DO NOW 10/20/2015 1. an= a1 + (n-1)(4) and a1=2 List the first 6 terms of the sequence. 2. Given: 4, 9, 14, 19… What is the rule that describes the nth term?

CC3 LT 3B Geometric & Arithmetic Sequences 1. I can write arithmetic and geometric sequences (both recursively and with an explicit formula) from a graph, a description of a relationship, or input/output pairs from a table. 2. I can use the sequences to model situations and translate between the two forms. ----- Meeting Notes (11/14/14 11:52) ----- T: Posts Powerpoint on board S: Analyze the LT and identify words/phrases that they don't know.

What Questions come to mind?? Approach Independently http://youtu.be/4sYSyuuLk5g Create 2 Plans that might work by communicating with partner Need: Student and Teacher actions for this IBE ----- Meeting Notes (11/14/14 11:52) ----- T: Posts IBE and says

I. Geometric Sequence - Definition Multiplying I. Geometric Sequence - Definition Common Ratio is the rate at which the sequence is changing. Same as Constant Rate A Geometric Sequence is a sequence of numbers (n terms) where the difference between each term has a common ratio. a1, a1r, a1r2, a1r3, … an a1= first term in a sequence 1st Term 2nd Term 3rd Term 4thTerm nth Term Thoughts do we need to add a thought bubble for exponents. T: how many terms do you see? T: What patterns did you notice? T: what does the exponents mean? ----- Meeting Notes (12/2/14 15:45) ----- T: what would the nth term be? Adding How is this different from an Arithmetic Sequence?

I. Geometric Sequence - Equation B. Explicit Form Why N-1? r F(x) = Starting Value (common ratio) Where will the students interact with the slide? What questions should be asked? n represents natural numbers so zero is not included -because the starting value is the 1st term, NOT the zero term. If you made a table, it would be the value when y=1. We minus one, so we can have the value when y=0

DO NOW 10/21/2015 Determine whether each sequence is Arithmetic or Geometric. Then find the common difference/common ratio. a) 5, 9, 13, 17 ... b) 6, 24, 96….   c) 64, 32, 16, 8… d) 19, 14, 9, 4…

DO NOW 10/22/2015 Find the 25th term for each sequence. a) 5, 9, 13, 17 ... b) 6, 24, 96….   c) 64, 32, 16, 8… d) 19, 14, 9, 4…

What could the decimal represent? I. Geometric Sequence - Example Divide 2nd number by 1st number: C. The table shows the spread of the flu virus. Number of people who get sick from the flu. 1 week 2 weeks 3 weeks 4 weeks 5 weeks 2 16 128 1024 8192 x8 x8 x8 What could the decimal represent? Number of healthy people during flu season. 1 week 2 weeks 3 weeks 4 weeks 5 weeks 2,500 875 306.25 107.19 37.5 x0.35 x0.35 x0.35 What is the common ratio for both tables? What will be the results on week 8?

I. Geometric Sequence - Example (Continued) Use the Geometric Sequence Formula More than 4 million people are going to be sick in 8 weeks 8th Term = 4,194,304 Only about 2 people will still be healthy after 8 weeks of spreading the flu. 8th Term = 1.6

Are you going to be affected? Culver City Population = 39,428 California Population = 38.33 million United States Population = 316.1 million OH NO!!!!!

Recall & Reproductions Goal Problems Recall & Reproductions Routine Find the nth term of the sequence: 1. 3, 12, 48, 192… n=10 2. List the first 3 terms of the sequence. The tuition fees for the first three years of a high school are given in the table below. How much will it be in 5 years? Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

Goal Problems Routine DOK 2 You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds? Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

Goal Problems Routine 2 Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

Goal Problems NON-Routine DOK 3    You complain that the hot tub in your hotel suite is not hot enough.  The hotel tells you that they will increase the temperature by 10% each hour.  If the current temperature of the hot tub is 75º F, what will be the temperature of the hot tub after 3 hours, to the nearest tenth of a degree? Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

Goal Problems NON-Routine DOK 3     Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

Goal Problems 10/26/2015 NON-Routine DOK 3    If you have a sequence starting with 5,15….. and some term 135 later in the sequence, Could the sequence be arithmetic? If so, what is the equation of the nth term and what term is 135? 2. Could the sequence be geometric? If so, what is the equation of the nth term and what term is 135? Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

I. Arithmetic Sequence - Definition The value from one term to the next. Must be the same amount. An Arithmetic Sequence is a sequence of numbers (n terms) where the difference between each term has a common difference. a1, a1 + d, a1 + 2d, a1 + 3d, … n a1= first term in a sequence 1st Term 2nd Term 3rd Term 4thTerm nth Term a1, a1 )+ d, a0 + 2d, a0 + 3d, … a0 + (n-1)d Goal: By the end of the slide, students should have notes on what “a1, n and d are” a0, a0 + d, a0 + 2d, a0 + 3d, … a0 + (n-1)d Where n is the number of terms in the sequence And a0 is the first term. a1, a1 + d, a1 + 2d, a1 + 3d, … a1 + (n)d

I. Arithmetic Sequence - Equation B. Explicit Form The only thing that changes for each sequence is the a1 and the d Definition: Straight forward way of finding an amount. Why (n-1) N is used to describe the terms in the sequence we are looking for. Where will the students interact with the slide? What questions should be asked? F(x) = Starting Value + Rate of Change (n-1)

C. Find a rule to describe the nth term of the following sequence. I. Arithmetic Sequence - Example C. Find a rule to describe the nth term of the following sequence. Approach from Unit 1: X is the figure number Y is the number tiles. Can I organize the details? Use y = mx +b to find the rule Approach : Can I use a table? Can organize it a different way? Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term? Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit Plan2:1.) organize data 2.) graph or find equation from table. Execute: Plan: X 1 2 3 Y 5 9 13 - 4 + 4 + 4

Plan from Unit 1 y = 4 x + 1 The rule for the nth term is y = 4n+1 C. Find a rule to describe the nth term of the following sequence. Plan: X 1 2 3 Y 5 9 13 - 4 + 4 + 4 Y-intercept Rate of change Rate of change Execute: y = mx + b y = 4 x + 1 The rule for the nth term is y = 4n+1 Approach : Can I use a table? Can organize it a different way? Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term? Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit Plan2:1.) organize data 2.) graph or find equation from table. Execute: Y-intercept is the number of tiles when x =0

Plan from Unit 2 C. Find a rule to describe the nth term of the following sequence. Approach: What kind of pattern? Adds 4 each time Arithmetic Sequence Re-write pattern as 5, 9, 13, 17 Plan : Use Sequence Equation Need to find parts of equation a1 , d, n, an Approach : Can I use a table? Can organize it a different way? Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term? Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit Plan2:1.) organize data 2.) graph or find equation from table. Execute: Common Difference What gets added each time First term

C. Find a rule to describe the nth term of the following sequence. Plan from Unit 2 C. Find a rule to describe the nth term of the following sequence. Execute: Equation an= a1+ d(n-1) a1 = the first term d = the common difference a1=5 5 +4 , 9 +4 , 13+4, 17 d= 4 The rule for the nth term is an = 5 + 4 (n-1) Approach : Can I use a table? Can organize it a different way? Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term? Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit Plan2:1.) organize data 2.) graph or find equation from table. Execute:

C. Find a rule to describe the nth term of the following sequence. I. Arithmetic and Geometric Sequence C. Find a rule to describe the nth term of the following sequence. Solution from Unit 1 y= 4n +1 Solution from Unit 2 an= 5 + 4(n-1) Approach : Can I use a table? Can organize it a different way? Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term? Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit Plan2:1.) organize data 2.) graph or find equation from table. Execute: Are they the same? Why or why not?

Recall & Reproductions Goal Problems (LT 2D #1) Recall & Reproductions Routine Given: an= a1 + 3 (n-1) and a1=2 List the first 6 terms of the sequence. Given: 4, 9, 14, 19… What is the rule that describes the nth term? Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

Active Practice (LT 2D #1) Recall & Reproductions Routine Insert Recall Practice here Insert Routine Practice Here Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration) Action on Feedback: Answer is 1,) 2.) an=4+5(n-1) Non-routine … applied problem or tiles… .

I. Arithmetic and Geometric Sequence E. Connections Sequences Arithmetic Ex. Explicit Recursive Geometric Ex Carol what do you think? Where would the equations go? .. I left places for students to add example problems. Thoughts?