MVP 14 Connecting the Dot Date 81919 Copy down the Agenda from the whiteboard No Essential Question Do the Warm Up Warm Up Do 14 Ready 1 Essential Question How do you tell if a sequence is arithmetic ID: 771673
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MVP 1.4 Connecting the Dot Date 8/19/19 Copy down the Agenda from the whiteboard No Essential Question. Do the Warm Up. Warm Up: Do 1.4 Ready. #1 Essential Question How do you tell if a sequence is arithmetic?
1.4 Ready Evaluate the given equation for the indicated function values.1.
1.4 Ready Evaluate the given equation for the indicated function values.1. )
1.4 Scott’s Workout Solidify Understanding TaskScott has decided to add push-ups to his daily exercise routine. He is keeping track of the number of push-ups he completes each day in the bar graph below, with day one showing he completed three push-ups . After four days, Scott is certain he can continue this pattern of increasing the number of push-ups he completes each day. Instructions: Represent the image in different representation.
1.4 Scott’s Workout
1.4 Scott’s Workout 1. How many push-ups will Scott do on day 10?21 push ups 2. How many push-ups will Scott do on day n?When they ask for a day n, they are asking for a formula using n.
1.4 Scott’s Workout 3. Model the number of push-ups Scott will complete on any given day. Include both explicit and recursive equations. Recursive equation: Explicit equation: Explicit equation : 4. Aly is also including push-ups in her workout and says she does more push-ups than Scott because she does fifteen push-ups every day. Is she correct? Explain. She is somewhat correct .
1.4 Scott’s Workout 4. Aly is also including push-ups in her workout and says she does more push-ups than Scottbecause she does fifteen push-ups every day. Is she correct? Explain. She is somewhat correct. She only does more up to day 7 then after Scott does more.
Note: Practice Problem on Arithmetic sequences
Note: Practice Problem on Arithmetic sequences Determine whether the areas of the figures form an arithmetic sequence, If so, write the recursive equation and explicit equation to represent the arithmetic sequence and then find the value of .1. 2. Recursive equation: Explicit equation: Explicit equation: No an arithmetic sequence
Note: Practice Problem on Arithmetic sequences The amount of money a movie earns each week after its release can be approximated by the sequence shown in the graph.Write the recursive equation and explicit equation to represent the movie earnings as a function of weeks. In what week does the movie earn millions? c. How much money will the movie earn overall? Recursive equation: Explicit equation: Explicit equation: 6 week $40+$32+$24+$16+$8+$0=$224
Notes: Error Analysis Practice1. 2. The common difference is -1 The explicit is
MVP 1.5 Connecting the Dot Date 8/20/19 Grab your binderCopy down the Agenda from the whiteboard Copy down the Essential Question. Do the Warm Up. Warm Up: Do 1.5 Ready. #1 Essential Question How is the common ratio different from the common difference?
The same sequence is shown in both a table and a graph. Indicate on the table where you see the rate of change of the sequence. Then draw on the graph where you see the rate of change. 1.5 Ready
Email: 1.5 Don’t Break the Chain
Assume that it takes a day for the email to be opened, forwarded, and then received by the next person. On day 1, Bill Weights starts by sending the email out to his 8 closet friends. They each forward it to 10 peoples so that on day 2 its is received by 80 people. The chain continues unbroken. Highlight the important information Visual Representation of the word problem. (1) Chart, (2) List of values, (3) graph1.5 Visual Representation
Tree Disgram
Is it arithmetic or geometric? Explain how you got your answer. Chart Format
Graph Format Is it arithmetic or geometric? Explain how you got your answer.
1.5 Don’t Break the ChainUsing your visual representation, answer the question. 1. How many people will receive the email on day 7?On the 6th day, there is 800,000 # of emailsSo on the 7th day, there is 8,000,000 # of emails
1.5 Don’t Break the Chain2. How many people with receive the email on day n? Explain your answer with as many representations as possible. 2a. Write the recursive equation in function form.2b. Write the explicit formula in function form
1.5 Don’t Break the Chain 2. How many people with receive the email on day n? Explain your answer with as many representations as possible.Geometric sequence 2a. Write the recursive equation in function form. 2b . Write the explicit formula in function form. first term equation
1.5 Don’t Break the Chain3. If Bill gives away a Super Bowl that costs $4.95 to every person that receives the email during the first week, how much will he have spent? Which one is the question asking for?a. Find 𝑓(𝑛) when n = 4.95b. Find 𝑛 when 𝑓(𝑛)=$4.95c. Find 𝑓(𝑛) when n= 8d. Find 𝑓(𝑛) when n= 10 None of them are correct
1.5 Don’t Break the Chain3. If Bill gives away a Super Bowl that costs $4.95 to every person that receives the email during the first week, how much will he have spent? first week = 8 people$4.95 to every personSolution = 8∙$4.95 $ 39.60 is total amount spent
Note: Practice Problem on Geometric sequences
Note: Practice Problem on Geometric sequences
Note: Practice Problem on Geometric sequences a)Write a function that represents the sequence of figures and b) describe the 10th figure1.2. Recursive equation: Explicit equation : Recursive equation: Explicit equation :
Notes: Error Analysis Practice1. 2. The common ratio is The common ratio is
Note on Arithmetic and Geometric sequence Date 8/21/19 You won’t need your binders .Copy down the Agenda from the whiteboard No Essential Question . ( same one as before) No on Warm Up. Warm Up : Get started on your worksheet, treat it as a quiz. Practice recalling by use your notes. Essential Question How is an arithmetic sequence different from a geometric sequence?
Arithmetic and Geometric Sequence Worksheet Determine if the sequence is arithmetic. If it is, find the common difference.
Arithmetic and Geometric Sequence Worksheet Find the common difference and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Find the common difference and the recursive formula.
Arithmetic and Geometric Sequence Worksheet Find the common difference, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Find the common difference, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Determine if the sequence is geometric. If it is, find the common ratio
Arithmetic and Geometric Sequence Worksheet Find the common ratio and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Find the common ratio and the recursive formula.
Arithmetic and Geometric Sequence Worksheet Find the common ratio, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Find the common ratio, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Given the first term and the common difference of an arithmetic sequence find the explicit formula and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Given the first term and the common ratio of a geometric sequence find the explicit formula and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Find the missing term or terms in each arithmetic sequence.
MVP 1.6 Something to Chew On Date 8/22/19Grab your binderCopy down the Agenda from the whiteboard Copy down the Essential Question. Do the Warm Up. Warm Up: Do 1.6 Ready. #1 Essential Question How does a negative common difference affect an arithmetic sequence?
. 1.6 Ready
The Food-Mart grocery store has a candy machine like the one pictured here. Each time a child inserts a quarter, 7 candies come out of the machine. The machine holds 15 pounds of candy. Each pound of candy contains about 180 individual candies. MVP 1.6 Something to Chew On
Represent the number of candies in the machine for any given number of customers. About how many customers will there be before the machine is empty?Visual Representation. Chart, (2) List of values, (3) graph, (4) Tree diagramMVP 1.6 Something to Chew On
MVP 1.6 Something to Chew On
MVP 1.6 Something to Chew On
Give me both the recursive formula and explicit formula in function notation, that describe the number of candies in the machine for any given number of customers Is it arithmetic or geometric ? arithmetic MVP 1.6 Something to Chew On
Arithmetic SequenceCommon difference was – 7Recursive equation in function form. Explicit formula in function form. or MVP 1.6 Something to Chew On r = common ratio d= common difference f(n-1) = previous term m = slope b = y-intercept
Represent the number of candies in the machine for any given number of customers. About how many customers will there be before the machine is empty?Empty mean Should you round up for down? MVP 1.6 Something to Chew On
2. Represent the amount of money in the machine for any given number of customers.Visual Representation. Chart, (2) List of values, (3) graph, (4) Tree diagramMVP 1.6 Something to Chew On
# costumer $ amount in machine10.252 0.53 0.75 4 1 5 1.25 6 1.5 7 1.75 8 2 9 2.25 10 2.5 For every 1 costumer Increase by .25 dollars
MVP 1.6 Something to Chew On
Give me both the recursive formula and explicit formula in function notation, that describe the number of candies in the machine for any given number of customers Is it arithmetic or geometric ? arithmetic MVP 1.6 Something to Chew On
Arithmetic SequenceCommon difference was – .25Recursive equation in function form. Explicit formula in function form. or MVP 1.6 Something to Chew On r = common ratio d= common difference f(n-1) = previous term m = slope b = y-intercept
Compare and contrastExplicit formula in function form. MVP 1.6 Something to Chew On
Quiz on Arithmetic and Geometric sequence Date 8/23/19 Use a paper clip, Turn in your homework ( 1.1,1.2,1.3,1.4,1.5) to the back tableYou won’t need your binders . Copy down the Agenda from the whiteboard No Essential Question . ( same one as before) No on Warm Up. Warm Up : Finish your worksheet, treat it as a quiz. Practice recalling by use your notes. Essential Question How is an arithmetic sequence different from a geometric sequence?
Arithmetic and Geometric Sequence Worksheet Determine if the sequence is arithmetic. If it is, find the common difference.
Arithmetic and Geometric Sequence Worksheet Find the common difference and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Find the common difference and the recursive formula.
Arithmetic and Geometric Sequence Worksheet Find the common difference, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Find the common difference, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Determine if the sequence is geometric. If it is, find the common ratio
Arithmetic and Geometric Sequence Worksheet Find the common ratio and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Find the common ratio and the recursive formula.
Arithmetic and Geometric Sequence Worksheet Find the common ratio, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Find the common ratio, the term named in the problem, and the explicit formula.
Arithmetic and Geometric Sequence Worksheet Given the first term and the common difference of an arithmetic sequence find the explicit formula and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Given the first term and the common ratio of a geometric sequence find the explicit formula and the three terms in the sequence after the last one given.
Arithmetic and Geometric Sequence Worksheet Find the missing term or terms in each arithmetic sequence.
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.