2. If two lines in a plane are cut by a transversal so that the alternate exterior angles are


l

m

3. If two lines in a plane are cut by a transversal so that the alternate interior angles are


l

m

4. If two lines in a plane are cut by a transversal so that a pair of consecutive interior

angles are supplementary, then the lines are parallel.

l

m

5. In a plane, if two lines are perpendicular to the same line, then the lines are parallel.

l

m

or m l

100o

80o


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Demonstrate how to apply the theorems algebraically.

Example 1:

Given: 1 m , find the measure of 1 2and if 3 = 60

l

m

If l m , then 2 3 (alternate exterior ' s).

2 = 60

1 and 2 are supplementary (linear pair).

1

1

1

= 180 - 2

= 180 - 60

= 120

Example 2:

Given: m n , find the measure of 1 if 2 = 2x+ 20 and 3 = 3x- 10.

m

n

3

1 2

12

3


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2 and 3 are consecutive interior angles. 2 and 3 are supplementary angles.

2 and 3 = 180

2x+ 20 + 3x- 10 = 180

5x+ 10 = 180 5x= 170

x= 34

2 = 2x+ 20

2= 2(34) + 20

2 = 68 + 20

2= 88

1 and 2 are vertical angles.

1=88

Remind students that vertical angles are congruent.

Have the students complete Proving Lines Parallel.






Connection(s)

Enrichment: Make a sketch to show that each statement is false: 1. If two lines are parallel to

the same plane, then the lines are parallel. 2. If two planes are parallel, then any line in one

plane is parallel to any line in the other plane.

Fine Arts: Have the students make a poster illustrating each of the ways to prove lines

parallel.



Technology:


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Assessment

Evaluate the in-class assignment using the Structured Curriculum Scoring Rubric.

Homework


Teacher Notes

Have students discuss when it is best to use each of the ways to prove two lines parallel.

Solutions to Proving Lines Parallel:

1. n||p alternate exterior angles are . 2. n||p alternate exterior angles are .3. n||p alternate interior angles are . 4. l||m corresponding angles are .5. x = 25 6. x = 10

7. x =17

2or 8.5 8. x =

198

5or 39.8

9. x = 130 10. x = 36


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PROVING LINES PARALLEL

Use the given information to determine which lines are parallel and explain your answer.

1. 3 162. 15 103. 6 94. 4 14Find the value ofxthat will make l || m.

5.

1 = (2x+40)and 5 =( 4x-10)

6. 8 = (2x+15)and 4 = (3x+5)7. 3 = (2x+5)and 6 = (4x-12)8. 4 = xand 6 = (3x-18)

Find the value ofx.

9. 10.

x

60

70

13

57

24

68

l

m

46

x58

1

3

5

7

2

4

6

8

15

13

16

14

11

9

12

10

l

n

m

p


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ACTIVITY

Have students draw two parallel lines and cut them by a transversal. Number each angle.

Identify the following:

g. Exterior angles

h. Interior angles

i. Consecutive interior angles

j. Alternate exterior angles

k. Alternate interior angles

l. Corresponding angles

After completing a-f, measure each of your angles with a protractor.

k. Consecutive interior angles

l. Alternate exterior angles

m. Alternate interior angles

n. Corresponding angles

3. Make a conjecture about the corresponding angles formed by two parallel lines cut by a

transversal.

4. Make a conjecture about alternate interior s, consecutive interior s, and alternate

exterior s.

Have students discuss their observations.


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TAP:

Identify, describe, compare, and classify

geometric figures

ISAT:


relationships

Unit Focus/Foci



Proving Lines Pareallel

Materials

Parallel or Not Parallel Activity


Have the students complete the Parallel or Not Parallel activity. (Allow 15-20 minutes.) Have

students share their solutions with the class.

Review the theorems and postulates that determine whether two lines are parallel.

1. If two lines are cut by a transversal so that the corresponding angles are congruent, the

lines are parallel.

2. If two lines are cut by a transversal so that the alternate exterior angles are congruent,

the lines are parallel.

3. If two lines are cut by a transversal so that a pair of consecutive interior angles are

supplementary, the lines are parallel.

4. If two lines are cut by a transversal so that the alternate interior angles are congruent,

then the lines are parallel.

5. If two lines are perpendicular to the same line, the lines are parallel.






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Connection(s)

Enrichment: Use 15 toothpicks to make this arrangement. Then take away three toothpicks to

leave three squares.

Solution:

Fine Arts:

Home: Have parents sign homework.

Remediation: Teachers Half Dozen

Technology:

Assessment

Evaluate student performance on the Parallel or Not Parallel activity using the Structured

Curriculum Scoring Rubric.

A

B

C

(Remove A, B, and C)


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Homework

Assign from your text appropriate problems on proving lines parallel.

Teacher Notes

Solutions to Parallel or Not Parallel Activity:

1. Yes Alternate interior angles are . 2. No Corresponding angles are not .

3. No Corresponding angles are not . 4. Yes Alternate interior angles are .

5. No Not supplementary. 6. Yes Alternate exterior angles.

7. No Corresponding angles are not . 8. Yes Alternate exterior angles are .

9. Yes Alternate exterior angles are . 10. Cannot determine.


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PARALLEL OR NOT PARALLEL: THAT IS THE QUESTION

For each, determine whether line l||m. Explain why or why not.

t t

1. 2. 80 l 69 l

m

3. 4.

5. 6.

7. 8.

9. 10.

70 m

101100t

l m t

l

m

115

60

l

m

l

t

m

t

l

m

2x

2x+ 2

2(x+ 1)m

l

t

3 4

4

x+

.75x+ 1

t

m

100 80l

80


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TAP:

Perform arithmetic operations involving

integers, fractions, decimals and percents,

explicitly stated or within context




formulas

Use variables, numbers sentences, and

equations to represent solutions and solve

problemsAnalyze and interpret data presented in charts,

graphs, tables, and other displays



ISAT:

Solve problems requiring computations with

whole numbers, fractions, decimals, ratios,

percents, and proportions


relationships

Understand and use methods of data collection

and analysis, including tables, charts, and

comparisons

Demonstrate and skills

Unit Focus/Foci



Finding the Slope of Lines

Materials

Copies of Rise Over Run

Graph grid for the overhead or a coordinate planer for the board

Graphing calculators

Graph paper


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Have students complete Rise Over Run.

Defineslope(m) as the ratio of the vertical change to the horizontal change in a line.

m = x y1 1, (A good way to remember it is to tell students m =rise vertical change

run - horizontal change

.

x1, y1b g and x2 , y2b g are the coordinates of two points on the line.

Have the students graph the following linear equations. This can be done with a graphing

calculator.

Parallel Lines:

y= 2xy= 2x- 1

y= 2x+ 4

Have the students calculate the slope of each line and make a conjecture about the slopes of

parallel lines. (Parallel lines have the same slope.)

Perpendicular Lines:

y x

y x

= +

= - -

2 4

1

22

R

S|T|

RS|

T|

y = 4x + 1

y = -1

4x - 3

Have the students calculate the slope of each line and make a conjecture about the slopes of each

pair of perpendicular lines. Perpendicular lines have slopes that are negative reciprocals of each

other m m1 2 1 = b g .






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Connection(s)

Enrichment: Give the students a graph and have them write the equation. Research

Rene Descartes, the first mathematician to introduce coordinatesinto the study of geometry.

Fine Arts:

Home: Have parents sign assignment sheet

Remediation: Model parallel and perpendicular lines using a geoboard and rubber bands.

Demonstrate finding the slopes by counting and relate this to the formula for slope.

Technology: Have students investigate parallel and perpendicular lines using a computer

drawing program.

Assessment

Teacher observation

Homework

Given the lines y = -4x+ 5 and y =1

3x+ 6 , write an equation of a line parallel to each line and

an equation of a line perpendicular to each line. Have students explain their methods: How are

the lines related?

Teacher Notes

Review that0

1and

1

0= 0 is undefined. Have students choose two pairs of points on a horizontal

and vertical line and try to apply the formula.


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RISE OVER RUN

I. For each of the following:

A. Draw a line parallel to AB and label it CD.B. Find the horizontal distance from A to B.C. Find the vertical distance from A to B.D. What is the ratio of the vertical to the horizontal change?E. Find the horizontal distance from C to D.F. What is the ratio of the vertical to the horizontal change?1. 2. 3.

II. Draw a line perpendicular to AB and label itEF.

A. Find the horizontal distance from E to F.B. Find the vertical distance from E to F.C. What is the ratio of the horizontal change to the vertical change?

B

A

B

A

BA


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TAP:







formulas







ISAT:





relationships



comparisons


concepts and skills

Unit Focus/Foci



Finding the Slopes of Lines

Materials

Graph paper

Rulers

Markers


Review the definition ofslopeand the formula for calculating slope given two points.


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Place the following examples on the chalkboard/overhead.

Example 1: Example 2:

m=7 4

3 0

m=

2 1

2 0

m=3

31= m=

3

2

Example 3: Example 4:

m=4 4

2 0

m=

4 4

4 4

m=0

2 m=

8

0

m= 0 m= undefined

(0, 4)

(3, 7) (0, 1)

(2, -2)

(0, 4) (2, 4)

(4, 4)

(4, -4)


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Explain to the students the following:

a. When the slope is positive, the line slants upward from left to right.

b. When the slope is negative, the line slants downward from left to right.

c. When the slope is zero, the line is horizontal.

d. When the slope is undefined, the line is vertical.

Have the students graph each line and calculate the slope.

1. A (3,3), B (4,4) 2. C (-3,1), D (2,3)3. E (0,2), F (2,0) 4. G (5,2), H (3,7)Solutions:

1. m=1 2. m= 25

3. m=-1 4. m=- 52

Have students work in groups of four. Using chart paper and markers, explain how to determine

whether lines are parallel, perpendicular, or neither.




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

Connection(s)

Enrichment:

Fine Arts:


Remediation: List the coordinates of two points on the chalkboard. Have half of the class usethe first point as (x1, y1) and the second point (x2, y2). The other half should use the first point as

(x2, y2) and the second as (x1, y1), Have students find the slope of the lines.

Technology: Have students graph linear equations using agraphing calculator and determine

whether the slope is positive, negative, zero, or undefined.


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Assessment

Teacher observation

Homework

Assign from your text appropriate problems on finding the slope of a line.

Teacher Notes

Emphasize that it does not matter which point is selected as (x1, y1) or (x2, y2), but both

coordinates must be in the correct place in the formula for the slope.


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Correlations (SG,CAS,CFS): 9A3,4

TAP:







formulas







ISAT:





relationships



comparisons

Unit Focus/Foci



Constructing Parallel Lines

Materials

Copies of Parallel Lines Quiz

Straightedges

Rulers

Compasses

Plain paper

Overhead projector


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Have students complete the Parallel Lines Quiz.

Review the solutions with the class and answer any questions.

Work along with the students to demonstrate the construction of a line parallel to a given line

through a point not on the line.

1. Have students draw a line on a piece of plain paper and label it land place a point on

the paper not on line land label itK.

2. Have the students label any two points on l,E,andH.

3. Draw line KE.

4. Construct an angle congruent to KEH withKas the vertex andKEas the base and

label the terminal side of the m.

Step 1: Step 2: l

l E H

Step 3: K Step 4: m

l l

E H H





Connection(s)

Enrichment: Have the students explain how to construct a line parallel to a given line from a

point not on the line using a mark and paper following.

Fine Arts: Have the students write their initials using one-or two-point perspective.


Remediation: Have the students select four pairs of coordinates. Graph each pair and draw the

line. Let them tell first if the slope ispositive, negative,zero, or no slopebefore finding the slope

algebraically.

K

E

K


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Technology: Have students graph parallel and perpendicular lines using a graphing calculator.

Assessment

State an example of a real object that has either a positive, negative, zero, or an undefined slope.For example, a handrail has a positive or negative slope depending on the viewpoint.

Homework

Have students explain how to construct a line parallel to a given line through a point not on the

line using a 50oangle.

Teacher Notes

Solutions to Parallel Lines Quiz:

1. 132. 43. x = 7, y = 454. m = 5

3


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Parallel Lines Quiz

Find the value ofxthat makes l || m.

1.

l

m

(7x-1)

2.

3.

l

m

(7x+3)o

(9x-5)o

(3y+8)o

(4x+9)o

(19x+10)o


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Find the slope of AB.

4.

A

B

(-2,2)

(1,-3)


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TAP:







formulas







ISAT:





relationships



comparisons

Unit Focus/Foci



Exploring Spherical Geometry

Materials

Globe

Spherical Geometry Scavenger Hunt Activity

Map of the United States


Define equator,prime meridian,latitude, and longitudefor the students.

Equator- an imaginary line around the earth dividing it into two equal parts (north and south).

Latitude- distance measured in degrees north or south of the equator.

Meridian- an imaginary line on the earths surface passing through the North and South Poles.

Prime Meridian- the 0omeridian, which passes through Greenwich, England, separating east

from west since there is no east or west pole.


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Longitude- distance from the Prime Meridian measured in degrees.

Explain to the students how to read longitude (horizontal location east or west of the Prime

Meridian). Longitude is measured in degrees ranging from 0oat the Prime Meridian to 180

oat

the International Date Line. Latitude provides the vertical location north or south of the Equator.

Latitude is measured by angles ranging from 0o

at the equator to 90o

at the poles.

Using a map or globe, have the students identify the latitude and longitude lines. Tell them that a

map is like a coordinate grid using the lines of latitude (vertical) and longitude (horizontal).

Example: Using a map of the United States, have the students locate Chicago and approximate

the latitude and longitude. (42oN, 88

oW)

Remind students that this is an ordered pair (latitude, longitude).

Have the students locate the state capital Springfield, IL. (40oN, 90

oW)

Working in pairs, have the students pick six cities. Give the approximate latitude and longitude

for each. Each pair should write the names of the cities on a sheet of paper and exchange papers

and have the other pair find the latitude and longitude. Return the answers to the original pair

and check their answers.

Using the scale on the map, approximate, in miles and kilometers, the distance between each city,

Chasla and Chicago.




SS: Read and interpret maps, charts, graphs, ad cartoons

Connection(s)

Enrichment:

Fine Arts:

Home: Have parents sign homework.

Remediation: Have students explain why there are no parallel lines in spherical geometry.

Technology:


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Assessment

Teacher observation

Homework

Locate and describe the seven wonders of the world (ancient, modern or natural).

Teacher Notes


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SPHERICAL GEOMETRY SCAVENGER HUNT

ACTIVITY

1. Locate the Home of Country Music.

2. Locate the Basketball Hall of Fame.

3. Locate the Baseball Hall of Fame.

4. What is the latitude of Yellowstone National Park?

5. What is the longitude of Disney World?

6. What is the location of Niagara Falls?

7. Locate the birthplace of Dr. Martin Luther King, Jr.

8. Where is the home of the Motown Sound?

9. Where is the City of Lights?

10. Locate the Eiffel Tower.

11. Locate the home of the Pope.

12. Where are the presidents etched in stone?

13. Locate the worlds longest ditch.


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Spherical Geometry Scavenger Hunt

Solutions:

1. Nashville, Tennessee (36oN, 87

oW)

2. Canton, Ohio (41

oN, 81

oW)

3. Cooperstown, New York (43

oN, 75

oW)

4. 45

oN, 110

oW

5. 29

oN, 81

oW

6. 43N, 79W7. Atlanta, Georgia (34N, 84W)

8. Orlando, Florida (29N, 81W)

9. Las Vegas, Neveda (36N, 115W)

10. Paris, France (49N, 2E)

11. Vatican City (42N, 12E)

12. Mt. Rushmore, South Dakota (44N. , 103W)

13. Panama Canal (10N., 80W)


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Correlations (SG,CAS,CFS): 9A3,4

TAP:


relationships

ISAT:


relationships


Unit Focus/Foci



Exploring Spherical Geometry

Materials

Styrofoam balls


Ask the students to list as many examples as they can of two-dimensional objects with three-

dimensional counterparts.

Example:

2D 3D

map globe

square cube

circle sphere

Model for the students how a line on a sphere becomes a circle. Have the students work in pairs

to transform the properties of lines on a plane to create circles in a sphere.

1. A line segment is the shortest distance between two points.2. Two points determine a unique straight line.

3. A straight line is infinite.

4. If three points are exactly collinear, one is between the other two.


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Discuss students solutions.

Have each pair create a map to locate a hidden treasure using latitude and longitude. Randomly

select three students to share their maps with the class.






Connection(s)

Enrichment:

Fine Arts:


Remediation: Teachers Half Dozen

Technology:

Assessment

Teacher observation

Homework

Study for the upcoming examination

Teacher Notes

Remind the students of the upcoming examination.


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TAP:



formulas

ISAT:

Understand and apply geometric properties and

relationships

Unit Focus/Foci



Reviewing Unit Three

Materials

Copies of Unit Three Practice Test


Have the students complete the Unit Three Practice Test.

Discuss the solutions and answer any questions the students may have.





Connection(s)

Enrichment:

Fine Arts:




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Technology:

Assessment

Teacher observation

Homework


Teacher Notes

Make copies of the Unit Three Assessment

Solutions to Unit Three Practice Test:

1. a. Slants downward to the rightb. Slants upward to the right

c. Vertical line

d. Horizontal line

2. Linear pairs

Interior angles on the same side of the transversal

Alternate exterior angles

Alternate interior angles

Corresponding angles

Vertical angles

3. Parallel m = 4

5

Perpendicular m =5

4

4. = 6 124 27.5. See student work.


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Unit Three Practice Test

1. Describe the graph of a line with slope:

a. -3

b. 3c. 0

d. undefined

2. State as many angle relationships as possible:

l m

1 2 3 4

5 6 7 8

3. Find the slope of a line parallel and perpendicular to the line through (4, 2) and (-1, 6).

4. Find the measure of 6 if lines are l m.

8x - 11 l

3x + 5 6 m

Note: Remind students to answer the question asked.

5. Draw a line mon the coordinate axis that has slope -1

2.


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TAP:


relationships




ISAT:


relationships


concepts and skills

Unit Focus/Foci



Assessing Unit 3

Materials

Copies of Unit Three Assessment


Administer the Unit Three Assessment.






Connection(s)

Enrichment:

Fine Arts:


Remediation: Teaches Half-Dozen


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Technology:

Assessment

Evaluate the Unit Three Assessment using the Structured Curriculum Scoring Rubric.

Homework

Assign from your text appropriate problems on the classification of triangles.

Teacher Notes

Return the assessment tomorrow.

Solutions to Unit Three Assessment:

1. Alternate exterior2. Corresponding3. Linear pair; supplementary; adjacent4. Vertical5. 1 = 101and 2 = 796. 3 = 52and 6 = 527. a. m= 3

4

b. m= -2

8.

a. the lines slant downward to the rightb. horizontal line

9. m= 6

10.a. 1 8 alternate exterior anglesb. 8 6 corresponding angles

8 1 transitive property

c. 8 3 vertical angles 3 1 corresponding angles

8 1 transitive property

Extra Credit

See student work.


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Unit Three Assessment

Identify the following pairs of angles.

1. 1 and 82. 5 and 73. 4 and 34. 2 and 5

5. If the m x = + 1 5 36( ) and m x = 2 7 12( ) ; find m mand 1 2 .

6. If the m x = 6 12 48( ) and m x = + 3 6 2( ) ; find m mand 3 6.

7. Find the slope of the line passing through.a) A(3,2) B(-1,-1)

b) A(-2,3) B(3,-7)8. Describe the line that has slope:

a) 3

b) 0

9. Find the slope of a line perpendicular to the line passing throughM (-1, 5) andH (11, 3).

12

5

84

73

6

m

l


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10.Give three ways of proving 1 8.

Extra Credit

Construct a line parallel to AB passing through C.

C

A B

1

2

5

84

73

6


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TAP:


relationships

ISAT:


relationships


Unit Focus/Foci

Reflecting on the Quarter


Evaluating Oneself With Respect to the Course

Materials


Have the students write an essay reflecting on their performance in the first quarter. Remind

students that an essay has a minimum of three paragraphs: introduction, body, and conclusion.

Invite the students to use the following questions as guidelines for writing their essays:

1.What is the course about?2.What did I wish to accomplish?3.Did I reach my goal?4.What gave me the most difficulty?5.Where do I need the most help?6.What methods or recourse did I use to improve myself?7.What would I do differently next time?8.What activities did I enjoy the most?






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Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Homework

Prepare copies of Classifying Triangles.

Teacher Notes

high school geometry days 041053

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