GEOMETRY; AGENDA; DAY 134; MON. APRIL . 02 , 2012 • Bell Ringer : See Power Point for question. • VOLUME of PYRAMIDS and CONES • Objective : Discover formulas for the volumes of pyramids and cones. • ACTIVITIES : Investigations 10.3; Examples A & B; Pg. 540 # 1 – 10; • HOME LEARNING : Pg. 542 # 17 - 21
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GEOMETRY; AGENDA; DAY 134; MON. APRIL. 02, 2012 Bell Ringer: See Power Point for question. VOLUME of PYRAMIDS and CONES Objective: Discover formulas for.
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GEOMETRY; AGENDA; DAY 134; MON. APRIL . 02, 2012
• Bell Ringer: See Power Point for question.• VOLUME of PYRAMIDS and CONES• Objective: Discover formulas for the volumes
of pyramids and cones.• ACTIVITIES: Investigations 10.3; Examples A &
• Bell Ringer: See Power Point for question.• THE 5 PLATONIC SOLIDS; { See Regentspreps}• Objective: Learn about the Platonic solids; • ACTIVITIES: Notes from online presentation.• HOME LEARNING: See worksheet on Killian
website, for instructions;
GEOMETRY; AGENDA; DAY 139; TUE. [APRIL . 10, 2012
• Bell Ringer: See Power Point for question.• Displacement and Density • Objective: Find volume of irregularly shaped
solids through displacement.• ACTIVITIES: Discuss examples A & B. Pg. 552
#1 - 8• HOME LEARNING: Pg. 553 3 10 – 16.
GEOMETRY; AGENDA; DAY 140; WED. [APRIL . 11, 2012
• Bell Ringer: See Power Point for question.• VOLUME OF A SPHERE• Objective: Apply volume formulas to
problems involving spheres of hemispheres.• ACTIVITIES: Discuss examples A & B. Pg. 559
#1 - 16• HOME LEARNING: Practice 10.6
GEOMETRY; AGENDA; DAY 141; THUR. [APRIL . 12, 2012
• Bell Ringer: See Power Point for question.• SURFACE AREA OF A SPHERE• Objective: Apply the surface areas formula to
solve problems.• ACTIVITIES: {Baseline Testing was done at
this time}; Discuss Pg. 559 #1 – 16 & Practice 10.6.; Pg. 563 5#1 - 10
• HOME LEARNING:Pg. 565 #14 – 19.
GEOMETRY; AGENDA; DAY 142; FRI. [APRIL . 13, 2012
• Bell Ringer: See Power Point for question.• FORMS OF VALID REASONING• Objective: Learn some symbols used in formal
logic. Use the forms of logical reasoning Modus Ponens and Modus Tollens.
• Bell Ringer: See Power Point for question.• REVIEW VOLUME PROBLEMS• Objective: Apply volume and surface area of
solids formula to solve problems• ACTIVITIES: Discuss Pg. 572 #1 – 12; Pg. 573
#13 – 21 (all)• HOME LEARNING: Pg. 579 #1 - 12
Related Conditionals
• People will often "twist words around" in an attempt to win an argument. In order to avoid becoming a victim of such tactics, you need to be aware of three new conditionals and their related truth values. Each of these new conditionals is formed by rearranging an original conditional statement.
• Remember that a "conditional statement" is a statementthat can be expressed in "if...then" form).
• The three new conditionals are:• CONVERSE, INVERSE, CONTRAPOSITIVE
Related Conditionals
• Before we begin, let's review some vocabulary:• hypothesis: This is the part of the sentence that
follows the word "If.... ,“conclusion: This is the part of the sentence that follows the word "then ... ." "If you are a surfer, then you like big waves."
• hypothesis: you are a surfer,• conclusion: you like big waves
The Converse
• The converse of a conditional statement is formed by interchanging the hypothesis and conclusion of the original statement.In other words, the parts of the sentence change places.The words "if" and "then" do not move.
• Conditional: "If the space shuttle was launched, then a cloud of smoke was seen."
• Converse: "If a cloud of smoke was seen, then the space shuttle was launched.“
The Inverse
• The inverse of a conditional statement is formed by negating the hypothesis and negating the conclusion of the original statement.In other words, the word "not" is added to both parts of the sentence.
• Conditional: "If you grew up in Alaska, then you have seen snow."
• Inverse: "If you did not grow up in Alaska, then you have not seen snow."
CONSIDER
• Conditional: "If you grew up in Alaska, then you have seen snow."Considering the climatic conditions in Alaska, this statement is true.
• Inverse: "If you did not grow up in Alaska, then you have not seen snow." Considering that there are other areas in the world that have snow (such as New York state), this statement is false.
CONSIDER
• Conditional: "If the space shuttle was launched, then a cloud of smoke was seen." This statement is true since the exhaust from the shuttle creates a cloud of smoke.
• Converse: "If a cloud of smoke was seen, then the space shuttle was launched." This statement is not always true since many other events (a fire, a running herd of buffalo, car exhaust, etc.) could have caused a cloud of smoke.
The Contrapositive
• The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. In other words, the contrapositive negates and switches the parts of the sentence. It does BOTH the jobs of the INVERSE and the CONVERSE.
• Conditional: "If 9 is an odd number, then 9 is divisible by 2." (true) (false)
• Contrapositive: "If 9 is not divisible by 2, then 9 is not an odd number." (true) (false)
• An important fact to remember about the contrapositive, is that it always has the SAME truth value as the original conditional statement.
REMEMBER!!!
• ** If the original statement is TRUE, the contrapositive is TRUE. If the original statement is FALSE, the contrapositive is FALSE.They are said to be logically equivalent.("equivalent" means "the same")
GEOMETRY; AGENDA; DAY 145; WED. [APRIL . 18, 2012
• Bell Ringer: See Power Point for question.• SIMILAR POLYGONS• Objective: Use the definition of similar
polygons to solve problems.• ACTIVITIES: Investigations 11.1.1 & 11.1.2;
Discuss Example on Pg. 584; Pg. 586 #7 – 15 (all)
• HOME LEARNING: Workbook 11.1
GEOMETRY; AGENDA; DAY 146; THUR. [APRIL . 19, 2012
• Bell Ringer: See Power Point for question.• SIMILAR TRIANGLES• Objective: Discover shortcut methods for
determining similar triangles.• ACTIVITIES: Investigations 11.2.1 & 11.2.2;
• Bell Ringer: See Power Point for question.• THE LAW OF SINES• Objective: Derive and apply the Law of Sines.• ACTIVITIES: Discuss Pg 657 # 1 – 17; Practice
workbook 12.3• HOME LEARNING: Practice 12.3
GEOMETRY; AGENDA; DAY 157; FRI. [MAY . 04, 2012]
• Bell Ringer: See Power Point for question.• THE LAW OF SINES• Objective: Derive and apply the Law of Sines.• ACTIVITIES: Discuss Practice 12.3; Test on
trigonometric ratios and Law of Sines.• HOME LEARNING: Practice 12.4
GEOMETRY; AGENDA; DAY 158; MON. [MAY . 07, 2012]
• Bell Ringer: See Power Point for question.• THE LAW OF SINES• Objective: Derive and apply the Law of Sines.• ACTIVITIES: Practice 12.4; Law of Sines.• HOME LEARNING:
GEOMETRY; AGENDA; DAY 159; TUE. [MAY . 08, 2012]
• Bell Ringer: See Power Point for question.• THE LAW OF SINES• Objective: Apply trigonometric ratios to solve