MVP 1.7 Connecting the Dot Date 8/19/19 - PowerPoint Presentation

MVP 1.7 Connecting the Dot Date 8/19/19 Pick up homework from the back table.Copy down the Agenda from the whiteboard Copy down the Essential Question. Do the Warm Up. Warm Up: Do 1.7 Ready. #1 Essential Question How does a decreasing common ratio affect a sequence?

1.7 Ready

Do Quiz correction for extra point on the quiz.Retake on the Quiz is only available after quiz correction are done.You will have to turn in your quiz correction to me when you want to retake the quiz. So don’t throw away your quiz. If you didn’t get the score you want then you have to change something . Understand that you need to change your study and in-class habit. What you are doing is not enough. Quiz

1.7 Chew on ThisSolidify Understanding TaskMr. and Mrs. Gloop want their son, Augustus, to do his homework every day. Augustus loves to eat candy, so his parents have decided to motivate him to do his homework by giving him candies for each day that the homework is complete. Mr. Gloop says that on the first day that Augustus turns in his homework, he will give him 10 candies. On the second day he promises to give 20 candies, on the third day he will give 30 candies, and so on. Highlight important information.

1.7 Chew on This1. Write both a recursive and an explicit formula that shows the number of candies that Augustus earns on any given day with his father’s plan.Before you do anything, you need to answer this question. Is it arithmetic or geometric ?Second, put the information in a visual representation.

day turn in homework # of candies recieve 110 220 3 30 4 40 5 50 6 60 7 70 8 80 9 90 10 100 Recursive equation   Explicit formula . or   Visual Representation

1.7 Chew on This2. Use a formula to find how many candies Augustus will get on day 30 in this plan.Recursive equation in function form. This is to find the candy on the 30 day, n=30  

1.7 Chew on This2. Use a formula to find how many candies Augustus will get on day 30 in this plan.Explicit formula in function form. This is to find the candy on the 30 day, n=30 or This is to find the candy on the 30 day, x=30  

1.7 Chew on ThisAugustus looks in the mirror and decides that he is gaining weight. He is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework. Mr. and Mrs. Gloop like Augustus’ plan and agree to it.Highlight important information. Before you do anything, you need to answer this question. Is it arithmetic or geometric ?Second, put the information in a visual representation.

1.7 Chew on This3. Model the amount of candy that Augustus would get each day he reaches his goals with the new plan. day turn in homework# of candies recieve 1 1 2 2 3 4 4 8 5 16 6 32 7 64 8 1289 25610512Recursive equation   Explicit formula.  

1.7 Chew on This4. Use your model to predict the number of candies that Augustus would earn on the 30th day with this plan.Recursive equation in function form. Let mean let it be the 30 th day The recursive equation is useless here. Explicit formula in function form. Let mean let it be the 30 th day on the 30 th day, Augustus earn 536,870,912 candies  

1.7 Chew on This5. Write both a recursive and an explicit formula that shows the number of candies that Augustus earns on any given day with this plan.Recursive equation Explicit formula in function form.  

1.7 Chew on ThisAugustus is generally selfish and somewhat unpopular at school. He decides that he could improve his image by sharing his candy with everyone at school. When he has a pile of 100,000 candies, he generously plans to give away 60% of the candies that are in the pile each day. Although Augustus may be earning more candies for doing his homework, he is only giving away candies from the pile that started with 100,000. (He’s not that generous.)Highlight important information. Before you do anything, you need to answer this question. Is it arithmetic or geometric ? Second, put the information in a visual representation.

1.7 Chew on This6. How many pieces of candy will be left on day 4? On day 8? # days# candies 0 100,000 1 40,000 2 16,000 3 6,400 4 2,560 5 1,024 6 410 7 164 8669261010

Core Concept: Decreasing Common ratio“ he generously plans to give away 60% of the candies that are in the pile each day.” # days # candies 0 100,000 1 40,000 2 16,000 3 6,400 4 2,560 5 1,024 6 4107 16486692610 10 = .40  For 1 day = common ratio  

1.7 Chew on This7. Model the amount of candy that would be left in the pile each day.Recursive equation Explicit formula first term geometric explicit or zero term geometric explicit  

MVP 1.8 What Comes Next? What Comes Later? Date 8/19/19 Grab your blinders .Copy down the Agenda from the whiteboard Copy down the Essential Question. Do the Warm Up.Warm Up: Do 1.8 Ready. #1 Essential Question How is a table of value useful when writing recursive and explicit formulas.

1.7 Chew on This5. Write both a recursive and an explicit formula that shows the number of candies that Augustus earns on any given day with this plan.Recursive equation Explicit formula in function form.  

1.7 Chew on ThisAugustus is generally selfish and somewhat unpopular at school. He decides that he could improve his image by sharing his candy with everyone at school. When he has a pile of 100,000 candies, he generously plans to give away 60% of the candies that are in the pile each day. Although Augustus may be earning more candies for doing his homework, he is only giving away candies from the pile that started with 100,000. (He’s not that generous.)Highlight important information. Before you do anything, you need to answer this question. Is it arithmetic or geometric ? Second, put the information in a visual representation.

1.7 Chew on This6. How many pieces of candy will be left on day 4? On day 8? # days# candies 0 100,000 1 40,000 2 16,000 3 6,400 4 2,560 5 1,024 6 410 7 164 8669261010

Core Concept: Decreasing Common ratio“ he generously plans to give away 60% of the candies that are in the pile each day.” # days # candies 0 100,000 1 40,000 2 16,000 3 6,400 4 2,560 5 1,024 6 4107 16486692610 10 = .40  For 1 day = common ratio  

1.7 Chew on This7. Model the amount of candy that would be left in the pile each day.Recursive equation Explicit formula first term geometric explicit or zero term geometric explicit  

A Practice Understanding Task For each of the following tables, • describe how to find the next term in the sequence, • write a recursive rule for the function, • describe how the features identified in the recursive rule can be used to write an explicit rule for the function, and • write an explicit rule for the function. • identify if the function is arithmetic, geometric or neither1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

To find the next term: Multiple by 2 to the previous term Reclusive rule: To find the term: start with 5 and multiple 2 n times. Explicit rule: Geometric   1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

To find the next term: Add by - 9 to the previous term Reclusive rule: To find the term: start with -8 and add -9 n times. Explicit rule: Arithmetic   1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

To find the next term: Multiple by 3 to the previous term Reclusive rule: To find the term: start with 2 and multiple 3 n times. Explicit rule: Geometric   1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

To find the next term: Add by 12 to the previous term Reclusive rule: To find the term: start with 3 and add 12 n times. Explicit rule: Arithmetic   1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

To find the next term: Add by .6 to the previous term Reclusive rule: To find the term: start with and add .6 n times. Explicit rule: Arithmetic   1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

Quadric

1.8 What Comes Next? What Comes Later?

To find the next term: Multiple by .2 to the previous term Reclusive rule: To find the term: start with 10 and multiple .2 n times. Explicit rule: Geometric   1.8 What Comes Next? What Comes Later?

1.8 What Comes Next? What Comes Later?

To find the next term: Multiple by -.2 to the previous term Reclusive rule: To find the term: start with -1 and multiple -.2 n times. Explicit rule: Geometric   1.8 What Comes Next? What Comes Later?

Notes on Geometric Decay and Growth Factor Date 8/28/19 You won’t need your binders .Copy down the Agenda from the whiteboard Copy down the Essential Question. Do the Warm Up Warm Up: Answer the following question. Determine whether the given information represents an arithmetic or geometric sequence. Then write the recursive and the explicit equation for each.   Isaac has a training routine. He will run 2 miles every day starting at the first of the day. He will run 25% farther each day after day 1. Essential Question How can you tell if a geometric sequence is growing or decaying?

He will run 25% farther each day after day 1. Percentage mean common ratio, which mean geometric Options(a) r = .25(b) r = .75(c) r = 1(d) r = 1.25 Xday Y miles 1 2 2 3 Multiple by the common ratio to get the next term Make a chart for each possible r value. Warm Up

(a) r = .25 (b) r = .75 (c) r = 1 (d) r = 1.25Xday Ymiles1 2 2 .50 3 0.25 X day Y miles 1 2 2 1.5 3 1.125 XdayYmiles122232XdayYmiles1222.533.125

Graphing different common ratios

The geometric sequence grows when the common ratio is greater than oneThe geometric sequence remain the same when the common ratio is equal to one The geometric sequence decays when the common ratio is less than one   Core Concept: Common ratio effects

Core Concept: Exponential Functions Exponential Growth Function Exponential Decay Function

Determine whether each function represents an exponential growth or exponential decay. Identify the initial amount and interpret the growth factor or decay factor. The function represents the value (in dollars) of a baseball card years after it is issued.The function represents the number of players left in a video game tournament after rounds. SOLUTIONS The function is growing. The initial amount is $0.50 and the growth factor is 1.07 where the r is each year. The function is decaying. The initial amount is 128 player and the decay factor is 0.8 where the r is each year.   Interpreting Exponential Functions

Math Talk Without performing any calculations, match each equation with its graph. Explain your reasoning.

MVP 1.9 What Comes Next? What Comes Later? Date 8/29/19 Grab your blinders .Copy down the Agenda from the whiteboard Copy down the Essential Question. Do the Warm Up.Warm Up: Do 1.9 Ready. #1 Essential Question How do you find missing terms in an arithmetic sequence?

1.9 What Does it Mean? READY Topic: Comparing arithmetic and geometric sequence How are arithmetic and geometric sequence similar? How are they different?

1.9 What Does it Mean? A Solidify Understanding Task Each of the tables below represents an arithmetic sequence . Find the missing terms in the sequence, showing your method.

Equation Subtract 18 to both sides Divide 4 to both sides Simplify   x 1 2 3 4 5 y 18 x 1 2 3 4 5 y 18 x12345y18 x 1 2345y18 Core Concept: Equation Method

Label Information Slope formula / common difference   x 2 3 4 5 6 y x 2 3 4 5 6y x23456 y 9 6 3 0 -3 x 2 3 4 5 6 y 9 6 3 0 -3 Core Concept: Slope Method

Here are a few more arithmetic sequences with missing terms. Complete each table, either using the method you developed previously or by finding a new method. Equation or Slope Formula method 1.9 What Does it Mean?

x 1234y50865. x 1 2 3 4 5 6 y 40 10 x 1 2 3 4 5 678y-2356.7.

x 1234y50627486 5. common difference d = 12 x 1 2 3 4 5 6 y 40 34 28 22 16 10 x 12345678y-23-19-15-11-7-3156. common difference d = - 67. common difference d = 4

7. common difference d = 4 x1234567 8y-23-19 -15 -11 -7 -3 1 5 8. The missing terms in an arithmetic sequence are called “ arithmetic mean ”. For example, in the problem above, you might say, “ Find the 6 arithmetic means between -23 and 5 ”. Describe a method that will work to find arithmetic means and explain why this method works.

The value of a car is . It loses % if its value every year.Write a function that represent the value of the car after years.What will be the value of the car at year 6.Create a table of values and graph the function. Is it discrete or continues.?   Review: Exponential Function

The value of a car is . It loses % if its value every year.SOLUTIONSWrite a function that represent the value of the car after years. Decay function = 12,500 What will be the value of the car at year 6. Let Create a table of values and graph the function. Is it discrete or continues.?   Review: Exponential Function

Quiz on Arithmetic and Geometric sequence 2 Date 8/30/19 Use a paper clip, Turn in your homework ( 1.6,1.7,1.8) to the back tableYou won’t need your binders .Copy down the Agenda from the whiteboard No Essential Question. Work on Warm Up. Warm Up : Do the following the questions. The inaugural attendance of an annual music festival is 150,000. The attendance increase by 8% each year. Write an exponential function that represents the attendance after years. How many people will attend the festival in the fifth year? Round your answer to the nearest thousand.   Essential Question

Exponential Function

Quiz Expectations 1. You can take all the time you need to, you can come back during lunch or after school to finish2. No talking to anyone. I will rip up your quiz. If you are not sure about a question, ASK ME. Don’t assume anything.3. The only question I don’t answer is “ am I doing this right?”4. Turn it in to the back table when done.