1. Homework Problems - to - on Study Guide Teaching Day 1 [Sarah & Drake] No Laptops Today :)

2. Learning Goal & Do Now Learning Goal: Be able to define explicit and recursive functions. Also be able to define geometric and arithmetic sequences. Be able to convert between explicit and recursive functions. Do Now: Label each function as either geometric or arithmetic a k =a 1 *d n-1 a k =a 1 +(k-1)d Define an explicit and recursive function

3. Agenda 11:50 -12:00 - Do Now & Copy Learning Goal 12:00 - 12:15 - Intro to sequences (Both Geometric and Arithmetic) 12:15 - 12:40- Explaining formulas for functions and notations 12:40-1:00 - Matching Game, match function to sequence 1:00 - 1:10 - Exit Ticket

4. Geometric & Arithmetic Sequences Arithmetic: When addition or subtraction is used to find the next number in the sequence. (1,2,3,4,5) Constant difference: +1 Geometric: When multiplication or division is used to find the next term in the sequence (1,2,4,8,16) Common Ratio: x2

5. Formulas for Functions & Notations Explicit: a k =a 1 +(k-1)d How it Works: The explicit function is a function that uses the first term number to find any value of any given sequence. Definition: An explicit function will give you the value of any term in a sequence Recursive: a k =a k-1 +d How it Works: The recursive function is a function that uses the previous term to find the next term in a sequence. Definition: A recursive function will only give you the value of the next term in the sequence

6. Arithmetic Notation: What are the parts & inputs? Explicit: a k =a 1 +(k-1)d Recursive: a k =a k-1 +d Key: a=set you are using (you use the term number to find the value of a) k =term number you're solving for, d= constant difference/ common ratio, Ex: {2,4,6,8}

7. Geometric Notation: What are the parts & inputs? Explicit: a k =a 1 (d k-1 ) Recursive: a k =a k-1 (d) Key: a=set you are using (you use the term number to find the value of a) k =term number you're solving for, d= constant difference/ common ratio, Ex: {-5, -25, -125, -625}

8. Practice Find the 5th, 6th, and 7th term using an explicit and recursive function. State the common ratio/ constant difference. Also Identify if the sequence is geometric or arithmetic 1.) {1,4,7,10} - We will be doing this as a class 2.) {-29, -34, -39, -44} 3.) { 1,5, 25, 125} 4.) { 160, 32, 6.4, 1.28} 5.) { 41, 44, 47, 50}

9. Example Problem { 2, 4,6, 8,10,_, _,_} This function is arithmetic because it involves addition. Recursive: a k = a k-1 + 2 Explicit: a k = 2 +(k- 1 ) 2 Common Ratio/ Constant Difference: +2 [ To find the next number in the sequence using recursive, I’d use the previous number such as 10 to find the 5th term Then plug 10 in for a] [ Using an explicit, plug the term number in for n,2,. If i was finding the 5th term, plug 5 in for k]

10. Sequence Game! Match the correct sequence with the correct Function under the four categories.

11. What we learned & Homework ●Learned what geometric and arithmetic sequences are. ●Learned what recursive and explicit functions are, and how they are used to find numbers in sequences. Homework Study Guide questions 1 - 6

12. Exit Ticket/Peer Feedback 1.Give an example of an arithmetic sequence and a geometric sequence. 2. Create an explicit and recursive function for this sequence: { 0, 5,10, 15, 20} Then give the constant difference/ common ratio 3.. Peer Feedback: Rate our teaching on a scale of 1-10. What were some things we did well & what were some areas we can improve?

13. Problems - to - on Study Guide Homework Teaching Day 2 [Artina & Drake]

14. Agenda ●11:50 - 12:15 - Learning Goal & Do Now (Writing + practicing) ●12:15 - 12: 25- Matching game ●12:25 - 12:50 - Create a function & create a sequence (notes) ●12:50 - 1:00 - Conversions (notes) ●1:00 - 1:05 - Review & Exit Ticket

15. Learning Goal & Do Now (12:00- 12:10) Learning Goal: One be able to identify when to use a specific function. Two be able to write an explicit or recursive function from a given scenario or sequence. Three be able to convert between explicit and recursive functions. Do Now: 1. Define the sequence, create a function & find the next #. (-12, -7, -2, 3, 8) (10, 20, 40, 80, 160) (160, 32, 6.4, 1.28, 0.25) Geometric ExplicitGeometric Recursive a k =___(__ k-1 ) a __ =a ___ (d)

16. Matching Game The goal of the game is to match the sequences and functions on the strips of paper to the function types on the flash card. Ex. a 3 =6 1 (6 3-1 )

17. How to create a function ➔ Figure out what type of sequence you are dealing with. ➔ Figure out what type of function the question is asking for. ➔ Input the values into the function. a k = a k-1 + d

18. Create function (Class Practice) Word Problem: A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning,how many bacteria will there be in 4 hours, 6 hours and 8 hours. Pattern:

19. Practice Individual Sequence: {1,8,15,22} Find the 5th, 6th and 7th terms in the sequence. Word Problem: A mine worker discovers an ore sample containing 500 mg of radioactive material. It is discovered that the radioactive material has a half life of 1 day. Find the amount of radioactive material in the sample at the beginning of the 7 th day.

20. Practice 2 {63, 59, 55, 51, 47} Word Problem: 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. What is the total distance the object will fall in 6 seconds?

21. Conversions: Arithmetic Functions a k = a 1 + d(k-1) a k = a k-1 +d Ex. {3, 5, 7, 9, 11} Explicit: Recursive: a 5 = 3 + (5-1)2 a 5 = 9 5-1 + 2

22. Conversions: Geometric Functions a k = a 1 (d k-1 ) a k = a k-1 (d) Ex. {4, 16, 64, 256, 1024} Explicit: Recursive: a 3 = 4 (4 3-1 ) a 3 = 16 3-1 (4)

23. What we learned & Homework ●How to convert between recursive and explicit functions ●How to build recursive and explicit functions from a scenario & sequence Homework Complete Study guide *Due: Tuesday 24th

24. Exit Ticket/Peer Feedback 1.Write the 4 types of functions under the sequence type. Geometric Arithmetic 2. Write the missing parts of these functions Geometric ExplicitGeometric Recursive a k =___(__ k-1 ) a __ =a ___ (d) How well do you understand the content? 1 2 3 4 5 6 7 8 9 10

25. Homework Answers -Tuesday 24th Mrs. Perez

26. Problems - to - on Study Guide Homework Teaching Day 3: REVIEW DAY [Byraaaaaaaan]

27. Agenda ●12:00 - 12:10- Learning Goal and Do Now ●12:10 - 12:25 - Practice Problems ●12:25 - 12:55 - Review Explicit Functions ●12:55 - 13:20 - Review Recursive Functions ●13:20 - 13:30 - Exit Ticket

28. Learning Goal & Do Now Learning Goal: Convert between, define and create recursive and explicit functions. Be able to define geometric and arithmetic sequences. Do Now ●Decide whether each sequence is arithmetic or geometric ●Create an explicit and a recursive function for each sequence ●Find the 5th term of each 1)5,10,15,20… 2)-1,5,-25,125…

29. All recursive functions must have the first term of the sequence it is based off of written nearby. Important to know... Arithmetic is a sequence, algorithmic is not. Ex: a k =16+7 a 1 =2 Ex: a 1 =67 a k =1675(5)

30. Common ratio RecursiveArithmetic Term number Geometric Explicit Activity

31. What we reviewed & Homework ●What are geometric and arithmetic sequences ●What are recursive and explicit functions and their notations ●Conversions ●How to apply geometric & recursive functions to a scenario or sequence Homework Review previous lessons on edmodo *Have study guide completed by tomorrow *Quest = TOMORROW

32. Exit Ticket/Peer Feedback List the 4 types of functions from this unit. 1.Recursive function for geometric 2.Recursive function for arithmetic 3.Explicit function for geometric 4.Explicit function for arithmetic Peer feedback and comments 1 2 3 4 5 6 7 8 9 10

33. Exit Ticket Create an explicit and a recursive function for this sequence: {1, 4, 16, 64, 256, 1024, 4096} Answer the questions below: If Jeremy won a lifetime supply of honey nut cheerios (960 boxes) and ate 2 boxes a month, how many boxes will he have left in 2 years? What about in 72 months, when he will have had 818 boxes left last month? Peer feedback and comments 1 2 3 4 5 6 7 8 9 10