WHY DOES AN IMPLICATION TABLE HAVE THESE RESULTS?
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1 WHY DOES AN IMPLICATION TABLE HAVE THESE RESULTS? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 15, Lesson 1 1. Warm up 2. Notes Tautology Contradiction Implication 3. ICA Week 15 Review 87 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm Up: Construct a truth table for the following: and T T F F T F T F 1
2 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 Tautology and Contradiction Tautology A compound statement is called a tautology when the entire final column of a truth table is all true i.e. Contradiction A compound statement is called a contradiction when the entire final column of a truth table is all false i.e. Summary: 2
3 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 Implication Truth Table Argument A compound statement includes implication (if/then) is called an argument p is called the antecedent q is called the consequent i.e. p: you do that again q: I will call your parents Summary: 3
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7 WHAT IS THE ESSENTIAL QUESTION? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 15, Lesson 2 1. Warm up 2. Week 15 Assessment 89 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Given the statements p, q, and r, translate the compound statement. p: I drive the speed limit q: I obey traffic signals r: I get a ticket 7
8 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 mid segment 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 two dimensional figures. Identify and classify polygons using manipulatives and create two dimensional figures. Identify and describe polygons (concave, convex, regular, pentagon, hexagon, n gonal, circles and sector areas). Identify and describe properties of a circle, kite, trapezoid, parallelogram, rectangle, square, and rhombus. Use congruent relationships of two dimensional 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 three dimensional figure. Compare and contrast three dimensional figures. Use manipulatives to create three dimensional figures Apply surface area and volume formulas for prisms, pyramids, cylinders, cones and spheres. Draw three dimensional figures with appropriate labels and make a three dimensional model from a net. Draw, describe, and analyze solid geometry figures. Language Objectives: classify compare compose contrast define demonstrate describe discuss edit elaborate evaluate experiment explain identify interview investigate justify label list listen match name paraphrase predict present present your point of view rephrase restate rewrite state summarize Materials Needed: Calculators Colored Pencils Colored Pens Compass Flash Light Graph Paper Hi Lighters Index Cards Navigator Pattern Blocks Protractor Ruler Scissors Staplers Staple Remover Straws String Tape Tape Measure Tangrams Worksheet Yard Stick Activities/Directions: Closure: 8
9 WHAT IS THE TRUTH VALUE OF EQUIVALENCE STATEMENTS? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 15, Lesson 3 1. Warm up 2. ICA Test Questions 3. Logic & Equivalence 91 Statements Warm up: Complete the following truth table: T T F F T F T F 9
10 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 Equivalence Equivalence The connection of two simple statements using the phrase "if and only if" i.e. p: I will go to the park q: John will go to the park Equivalence Truth Table p: q: "I will go to the park if and only if John will go to the park" is only true when BOTH statements are true or both statements are false Summary: 10
11 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: 11
12 w Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Complete the following truth table: 12
13 Lesson Plan: Week 1, Lesson 4 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 mid segment 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 two dimensional figures. Identify and classify polygons using manipulatives and create two dimensional figures. Identify and describe polygons (concave, convex, regular, pentagon, hexagon, n gonal, circles and sector areas). Identify and describe properties of a circle, kite, trapezoid, parallelogram, rectangle, square, and rhombus. Use congruent relationships of two dimensional 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 three dimensional figure. Compare and contrast three dimensional figures. Use manipulatives to create three dimensional figures Apply surface area and volume formulas for prisms, pyramids, cylinders, cones and spheres. Draw three dimensional figures with appropriate labels and make a three dimensional model from a net. Draw, describe, and analyze solid geometry figures. Language Objectives: classify compare compose contrast define demonstrate describe discuss edit elaborate evaluate experiment explain identify interview investigate justify label list listen match name paraphrase predict present present your point of view rephrase restate rewrite state summarize Materials Needed: Calculators Colored Pencils Colored Pens Compass Flash Light Graph Paper Hi Lighters Index Cards Navigator Pattern Blocks Protractor Ruler Scissors Staplers Staple Remover Straws String Tape Tape Measure Tangrams Worksheet Yard Stick Activities/Directions: Closure: 13
14 Week 1, Lesson 4 1. Warm up 2. Notes 3. ICA WHAT IS THE ESSENTIAL QUESTION? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question 1 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Answer the following questions. 14
15 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 Notes Summary: 15
16 ity 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 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 16
17 QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ 17
18 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure 18
19 Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation tigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation Investigation 19
20 w Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review 20
21 Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra Practice Extra 21
22 Lesson Plan: Week 1, Friday 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 mid segment 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 two dimensional figures. Identify and classify polygons using manipulatives and create two dimensional figures. Identify and describe polygons (concave, convex, regular, pentagon, hexagon, n gonal, circles and sector areas). Identify and describe properties of a circle, kite, trapezoid, parallelogram, rectangle, square, and rhombus. Use congruent relationships of two dimensional 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 three dimensional figure. Compare and contrast three dimensional figures. Use manipulatives to create three dimensional figures Apply surface area and volume formulas for prisms, pyramids, cylinders, cones and spheres. Draw three dimensional figures with appropriate labels and make a three dimensional model from a net. Draw, describe, and analyze solid geometry figures. Language Objectives: classify compare compose contrast define demonstrate describe discuss edit elaborate evaluate experiment explain identify interview investigate justify label list listen match name paraphrase predict present present your point of view rephrase restate rewrite state summarize Materials Needed: Calculators Colored Pencils Colored Pens Compass Flash Light Graph Paper Hi Lighters Index Cards Navigator Pattern Blocks Protractor Ruler Scissors Staplers Staple Remover Straws String Tape Tape Measure Tangrams Worksheet Yard Stick Activities/Directions: Closure: 22
23 Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Week 1, Friday 1. Warm up 2. Notes 3. ICA 4. Extra Practice: Warm up: Answer the following questions. Language Objectives I will listen and take notes as the teacher guides me through... I will explain the steps required to... I will write a summary for... I will discuss... members of my group. I will demonstrate how to... with the Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up 23
24 ity 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 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 24
25 w Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review Spiral Review 25
26 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure 26
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