Week 8, Lesson 1 1. Warm up 2. ICA Scavanger Hunt 3. Notes Arithmetic Series
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1 CAN WE ADD AN ARITHMETIC SEQUENCE? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 8, Lesson 1 1. Warm up 2. ICA Scavanger Hunt 3. Notes Arithmetic Series 51 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: Find the explicit formula for the following arithmetic sequence, then find the 12th term 1
2 s 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 ICA: In Class Activity ICA: In Class Activity You have 15 minutes to complete the scavenger hunt. You will now be participating in a scavenger hunt. You will start off at a specific question. The answer to that question will be at the top of the paper for another problem. That is the next problem you will do. Continue until you finish at the problem you originally started with. EXAMPLE Does anyone have any more questions or points of confusion they would like to go over? 4 5 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 Arithmetic Series Arithmetic Series An arithmetic series is the sum of the terms from an arithmetic sequence i.e i.e In order to properly use the formula below, you will usually need to find the last term that you are looking for. You will need to find the n th term The Sum of an Arithmetic Series Summary: 3
4 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 Arithmetic Series Example 1 Find the sum of the following arithmetic series Example 2 Find the sum of the following arithmetic series Example 3 Find the sum of the first 12 terms of an arithmetic series where a 1 = 16 and d = 3 Summary: 4
5 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 QUIZ QUIZ QUIZ QUIZ QUIZ Quiz Like Question Find the sum of the first 100 natural numbers 5
6 Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 8, Lesson 2 1. Warm up 2. Notes Geometric Series 3. ICA QUIZ like Question HOW IS THE FORMULA DIFFERENT FOR GEOMETRIC SERIES? 53 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: Find the sum of the first 8 terms of an arithmetic series when a 1 = 32 and a 2 = 26 6
7 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 Geometric Series Geometric Series A geometric series is the sum of the terms of a geometric sequence i.e i.e Just like an arithmetic series, many times you will need to find the n th term. For GEOMETRIC series, you will also need to find r The Sum of a Geometric Series Summary: 7
8 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 Geometric Series Example 1 Find the sum of the first 7 terms of a geometric series when a 1 = 243 and r = 1/3 Example 2 Find the sum of the first 10 terms of the following geometric series 400, 300, 225,... Example 3 Look at the series below. For what value of n will the sum of the series first exceed 384.4? Summary: 8
9 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 QUIZ QUIZ QUIZ Test Like Question Consider the geometric sequence 512, 256, a, 64, b,... Find a and b Find the explicit formula for the sequence Find a 10 Find S 10 For what value of n will the series first exceed ? 9
10 HOW CAN WE USE SEQUENCES AND SERIES IN WORD PROBLEMS? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 8, Lesson 3 1. Warm up 2. Notes Applying Series 3. ICA Allowance Scam 55 Warm up: Find the sum of the first 6 terms of the geometric sequence where a 1 = 56 and r = 2/3 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 Series as a Word Problem Clara wants to buy some land. She can choose between two different payment options.both options require her to pay for the land in 20 monthly installments. Option 1: The first installment is $2500. Each installment is $200 more than the one before. (a) Write the explicit formula for Option 1 (b) Write down the values of the second and third installments (c) Calculate the value of the final installment; (d) show that the total amount that Clara would pay for the land is $88,000. Summary: 11
12 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 Series as a Word Problem Clara wants to buy some land. She can choose between two different payment options.both options require her to pay for the land in 20 monthly installments. Option 2: The first installment is $2000. Each installment is 8% more than the one before. If Clara chooses option 2, (a) find the value of the second installment; (b) show that the value of the fifth installment is $2721. (d) Clara knows that the total amount she would pay for the land is not the same for both options. She wants to spend the least amount of money. Find how much she will save by choosing the cheaper option. Summary: 12
13 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 Julian decides that he wants to make some money off of his parents. He makes the deal with his parents that he will do any chores that they want, as long as they pay him $1 on the first day of the month, and each day give him one more dollar than the day before. How much would his parents give him on the last (31 st ) day of the month? How much would his parents have paid him in total over the entire month? His parents laughed at him because they know that is too expensive, so he comes up with a different plan. He said instead, they need to give him $0.01 on the first day, and all they need to do is double it. His parents agree. How much do they owe him on the 7th day? How much in total have they paid him on the 7th day? How much do they owe him on the last (31 st ) day of the month? How much in total have they paid him? 13
14 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 ICA: In Class Activity Consider the geometric series where Find S 4 Mentally estimate the following: S 6 S 10 S 50 S 1000 Calculate the following using the formula S 6 S 10 S 50 S
15 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: 15
16 CAN YOU DEMONSTRATE YOUR KNOWLEDGE OF SEQUENCES AND SERIES? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 8, Lesson 4 1. Warm up 2. Sequences and Series Quiz 3. Midterm Review 57 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: Find a 10 and S 10 of the arithmetic sequence 17, 22, 27,... 16
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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
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