Essentials of Geometry Eleanor Roosevelt High School Geometry Mr. Chin-Sung Lin.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 042 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4; 9B1
TAP:
Understand number systems
Understand geometric properties and
relationships; apply geometric concepts and
formulas
Demonstrate understanding of measurement
concepts and apply measurement skills
ISAT:
Understand and apply geometric concepts and
relationships
Demonstrate an understanding of measurement
concepts and skills
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Identifying Angles Formed by Two Lines and a Transversal
Materials
Ruler
Plain paper
Educational Strategies/Instructional Procedures
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
2 3and 3 4 7 8and and
6 7and 1 3 5 7and and
5 8and 2 4 6 8and 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
Integration with Core Subject(s)
LA:Understand explicit, factual information
Understand the meaning of words in context
SC: Apply scientific method to solve problems
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 043 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Understand geometric properties and
relationships
Apply geometric concepts and formulas
Demonstrate understanding of measurement
concepts and apply measurement skills
ISAT:
Understand and apply geometric concepts and
relationships
Demonstrate an understanding of measurement
concepts and skills
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Identifying Angles and Parallel Lines
Materials
Protractors
Colored pencils
Rulers
Copies of Angles and Parallel Lines Activity
Plain paper
Educational Strategies/Instructional Procedures
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.
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
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 044 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Understand geometric properties and
relationships
Apply geometric concepts and formulas
ISAT:
Understand and apply geometric concepts and
relationships
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Proving Lines Parallel
Materials
Copies of Proving Lines Parallel
Educational Strategies/Instructional Procedures
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
congruent, then the lines are parallel.
l
m
3. If two lines in a plane are cut by a transversal so that the alternate interior angles are
congruent, then the lines are parallel.
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.
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: 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.
Home: Have parents sign assignment sheet.
Remediation: Teachers Half-Dozen
Technology:
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Assessment
Evaluate the in-class assignment using the Structured Curriculum Scoring Rubric.
Homework
Assign from your text appropriate problems.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 045 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Identify, describe, compare, and classify
geometric figures
ISAT:
Understand and apply geometric concepts and
relationships
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Proving Lines Pareallel
Materials
Parallel or Not Parallel Activity
Educational Strategies/Instructional Procedures
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.
Integration with Core Subject(s)
LA: Understand explicit, factual information
Understand the meaning of words in context
SC: Apply scientific method to solve problems
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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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STRUCTURED CURRICULUM LESSON PLAN
Day: 046 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Perform arithmetic operations involving
integers, fractions, decimals and percents,
explicitly stated or within context
Understand number systems
Understand geometric properties and
relationships; apply geometric concepts and
formulas
Use variables, numbers sentences, and
equations to represent solutions and solve
problemsAnalyze 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
Understand and use methods of data collection
and analysis, including tables, charts, and
comparisons
Demonstrate and skills
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional 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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Educational Strategies/Instructional Procedures
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 .
Integration with Core Subject(s)
LA: Understand explicit, factual information
Understand the meaning of words in context
SC: Apply scientific method to solve problems
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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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STRUCTURED CURRICULUM LESSON PLAN
Day: 047 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Perform arithmetic operations involving
integers, fractions, decimals and percents,
explicitly stated or within context
Understand number systems
Understand geometric properties and
relationships; apply geometric concepts and
formulas
Use variables, numbers sentences, and
equations to represent solutions and solve
problemsAnalyze 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
Understand and use methods of data collection
and analysis, including tables, charts, and
comparisons
Demonstrate an understanding of measurement
concepts and skills
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Finding the Slopes of Lines
Materials
Graph paper
Rulers
Markers
Educational Strategies/Instructional Procedures
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.
Integration with Core Subject(s)
LA: Understand explicit, factual information
Understand the meaning of words in context
SC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information
Connection(s)
Enrichment:
Fine Arts:
Home: Have parents sign assignment sheet.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 048 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A3,4
TAP:
Perform arithmetic operations involving
integers, fractions, decimals and percents,
explicitly stated or within context
Understand number systems
Understand geometric properties and
relationships; apply geometric concepts and
formulas
Use variables, numbers sentences, and
equations to represent solutions and solve
problemsAnalyze 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
Understand and use methods of data collection
and analysis, including tables, charts, and
comparisons
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Constructing Parallel Lines
Materials
Copies of Parallel Lines Quiz
Straightedges
Rulers
Compasses
Plain paper
Overhead projector
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Educational Strategies/Instructional Procedures
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
Integration with Core Subject(s)
LA: Understand explicit, factual information
Understand the meaning of words in context
SC: Apply scientific method to solve problems
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.
Home: Have parents sign assignment sheet.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 049 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A3
TAP:
Perform arithmetic operations involving
integers, fractions, decimals and percents,
explicitly stated or within context
Understand number systems
Understand geometric properties and
relationships; apply geometric concepts and
formulas
Use variables, numbers sentences, and
equations to represent solutions and solve
problemsAnalyze 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
Understand and use methods of data collection
and analysis, including tables, charts, and
comparisons
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Exploring Spherical Geometry
Materials
Globe
Spherical Geometry Scavenger Hunt Activity
Map of the United States
Educational Strategies/Instructional Procedures
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.
Integration with Core Subject(s)
LA: Understand explicit, factual information
Understand the meaning of words in context
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 050 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A3,4
TAP:
Understand and apply geometric concepts and
relationships
ISAT:
Understand geometric properties and
relationships
Apply geometric concepts and formulas
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Exploring Spherical Geometry
Materials
Styrofoam balls
Educational Strategies/Instructional Procedures
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.
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:
Fine Arts:
Home: Have parents sign assignment sheet.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 051 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Understand geometric properties and
relationships; apply geometric concepts and
formulas
ISAT:
Understand and apply geometric properties and
relationships
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Reviewing Unit Three
Materials
Copies of Unit Three Practice Test
Educational Strategies/Instructional Procedures
Have the students complete the Unit Three Practice Test.
Discuss the solutions and answer any questions the students may have.
Integration with Core Subject(s)
LA:Understand explicit, factual information
Understand the meaning of words in context
SC: Apply scientific method to solve problems
Connection(s)
Enrichment:
Fine Arts:
Home: Have parents sign assignment sheet.
Remediation: Teachers Half-Dozen
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Technology:
Assessment
Teacher observation
Homework
Assign from your text appropriate problems.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 052 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Understand geometric properties and
relationships
Apply geometric concepts and formulas
Demonstrate understanding of measurement
concepts and apply measurement skills
ISAT:
Understand and apply geometric concepts and
relationships
Demonstrate an understanding of measurement
concepts and skills
Unit Focus/Foci
Using Perpendicular and Parallel Lines
Instructional Focus/Foci
Assessing Unit 3
Materials
Copies of Unit Three Assessment
Educational Strategies/Instructional Procedures
Administer the Unit Three Assessment.
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:
Fine Arts:
Home: Have parents sign assignment sheet.
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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STRUCTURED CURRICULUM LESSON PLAN
Day: 053 Subject: Geometry Grade Level: High School
Correlations (SG,CAS,CFS): 9A4
TAP:
Understand and apply geometric concepts and
relationships
ISAT:
Understand geometric properties and
relationships
Apply geometric concepts and formulas
Unit Focus/Foci
Reflecting on the Quarter
Instructional Focus/Foci
Evaluating Oneself With Respect to the Course
Materials
Educational Strategies/Instructional Procedures
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?
Integration with Core Subject(s)
LA:Understand explicit, factual information
Understand the meaning of words in context
SS: Distinguish fact from opinion and relevant from irrelevant information
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Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation:
Technology:
Assessment
Homework
Prepare copies of Classifying Triangles.
Teacher Notes