Week 14­ Truth Tables.notebook
November 18, 2013
WHAT IS THE ESSENTIAL QUESTION?
Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question
Week 14, Lesson 1
1. Warm­up
2. Notes ­ Truth Tables
Inclusive Disjunctions
3. ICA ­ Are They Equivalent?
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Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up
Warm Up: Copy and complete the truth table for 1
Week 14­ Truth Tables.notebook
November 18, 2013
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Inclusive Disjunction
Inclusive Disjunctions – little or, symbol ∨, are logic statements with a value of true provided at least one statement is true. **If both statements are true, the inclusive Disjunction is still true.**
Example: p: I eat cake q: I eat ice cream
Translate the following into words, then complete the truth table:
p∨q
p∨q:
Summary:
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Week 14­ Truth Tables.notebook
November 18, 2013
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Negated Conjunction Truth Tables
The truth tables will change when negating one of the simple statements
i.e.­
Summary:
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ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity
Week 14­ Truth Tables.notebook
November 18, 2013
ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity
Are the Compound Statements Equivalent? Use 3 truth tables to determine whether they have the same truth values.
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Week 14­ Truth Tables.notebook
November 18, 2013
How can we visually negate a statement?
Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question
Week 13, Lesson 2
1. Warm­up
2. Notes­ Truth Tables
Negation
3. ICA­ Matching 77
Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up Warm­up
Warm Up: Write an example of a true statement. Then write an example of a false statement. Share these with a neighbor. See if they know which is true or false.
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Week 14­ Truth Tables.notebook
November 18, 2013
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Statements and Negation
In logic, we use symbols to represent statements
p represents the 1st statement
p
q represents the 2nd statement
q
r represents the 3rd statement
r
If you are using p and q and r, then you must use the connective symbols
Example 1­
p: It is raining outside
q: The streets are wet
Write out the following­ The streets are wet
It is raining outside
The streets are wet
Negations­
It is raining outside
The negation of a statement p is written This is pronounced "not p"
This DOES NOT mean opposite
i.e.­ p: It is raining outside
Therefore, would say "It is NOT raining outside"
Negations are very similar to compliments
Example 2­
Write the negations of the following statements
p:
John is a student counsel member
q:
ABCD is a parallelogram
r:
Barack Obama is the U.S. President
Summary:
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Week 14­ Truth Tables.notebook
November 18, 2013
Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes
Truth Tables
We can actually organize statements into organized tables
We call them truth tables
If a statement is true, what does that mean about the negation?
p
Example 3­
If a statement is false, what does that mean about the negation?
Identify if the two statements are negations. If they are not negations, give an explanation why
p:
q:
James is older than me
James is younger than me
r:
s:
Meghan has 2 sisters
Meghan does not have 2 sisters
Summary:
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ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity
Week 14­ Truth Tables.notebook
November 18, 2013
ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity
Match the statement with its negation
a)
a)
b)
b)
c)
c)
d)
d)
e)
e)
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Week 14­ Truth Tables.notebook
November 18, 2013
Lesson Plan: Week 1, Lesson 3
Content Objectives:
Determine the theoretical probability of events, estimate probabilities using experiments, and compare the results.
Use concepts and formulas of area to calculate geometric probabilities.
Determine the number of possible outcomes of an event.
Apply appropriate means of computing the number of possible arrangements of items using permutations where order matters, and combinations where order does not matter.
Apply the addition and multiplication principles of counting and represent these principles algebraically using factorial notation.
­ ­ ­ ­ ­ ­ ­ ­ ­ ­ Solve applied problems using the attributes of similar triangles.
Identify similar polygons.
Show that two triangles are similar using AA, SSS, and SAS Theorems.
Use the triangle proportionality and mid­segment theorem.
Solve problems using ratio and proportions.
­ ­ ­ ­ ­ ­ ­ ­ ­ ­ Know that after any of transformation (rotation, reflection, and translation), the shape still has the same size, area, angles and side lengths.
Know that if one shape can become another using rotation, reflection, and translation, then the two shapes are called congruent.
Understand that during transformation called a dilation, (enlargement or reduction), the shape becomes bigger
or smaller.
Dilation does not result in congruent shapes, the shapes will be similar. Same shape, yet different sizes are
similar shapes. Discover the line of reflection, the center of rotation, and the center of dilation.
­ ­ ­ ­ ­ ­ ­ ­ ­ ­ Understand that the term “solving the triangle” means that if we start with a right triangle and know any two sides, we can find or solve for the unknown side. Investigate the fundamental concepts behind trigonometry: three basic trig functions and how to determine
which trig function to use.
Know that recognizing special right triangles (30, 60 and 90) in geometry can help you to problem solve.
Use SOHCAHTOA to memorize the three main trigonometric functions.
­ ­ ­ ­ ­ ­ ­ ­ ­ ­ Identify and name parts of a circle
Find the circumference and area of circles
Use properties of tangents
Use properties of arcs and central angles; identify and name
Solve problems by applying the relationship between radii, diameters, chords, and tangents.
Determine measures of central and inscribed angles and their intercepted arcs.
­ ­ ­ ­ ­ ­ ­ ­ ­ ­ Identify how many vertices, sides, edges a polygon has.
Compare and contrast polygons two­dimensional figures.
Identify and classify polygons using manipulatives and create two­dimensional figures.
Identify and describe polygons (concave, convex, regular, pentagon, hexagon, n­gonal, circles and sector areas).
Identify and describe properties of a circle, kite, trapezoid, parallelogram, rectangle, square, and rhombus.
Use congruent relationships of two­dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference and areas.
Apply the interior and exterior angle sum of convex polygons to solve problems.
­ ­ ­ ­ ­ ­ ­ ­ ­ ­ Identify how many vertices, sides, edges, and/or faces of a three­dimensional figure.
Compare and contrast three­dimensional figures.
Use manipulatives to create three­dimensional figures
Apply surface area and volume formulas for prisms, pyramids, cylinders, cones and spheres.
Draw three­dimensional figures with appropriate labels and make a three­dimensional model from a net.
Draw, describe, and analyze solid geometry figures.
Language Objectives:
compare
discuss
explain
label
paraphrase
restate
classify
describe
experiment
justify
name
rephrase
compose
edit
identify
list
predict
rewrite
contrast
elaborate
interview
listen
present
state
Colored Pens
Index Cards
Scissors Tape
Compass
Navigator
Staplers
Tape Measure
define demonstrate
evaluate
investigate
match
present your point of view
summarize
Materials Needed:
Calculators
Graph Paper
Protractor Straws
Worksheet
Colored Pencils Hi­Lighters
Ruler
String
Yard Stick
Flash Light
Pattern Blocks
Staple Remover
Tangrams
Activities/Directions:
Closure:
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Week 14­ Truth Tables.notebook
November 18, 2013
WHAT IS THE ESSENTIAL QUESTION?
Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question
Week 13, Lesson 3
1. Warm­up
2. Notes­ Conjunction
3. ICA­ Is It True?
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Warm­up: Make up your own statement for p
Now negate that statement:
Now negate THAT statement:
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Week 14­ Truth Tables.notebook
November 18, 2013
Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes
Conjunction
Conjunction
­Conjunction is the connection of two simple statements using "and"
­This implies both simple statements at the same time
i.e.­ I ate pizza and I drank a Coke
Conjunction Truth Table
p:
q:
is only true when BOTH statements are true Summary:
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Week 14­ Truth Tables.notebook
November 18, 2013
Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes
Negated Conjunction Truth Tables
The truth tables will change when negating one of the simple statements
i.e.­
Summary:
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ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity
Week 14­ Truth Tables.notebook
November 18, 2013
ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity
Is It True?!
Construct the truth tables for the following. Make up your own statements for p, q, and r if needed
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Week 14­ Truth Tables.notebook
November 18, 2013
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