high school geometry days 025040

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STRUCTURED CURRICULUM LESSON PLAN

Day: 025 Subject: Geometry Grade Level: High School

Correlations (SG,CAS,CFS): 6C1,2; 8B2; 9A1; 9B2

TAP:Choose and apply appropriate operational

procedures and problem-solving strategies toreal-world situations

Understand geometric properties andrelationships; apply geometric concepts andformulas

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

ISAT:Understand and apply geometric concepts and

relationshipsUse mathematical skills to estimate,

approximate, and predict outcomes and tojudge reasonableness of results

Understand and use methods of data collectionand analysis, including tables, charts, andcomparisons

Unit Focus/Foci

Reasoning and Proof

Instructional Focus/Foci

Introducing Deductive Reasoning

Materials

PBS Video: Agatha Christie or Sir Arthur Conan Doyle ( Sherlock Holmes)

Educational Strategies/Instructional Procedures

Have the students view the video and take notes.

Collect the book selections from the students.

Integration with Core Subject(s)

LA: Understand explicit, factual informationUnderstand the meaning of words in context

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

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Connection(s)

Enrichment: On Sunday morning you notice Otto the snail climbing up a 9-foot fence.Everyday the snail would crawl 30 inches up the fence. However, when Otto slept at night, heslipped down 12 inches. On what day will Otto reach the top of the fence?(Solution: Friday)

Fine Arts: Have students write a short story using deductive reasoning.

Home: Have the students discuss with family members the book selected.

Remediation: Teachers Half Dozen

Technology: Have the students research their favorite author on the Internet.

Assessment

Teacher observation

Homework

Have the students make a list of the movies and television programs they view where deductivereasoning is used, and give at least three examples.

Teacher Notes

Remind the students that the movie and the book may differ.Prepare copies of the Book Review Format.

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





Unit Focus/Foci

Reasoning and Proof


Introducing Deductive Reasoning

Materials

Chart paperMarkersCopies of the Book Review Format


Have the students solve the following problem: Karen, Marcia, Candy, and Kelly each have afavorite sport: basketball, tennis, bowling, and swimming, respectively Karens brothersfavorite sport is basketball. Candy and Kelly do not like swimming. Marcias favorite sport istennis. Kelly no longer likes bowling. What is Karens favorite sport?

Answer: Swimming

Discuss the movie stressing the usage of deductive reasoning.

Distribute the Book Review Format.

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SC: Apply scientific method to solve problems

Connection(s)

Enrichment: Have students write a short story using deductive reasoning.

Fine Arts:

Home: Have the students play the game Clue, if available, with family members.


Technology:

Assessment

Teacher observation

Homework

Have the students begin reading their novels.

Teacher Notes

Make copies of the Tower of Hanoi Activity.

97












Unit Focus/Foci

Connecting Reasoning to Proof


Make Conjectures Based on Inductive Reasoning

Materials

Copies of Tower of Hanoi Activity


Have the students complete the following: A farmer buys 100 animals consisting of chicken,pigs, and goats for $100. If chickens are 75 each, pigs are $2.50 each, and goats are $3 each,how many of each does he buy?

Solution: 1 goat, 13 pigs, 86 chickens or 8 goats, 4 pigs, 88 chickens.

Tell students the legend of the Tower of Hanoi:

In ancient India, the monks in a temple were given a stack of 64 sacred gold dishes. Each dishwas slightly smaller than the one beneath it. Their assignment was to place the dish on the altarwhere a larger dish could never be placed on top of a smaller one. The dishes were fragile andcould only be moved one at a time. The monks worked day and night on the task. The legendsays that when the final move is made, the temple would crumble and the world will end.

Have the students complete the Tower of Hanoi Activity.

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LA: Understand explicit, factual informationSC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment: Have students create their own Tower of Hanoi.

Fine Arts: See Enrichment and Home.

Home: Have the students play the Tower of Hanoi game with family members.


Technology: Have the students play the Tower of Hanoi on the computer athttp://www.math.toronto.edu/mathnet/games/towers

Assessment

Homework

Teacher Notes

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TOWER OF HANOI GUIDELINES

1. Students will work in pairs.

2. Each pair of students will cut out five disks.

3. Each pair of students should record their results in the chart provided.

4. Students will form groups of four and answer questions.

5. Each group will present their solution to the class.

Carefully cut out the following circles

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Correlations (SG,CAS,CFS): 6C1,2; 9A1; 9B2

TAP:Understand geometric properties and

relationships; apply geometric concepts andformulas



relationshipsUnderstand and use methods of data collection

and analysis, including tables, charts, andcomparisons

Unit Focus/Foci

Connecting Reasoning and Proof


Making Conjectures Based on Inductive Reasoning

Materials


Ask the students to give a definition of conjecture, counter example, and inductive reasoning.Discuss their definitions before providing the following:

Conjecture--An educated guess based on little evidence. A conjecture may or may not be true.

Counter example--An example that shows a statement is not always true.

Inductive reasoning--Making a conjecture based on pattern of specific examples on past events.

Model the process of testing a conjecture by using:

Dr. Mac discovered a new bacteria that doubles in quantity every hour. At midnight, shediscovered that the jar in which they were kept was full. At what time was the jar half-full?

Solution: 11:00 p.m.

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Use the flow chart to test the following conjecture:

1. If you go to California, you will see the Pacific Ocean.2. All triangles have their sides.3. Lines that intersect are perpendicular.4. The square of any real number is positive.

Solutions:

1. False--A counter example is Bakersfield, Ca. It is not near the coast.2. True3. False--A counter example is a linear pair of 100 and 804. False--A counter example is 02 = 0.

Remind students to check the wording of their conjecture.

Example 1:

All birds can fly--false, a counter example is a turkey.

Example 2:

Some birds can fly--true

Is everyexample aninstance of theconjecture?

Is thespecifictrue?

Observe apattern

Make a conjectureabout the pattern

Examine thespecifics carefully

Test it out witha variety of

conjectureis true

Conjectureis false

yes

no

You have found acounter example

Conjecture istrue

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Example 3:

No birds can fly--false; a counter example is a robin.

Have the students complete the Tower of Hanoi Activity.


LA: Understand explicit, factual informationSC: Apply scientific method to solve problems

Connection(s)

Enrichment: Have the students find examples of conjectures in newspapers or magazines.

Fine Arts: Have the students write ten statements they hear in a 24-hour period, using the termsall, some, or none.

Home: See Enrichment and Fine Arts.

Remediation: Review finding counter examples with the students.

Technology: Write a program for the graphing calculator to calculate the number of moves ittakes to move n disks for the Tower of Hanoi.

Assessment

Teacher observation. Assess students understanding through reading, writing, speaking, andmodeling.

Homework

Assign appropriate problems from your text.

Teacher Notes

Tell the students there will be a quiz. Remind students to note the wording of their conjectures.A statement must always be true or it is false.

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Correlations (SG,CAS,CFS): 6C1; 8B2; 9B; 10A



Understand number systemsUnderstand geometric properties and






Unit Focus/Foci

Connecting Reasoning and Proofs


Writing a Statement in If-Then Form

Materials


Review last nights homework.

Have the students complete the following analogies:

1. Add: Sum as divide: ________2. Polygon: Perimeter as circle: ________3. Weight: Scale as air pressure: ________4. Botany: Biology as Geometry: ________5. Inch: Foot as ounce: _______

Solutions:

1. Quotient2. Circumference3. Barometer4. Mathematics

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5. Pound

Have the students work in pairs to explain what the numbers 1-7 represent.

Randomly select pairs to present their explanations to the class.

Solutions:

1. Soft Drinks Only 5. Soft Drinks, Milk or Water2. Soft Drinks or Water 6. Water or Milk3. Water Only 7. Milk Only4. Soft Drinks or Milk

Explain to students that this is called circle logic.

Introduce the term Venn diagram, and present the definition as follows:Venn diagrams are diagrams that use circles or ovals inside a rectangle to show relationships ofsets.

A Venn diagram can be useful in explaining conditional statements. A Venn diagram uses circlelogic.

Consider the statement: The salesman was in Chicago only on Saturday. To make a Venndiagram of this statement, draw a large circle to represent days on which the salesman was inChicago. Since Saturday is the only day that he was in Chicago, the smaller circle is called asubset of Saturday.

Soft Drinks

4 5 6

1 2 3

7

Water

Milk

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Saturdays Days The Salesman Was in Chicago

The Venn diagram can also explain how to write the given statement in if-then form.

If the salesman was in Chicago, then it was Saturday. Have the students complete the followingexamples. Allow 15 minutes for completion.For each statement, draw a Venn diagram and write the sentence in if-then form.

1. Every dog has a tail.2. All rational numbers are real.3. People who live in Idaho grow potatoes.4. Employees are allowed in the lounge.

Discuss the examples with the class.

Have students note that every statement written in if-then form is not true.




Connection(s)

Enrichment: Find at least three things that belong in region 2 (lungs, 4 chamber heart, suckletheir young, live birth, communication).

Man Dolphin1 3

2 Arm Fin Legs Tail Toes Blowhole

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Fine Arts:

Home: Have parents sign the assignment sheet. Have students and family members visit thedolphin show at the Shedd Aquarium or Brookfield Zoo.


Technology: Have students look up dolphins on the Internet.

Assessment

Teacher observation and student responses

Homework


Teacher Notes

Explain to students that various forms of logical reasoning will be explained throughout the unit.

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Unit Focus/Foci



Using Conditional Statements

Materials

Copies of Vertical Angles ActivityRulerProtractor


The five Jackson children must clean the living room, family room, kitchen, bathroom, and onebedroom.

1. Marlon dislikes cleaning sinks.2. Tito refuses to make beds.3. Michael and Germaine find money under the cushions when they clean.4. The family room is next to the kitchen. Jackie and Germaine sing 2-part harmony while they

work.

Which room does each child clean?

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Solution:

Marlon--Bedroom MichaelLiving room Tito--BathroomGermaine--Family room Jackie--Kitchen

Have the students work on Vertical Angles Activity. Allow 15 minutes.

Randomly select two pairs to present their conjectures to the class. The students have discoveredthat the vertical angles are congruent.

Have the students write their conjecture as an if-then statement. Explain to students that this iscalled a conditional statement. The if is called a conditional statement. The if is called thehypothesis, and the then is called the conclusion. (p q)

If two lines intersect, then the vertical angles formed are congruent.

If we exchange the hypothesis and conclusion of an if-then statement, the new statement is calledthe converse (q p).

If the vertical angles formed are congruent, then two lines intersect. Have students note that theconverse of a true statement may not be true.

Review these examples:

Example 1: Find the number of angles formed by 10 distinct lines with a common intersection point. (20)

Example 2: If a vehicle is a car, then it has four wheels is a true conditional statement. A sedan is a car. Use the Law of Detachment to reach a valid conclusion. (A sedan has four wheels.)

Have the students work in pairs. Have each student write a true if-then statement on a sheet ofpaper. Have the students exchange papers, write the converse of the statement they are given,and tell if it is true or false. Select some examples for class discussion.


LA: Understand explicit, factual information Understand the meaning of words in contextSC: Apply scientific method to solve problems

Connection(s)

Enrichment: Have students find two examples of Venn diagrams in newspapers or magazinesand explain each section.

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Fine Arts:

Home: Have the students make a Venn diagram of 3 rooms of their home describing theircontents.

Remediation: See Home.

Technology: Have students create Venn diagrams using a computer drawing program.

Assessment

Teacher observation

Homework


Teacher Notes

Remind students to study for tomorrows quiz.Prepare copies of Deductive Reasoning Quiz.

111

VERTICAL ANGLES ACTIVITY

Guidelines

1. Students will work in pairs.

2. Partners must agree on all measurements.

3. Report your conjecture to the class.

Activity

Draw in the space provided four different pairs of intersecting lines. Number the angles 1, 2, 3,and 4. Use a protractor to measure each angle.

1.

m1 = m3 =m2 = m4 =

3.

m1 = m3 =m2 = m4 =

2.

m1 = m3 =m2 = m4 =

4.

m1 = m3 =m2 = m4 =

What is the relationship between 1, 2, 3, and 4? Make a conjecture.

112












Unit Focus/Foci



Applying Deductive Reasoning

Materials

Copies of Deductive Reasoning Quiz


Review the homework and answer student questions.

Have the students complete the Deductive Reasoning Quiz.

Have the students work in cooperative groups of four to complete the following:

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Marva, Rhonda, Jackie, Lewis, Bob, Tom, andRita formed a study group.

a) Rhonda sits to the right of Marva.b) Jackie sits between Lewis and Rita.c) Bob sits next to Lewis.d) Tom sits next to Bob, but not next to Rhonda.

Who sits in each seat?

Solution:




Connection(s)

Enrichment: Have the students find 3 television commercials that use conditional statements.

Fine Arts: Have students create a commercial for Euclid to sell geometry to the people.

Home: See Enrichment and Fine Arts.


Technology:

Tom

Bob Lewis Jackie

Marva Rhonda

Rit

a

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Assessment

Evaluate student quizzes using the Structured Curriculum Scoring Rubric.

Homework

Assign from your text appropriate problems on properties of equality.

Teacher Notes

Solutions to Deductive Reasoning Quiz:

Hypothesis-italicizedConclusion-bolded

1. a) If two angles have the same measure, then the angles are congruent.b) If the angles are congruent, the two angles have the same measure.

2. a) An angle is obtuse if its measure is greater than 90.b) If an angle is obtuse, then its measure is greater than 90.

3. a) If two angles are supplementary, then the sum of their measures is 180.b) If the sum of their measures is 180, then the angles are supplementary.

4. a) Students taking geometry onlyb) Students taking geometry and chemistryc) Students taking chemistry onlyd) Students taking geometry and Spanishe) Students taking geometry, chemistry, and Spanishf) Students taking chemistry and Spanishg) Students taking Spanish only

5. a)

b) If Denise goes to the movies, then it is Sunday.

Sundays

DaysDenisegoes to

the movies

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Deductive Reasoning Quiz

For each statement below:

a) Underline the hypothesis of each statement once and the conclusion twice.b) Write the converse of each statement.

1. If two angles have the same measure, then the angles are congruent.

2. An angle is obtuse if its measure is greater than 90.

3. If two angles are supplementary, then the sum of their measures is 180.

4. Describe what each region represents.

Draw a Venn diagram and translate the statement to if-then form.

5. Denise goes to the movies only on Sundays.

Geometry Chemistry

A B C

D E F

G

Spanish

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Correlations (SG,CAS,CFS): 6C1,2; 9B2; 10A






ISAT:Solve problems requiring computations with

whole numbers, fractions, decimals, ratios,percents, and proportions

Understand and apply geometric concepts andrelationships


Unit Focus/Foci




Materials

Copies of Detachment and Syllogism Worksheet


Have the students solve the following:

Mrs. Browns math class has 25 students. Surveying the class to see who participates in sports,she discovered 4 students on the swim team, 13 students on the track team, and 5 students whodid both. How many students do not participate in either activity?

Solution: 8

Review conditional statements with the class.

p hypothesis (if clause)q conclusion (then clause) implies therefore

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~ negation (not)

Have students note that every conditional statement can be written in the form:

p q

Explain to students that there are two kinds of logical reasoning that use conditional statements:

1. Law of Detachment--If p q is a true statement and p is true, then q is true.

p q If two numbers are odd, then their sum is even.

2. Law of Syllogism--If p q and q r are true conditional statements, then p q is alsotrue. (Similar to the transitive property of equality).

p q If the moon is full, the werewolf will appear.q r If the werewolf appears, the villagers will hide.p r If the moon is full, the villagers will hide.

The Law of Detachment and the Law of Syllogism can be used to help make logical conclusions.Remind students that if a counter example can be found, the conclusion is invalid.

Have the students work in pairs to complete Detachment and Syllogism Worksheet. Discuss theresults.


LA: Understand explicit, factual information Understand the meaning of words in contextSC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment: Have the students survey lawyers asking:1. Did you take geometry in high school?2. Was it useful in law school?3. Is it useful in law school?

Fine Arts: Have students write an essay on how logic is used in all walks of life.

Home: Have the students watch Court TV and determine if the judges are using the Law ofDetachment or Law of Syllogism and cite examples.


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Technology: Have the students find a famous court case on the Internet and explore the logicalarguments.

Assessment

Teacher observation

Homework


Teacher Notes

Solutions to Detachment and Syllogism Worksheet:

1. Law of Detachment2. Law of Detachment3. Law of Syllogism4. Law of Detachment5. Bobby Jones is 16 years of age or older--Syllogism6. XYZ is an isosceles triangle--Detachment7. A = 180--Detachment8. All squares are quadrilaterals--Syllogism9. No triangle is a square--Syllogism10. BC bisects ACD

119

Detachment and Syllogism Worksheet

Determine whether the conclusion was reached using the Law of Detachment or the Law ofSyllogism.

1. a) If an angle is acute, then its measure is less than 90.b) m A is acute A is less than 90

2. a) If an angle is obtuse, then it is not right.b) ABC is obtuse ABC is not right

3. a) If two angles have the same measure, then they are congruent.b) If two angles are vertical, then they have the same measure. vertical angles are congruent

4. a) In a right triangle, one angle is a right angle.b) ABC is a right triangle ABC has a right triangle

Deduce a conclusion for each of the following. State whether the conclusion is a detachment orsyllogism.

5. a) All licensed drivers in the state of Illinois must be 16 years of age or olderb) Bobby Jones has an Illinois drivers license ____________________________________

6. a) A triangle with two congruent sides is an isosceles triangleb) XYZ has two congruent sides ____________________________________

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7. a) All straight angles contain 180b) A = is a straight angle ____________________________________

8. a) All squares are rectanglesb) All rectangles are quadrilaterals ____________________________________

9. a) All triangles have three sidesb) No three-sided figures are squares ____________________________________

10. a) The bisector of an angle divides the angle into two congruent anglesb) BC divides ACD into two congruent angles ____________________________________

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Correlations (SG,CAS,CFS): 6C1,2; 8B2; 9B; 10A

TAP:Understand geometric concepts and formulasAnalyze and interpret data presented in charts,

graphs, tables, and other displays




Unit Focus/Foci



Using Properties of Equality in Algebraic and Geometric Proofs

Materials

Copies of Properties QuizCopies of Applying Properties Worksheet #1


Have students solve the following:

Mary made the announcement that she and four other students from Brand New High Schoolwon athletic scholarships to the University of Big Dreams. Each plays a different sport. Edwarddoes not swim. None of the girls run track. Neither Anne nor Charles plays soccer. John is thecaptain of the Brand New High School basketball team. One of the girls is captain of the soccerteam.

Solution:

John--BasketballMary--SoccerAnne--TennisEdward--TrackCharles--Swimming

Review the algebraic properties and give students an example of each property.

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Example 1:Addition Property: 4 = 3+1, 4+3 = (3+1)+3

Example 2:Distributive Property: 5(4)+7(4) = 4(5+7)

Have the students complete in pairs the Applying Properties Worksheet #1. Allow 15-20-minutes for completion. Remind the students that each pair should agree on the final answer foreach problem. Have two pairs report their answers to the class (assign one problem for eachgroup).

Administer the Properties Quiz.




Connection(s)

Enrichment:

Fine Arts:

Home: Have parents sign homework.

Remediation: Teachers Half Dozen and have the students solve simple equations and writedirections to be followed by a classmate.

Technology:

Assessment

Evaluate the Properties Quiz using the Structured Curriculum Scoring Rubric.

Homework


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Teacher Notes

Solutions to Properties Quiz:

Property1. Reflexive For every number a, a = a.2. Symmetric Property If a = b, then b = a3. MultiplicativeProperty

If a = b, then ac = bc.

4. Addition Property If a = b, then a + c = b + c5. Transitive Property If a = b and b = c, then a = c.6. Division Property

If a = b and c 0, then a

c =

b

c.

7. Distributive Property For all numbers a, b, and c, a (b+c) = ab+ac.8. Substitution For all numbers a and b, if a = b, then a may replace b in any equation

or expression.9. Additive Inverse a + (-a) = 010. CommutativeProperty of Addition a + b = b + a

Solutions to Applying Properties Worksheet #1:

1. Distributive property 2. Substitution property of equality

3. Division property of equality 4. Subtraction property of equality

5. Substitution property of equality 6. Reflexive property

7. Transitive property of equality 8. Substitution property of equality

9. Division property of equality 10. a. Addition propertyb. Substitution property of equalityc. Subtraction property of equality

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Properties Quiz

Complete the table.

Property1.

For every number a, a = a.2. Symmetric Property

3.If a = b, then ac = bc.

4. Addition Property

5.If a = b and b = c, then a = c.

6.

If a = b and c 0, then a

c =

b

c.

7.For all numbers a, b, and c, a (b+c) = ab+ac.

8.For all numbers a and b, if a = b, then a may replace b in

any equation or expression.9.

a + (-a) = 010. CommutativeProperty of Addition

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Applying Properties Worksheet #1

Give a reason for each statement.

1. If 2(x - 3) = 8, then 2x 6 = 8

2. If x = 10, then 14 x = 4

3. If B is the midpoint of AC, then AB = BC.

4. If AD AB = PQ AB, then AD = PQ.

5. If 1 + 2 = 180 and 2 = 3, then 1 + 3 = 180

6. mABC = mABC

7. If AB = DE and DE = GH, then AB = GH

8. If MH + JK = 14 and MH = 7, then 7 + JK = 14

9. If 2 A = 90, then A = 45

10.

a. x + y = 180b. x + 70 = 180c. x = 110

70y = x

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Correlations (SG,CAS,CFS): 6C1,2; 8B2




relationships

Unit Focus/Foci



Completing Proofs Involving Segment Theorems

Materials



Assuming that the following are true statements, find the value of a, b, c, and d.

14

22

0

3 4

4 4

.

.

.

.

db c

ab

c b a

b

=

+ =

=

=

Solution:

a = -12, b = 4, c = -2, d = 8

Review the homework assignment and answer students questions.

Discuss the five essential parts of a proof:

1. State the problem2. List the given information

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3. Draw a diagram4. State what is to be proven5. Give a logical arrangement of statements and their reason

Give the students an example of a two-column algebraic and geometric proof and model for themhow the five parts are applied.

Traditionally each problem has this layout:

1. State the problem2. Given:

3. Diagram 4. Prove

5.Statements Reasons

1.2.3.4.

1.2.3.4.

Model an algebraic proof for the students. Explain to students that in an if-then statement, thehypothesis is the given information and the then is to be proven.

Example 1:

If 3(a + 1) = 7a 9, then a = 3

Given: 3(a + 1) = 7a 9Prove: a = 3

Statements Reasons

1. 3(a + 1) = 7a 92. 3a + 3 = 7a 93. 3 = 4a - 94. 12 = 4a5. 3 = a6. a = 3

1. Given2. Distributive property3. Distributive property of equality4. Addition property of equality5. Division property of equality6. Symmetric property

Diagramnot

needed

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Example 2:

If two lines intersect, then the vertical angles formed are congruent.

Given: AD EC Bintersects at .

Prove: 1 3

Statements Reasons

1. AD EC Bintersects at .2. 1 and 2 are a linear pair3. 1+ 2 = 1804. 2 3and are a linear pair5. 2 3+ = 1806. 1 2 2 3+ = +7. 1 3=

1. Given2. Definition of linear pair3. Definition of supplementary angles4. Definition of linear pair5. Definition of supplementary angles6. Substitution property7. Subtraction property

Have the students complete a simple two-column proof (teachers choice) and monitor theirprogress.



Connection(s)

Enrichment:

Fine Arts:

Home:


Technology:

A C

DE

B 34

21

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Assessment

Teacher observation

Homework

Assign from your text appropriate problems on completing two-column proofs.

Teacher Notes

130



Correlations (SG,CAS,CFS): 6A1; 6C1,2; 8B2; 9B2




relationships

Unit Focus/Foci



Completing Proofs Involving Segment Theorems

Materials

Copies of Applying Properties Worksheet #2



Bob, Bern, and Bernice received degrees in Education, Engineering, and Ecology. Find thedegree and correct age of each person.

1. Bob does not like children.2. Bern is not 25 years old, but her friend is.3. The engineer is not 30 years old.4. Bern always wanted to work with children, and Bob is 30 years old.

Solution:

Name Degree AgeBob Ecology 30Bern Education 22

Bernice Engineering 25

Review last nights homework.

Have students complete the Applying Properties Worksheet #2.

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Note: Have two students explain how they used the five parts of a proof to complete theassignment.



Connection(s)

Enrichment: Have students write an essay comparing inductive and deductive reasoning.

Fine Arts:

Home: Have parents sign assignment sheet.


Technology:

Assessment

Evaluate the Applying Properties Worksheet #2 using the Structured Curriculum Scoring Rubric.

Homework

Assign from your text appropriate problems on proofs.

Teacher Notes

Solutions to Applying Properties Worksheet #2:

1. a. Givenb. Addition property of equalityc. Substitution property of equalityd. Multiplication property of equality

2. a. Givenb. Substitution property of equalityc. Substitution property of equalityd. Substitution property of equality

3. See student work 4. See student work

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Applying Properties Worksheet #2

Name the property that justifies each statement.

Given: 2

35

1

32x x+ =

Prove: x = -2

1. If 2

35

1

32x x+ = , then x = -2

Statements Reasons

a. 2

35

1

32x x+ =

a.

b. 22

35

1

3x x+ + =

b.

c. 8

3

16

3x =

c.

d. x = -2 d.

2. If MO = PR and MN = PQ, then NO = QR

M N O

P Q R

Given: MO = PR and MN = PQ

Prove: NO = QR

Statements Reasons

a. MO = PRMN = PQ

a.

b. MN + NO = NOPQ + QR = PR

b.

c. MN + NO = PQ + QR c.

d. NO = QR d.

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Complete a proof for each of the following:

3. If AB = BC, AB = 3x + 7 and BC = 5x 11, then x = 9

Given:

Prove:

Statements Reasons

4. If ABC = DBE, prove ABD = CBE

Given:

Prove:

Statements Reasons

AC

D

EB

1 23

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Correlations (SG,CAS,CFS): 6C1,2; 8B2; 9B2

TAP:Perform arithmetic operations involving

integers, fractions, decimals, and percentsexplicitly stated or within context

Choose and apply appropriate operationalprocedures and problem-solving strategies toreal-world situations


Demonstrate understanding of measurementconcepts and apply measurement skills




Demonstrate an understanding of measurementconcepts and skills

Unit Focus/Foci



Exploring Angle Relationships

Materials

Copies of Exploring Angles Worksheet



Johns Auto Body Shop painted 324 cars last year. One-ninth of the cars were painted red. Theypainted 4 cars black for every red one, and for every 3 black cars, 2 were painted white. Two-thirds of the remaining cars were blue and the rest green. How many cars are painted in eachcolor?

Solution:

Red Black White Blue Green36 144 96 32 16

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Review the angles and angle relationships discussed in Unit Two.

acute an angle whose measure is less than 90

obtuse an angle whose measure is greater than 180

adjacent two angles that share a common side and a common vertex

right an angle whose measure is 90

complementary two adjacent angles whose non-common sides are opposite rays

straight an angle whose measure is 180

supplementary two angles whose sum is 180

linear pair two adjacent angles whose non-common sides are opposite rays

Have students complete the Exploring Angles Worksheet.



Connection(s)

Enrichment: Have the students write a report on how the ancient Egyptians measured angles.

Fine Arts: See Enrichment.


1 2

1 2

1 2

1 2

1 2

136


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

Assessment

Evaluate the Exploring Angles Worksheet using the Structured Curriculum Scoring Rubric.

Homework


Teacher Notes

Solutions to Exploring Angles Worksheet:

1 3a. adjacent a. alwaysb. verticalsupplementary

b. sometimes

c. complementary c. sometimesd. vertical d. sometimese. supplementary e. alwaysf. linear pairadjacentsupplementary

f. always

g. adjacent2

a. 1 = 110 2 = 70 3 = 110b. 4 = 80 5 = 52 6 = 52 7 = 483. a. alwaysb. sometimesc. sometimesd. sometimese. alwaysf. always

137

Exploring Angles Worksheet

1. State the relationship between 1 and 2

a. b. c.

d.

1 2

e.

1 = 20 160 = 2

f. g.

2. Find the measure of each numbered angle.

a. b.

3. Answer each of the following always, sometimes, or never.a. Complementary angles are acuteb. Supplementary angles are adjacentc. Adjacent angles form a linear paird. Supplementary angles are righte. Complements of the same angle are congruentf. Supplements of congruent angles are congruent

1 270 3

48 4 5 6 7

80

1 2

C

1

2

12

1 2 3

M

D 21

138




TAP:Perform arithmetic operations involving

integers, fractions, decimals and percentsexplicitly stated or within context





Unit Focus/Foci



Completing Proofs Involving Angle Theorems

Materials

Copies of Angle Relationships WorksheetChart paperMarkers


Have the students complete the Angle Relationships Worksheet. Allow 10-15 minutes forcompletion.

Have the students write a paragraph on Verifying Angle Relationships. Choose three studentsto read their paragraphs aloud.

Have the students work in groups of four. Have each group create a poster illustrating anglerelationships.

Monitor the class, offering assistance when needed.

139



Connection(s)

Enrichment:

Fine Arts:



Technology:

Assessment

Teacher observation as the students work on the examples

Homework


Teacher Notes

Inform the students that the Unit Assessment will be given within the next two days.

Solutions to Angle Relationships Worksheet:

A.1. Given2. Given3. Definition of perpendicular lines4. Definition of right angles5. Substitution property6. Transitive property7. Substitution property

B.1. Given2. Definition of supplementary angles3. Definition of supplementary angles4. Substitution property5. Subtraction property of equality

140

Angle Relationships Worksheet

Complete the following proofs:

A. Given: AB BC m 2 = m 1

Prove: m 1 + m 3 = 90

Statements Reasons

1. AB BC 1.2. m 2 = m 1 2.3. ABC is a right triangle 3.4. m ABC = 90 4.5. m ABC = m 2 + m 3 5.6. m 2 + m 3 = 90 6.7. m 1 + m 3 = 90 7.

B. Given: 1 and 2 form a linear pair andm 2 + m 3 + m 4 = 180

Prove: m 1 = m 3 + m 4

Statements Reasons

1. 1 and 2 form a linear pairm 2 + m 3 + m 4 = 180

1.

2. 1 and 2 are supplementary angles 2.3. m 1 + m 2 = 180 3.4. m 1 + m 2 = m 2 + m 3 + m 4 4.5. m 1 = m 3 + m 4 5.

A

B

D

C

E3 2

1

141











Unit Focus/Foci



Reviewing Unit Two

Materials


Review the homework assignment and answer students questions.

Select a review format from Appendix D.



Connection(s)

Enrichment:

Fine Arts:.


142


Technology:

Assessment

Teacher observation

Homework

Study for the exam.

Teacher Notes

Prepare copies of the Unit Two Assessment.Collect the book reviews.

143










Unit Focus/Foci



Assessing Unit Two

Materials

Copies of Unit Two Assessment


Administer the Unit Two Assessment


LA: Understand explicit, factual information Understand the meaning of words in contextSC: Apply scientific method to solve problemsSS: Distinguish fact from opinion and relevant from irrelevant information

Connection(s)

Enrichment:

Fine Arts:.

Home: Have parents proofread book reviews.

Remediation:

144

Technology:

Assessment

Evaluate the Unit Two Assessment

Homework

Proofread book reviews for class tomorrow.

Teacher Notes

Solutions to Unit Two Assessment:

1. Odd numbers less than 10 are prime. Counterexample :9 and 1 are an odd number less than10 that are not prime.

2. If the third angle of a triangle is 90, then the two remaining angles are complementary.3. If they are collinear, three points lie on a plane. False. Counter example: Three points that

lie in a plane that are not collinear.

4. Addition property of equality5. Reflexive property6. Substitution property7. 2 = 1558. 2 = (190 5x) 9. Induction--making conjectures from general observations

Deduction--making general observations from specific conclusions10. Given: 1 4

Prove: 2 3

Statements Reasons

1. 1 4 1. Given2. 1 and 2 are vertical angles 3 and 4 are vertical angles

2. Definition of vertical angles

3. 1 2 3 4

3. Vertical angles are congruent

4. 2 3 4. Substitution

B CA

145

Unit Two Assessment

Write the converse of each conditional statement. If the statement is false, give a counterexample.

1. If an odd number is less than 10, then the number is prime.

2. If two angles of a triangle are complementary, then the third angle is 90.

3. If three points lie in a plane, then they are collinear.

Name the property that satisfies each statement.

4. If AB = MN, then AB + GH = MN + GH

5. A = A

6. If B + C = 90 and B = 70, then 70 + C = 90

Find the measure of 2 .

7.

8.

9. Explain the difference between inductive and deductive reasoning.

13x + 7

2x + 19

(5x - 10) 2

146

10. Complete the proof.

Given: 1 4Prove: 2 3

Statements Reasons

2 31 4

147










Unit Focus/Foci




Materials

Chart paperMarkers


Return the Unit Two Assessment.

Discuss and collect the student book reviews. Have the students work in groups of four to createa poster illustrating each authors use of deductive reasoning.



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

Connection(s)

Enrichment:

Fine Arts:

148

Home:

Remediation:

Technology:

Assessment

Evaluate students book reviews.

Homework

Assign from your text appropriate readings on parallel and perpendicular lines.

Teacher Notes

high school geometry days 025040

Documents

book selections

graphs tables

geometry grade level

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