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

Homework

Problems - to - on Study Guide

Teaching Day 1[Sarah & Drake]

No Laptops Today :)

ARTINA DANIELS

Pattern example anyone? On study guide.

SARAH JACOB

That's your day I believe

DRAKE MCCUNE

The pattern example is another way of using a geometric sequence in a similar word problem style. It could also be done with arithmetic sets in order to give a better idea of how to display what is going on.:)

ARTINA DANIELS

Should we edit this?

DRAKE MCCUNE

Things we have to do:Need to teach transferring from explicit functions into recursive and viceversa. (Byron's Day)Elaborate more on Geometric Functions. (Day 1&2)More word problem examples.More practice problems to give out during lessons. (Every Day)Feel free to reply with other things that we need to do.

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

ak=a1*dn-1

ak=a1+(k-1)d Define an explicit and recursive function

SARAH JACOB

So we'll be putting up examples of recursive and explicit and asking for them to figure out which is which? While also asking them to create a sequence for both equations?

DRAKE MCCUNE

We have very little on Geometric equations.

SARAH JACOB

I can add practice problems on geometric , btw do you need me to create all the cards for the matching sequence game?

DRAKE MCCUNE

I haven't done anything to progress towards that

SARAH JACOB

Okay I'll create those tomorrow, along with the answer key for practice problems. I'll have copies to hand out to you guys on Wednesday as long with the student teaching snapshot. So everyone knows whats going on

Agenda

11:50 -12:00 - Do Now & Copy Learning Goal12:00 - 12:15 - Intro to sequences (Both Geometric and Arithmetic) 12:15 - 12:40- Explaining formulas for functions and notations12:40-1:00 - Matching Game, match function to sequence1:00 - 1:10 - Exit Ticket

ARTINA DANIELS

I see the spinning walemer lol XD

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

Formulas for Functions & Notations

Explicit: ak=a1+(k-1)dHow 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: ak=ak-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

Arithmetic Notation: What are the parts & inputs?

Explicit: ak=a1+(k-1)d

Recursive: ak=ak-1+dKey: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}

DRAKE MCCUNE

Changed +(-) to +/- to better display that it is either or, and not both at the same time.

SARAH JACOB

How will we explain the k-1 in the recursive equation, we will probably get a lot of questions about that. It doesn't really serve a purpose in solving out the whole equation?

ARTINA DANIELS

Yes is does have a purpose it tells you what previous number you are using to solve for the next term....oh your right it doesn't serve much of a purpose to solving.

ARTINA DANIELS

but we should keep it anyway because it serves a purpose in the explicit functions

DRAKE MCCUNE

The point of the sub numbers is to notate which number you are solving for. In the explicit function you will use the sub 1 and the k-1 to tell what number you have to import in the respective numbers. The recursive equation RELIES on the subnumbers, as in the nk-1 part the value of n is the value you are searching for (k's value) subtracted by one. So if you are looking for 8 in a sequence that adds by 3, the nk-1d section would become nk-1= whatever sequence part you are looking for (8) and subtract one to go the value you previously found. (5) and then add the d value (3) to get your final answer of eight.

Geometric Notation: What are the parts & inputs?

Explicit: ak=a1(dk-1) Recursive: ak=ak-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}

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 class2.) {-29, -34, -39, -44}3.) { 1,5, 25, 125}4.) { 160, 32, 6.4, 1.28} 5.) { 41, 44, 47, 50}

DRAKE MCCUNE

Do we have an answer key for this?

SARAH JACOB

Yes, I'm creating the answer keys right now

Example Problem { 2, 4,6, 8,10,_, _,_}This function is arithmetic because it involves addition.

Recursive: ak = ak-1 + 2

Explicit: ak = 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]

Sequence Game!

Match the correct sequence with the correct Function under the four categories.

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.

HomeworkStudy Guide questions 1 - 6

SARAH JACOB

Why are the problems only 1-2, we also need to add in finding the composite/ common ratio

ARTINA DANIELS

Because they haven't leaned how to convert in between explicit and recursive functions, but I was looking at the study guide and it would make sense to put #1-6 as hw.

SARAH JACOB

Yeah also what does she exactly mean converting between the two? Because in the study guide, I think the converting between the two are problems 3-6 because your just exchanging between the two recursive and explicit

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?


HomeworkTeaching Day 2[Artina & Drake]

ARTINA DANIELS

http://www.regentsprep.org/regents/math/algtrig/atp2/sequencewordpractice.htm

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

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 Explicit

Geometric Recursiveak=___(__k-1)

a__=a___(d)

DRAKE MCCUNE

I chucked some of the exit ticket into the do now for some diagnostics.

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.a3=61 (63-1)

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.

ak = ak-1+ d

ARTINA DANIELS

constant difference, comon ratio

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:

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 7th day.

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?

Conversions: Arithmetic Functions

ak= a1+ d(k-1) ak = ak-1 +d

Ex. {3, 5, 7, 9, 11} Explicit: Recursive: a5 = 3 + (5-1)2 a5 = 95-1 + 2

Conversions: Geometric Functions

ak = a1 (dk-1) ak = ak-1 (d)

Ex. {4, 16, 64, 256, 1024}Explicit:

Recursive:a3 = 4 (43-1) a3 = 163-1(4)

What we learned & Homework

● How to convert between recursive and explicit functions

● How to build recursive and explicit functions from a scenario & sequence

HomeworkComplete Study guide*Due: Tuesday 24th


1. Write the 4 types of functions under the sequence type.Geometric Arithmetic

2. Write the missing parts of these functionsGeometric Explicit Geometric Recursiveak=___(__k-1)

a__=a___(d)

How well do you understand the content?1 2 3 4 5 6 7 8 9 10

Homework Answers-Tuesday 24thMrs. Perez


HomeworkTeaching Day 3:REVIEW DAY[Byraaaaaaaan]

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

ARTINA DANIELS

How do we arrange this if we let the students choose

DRAKE MCCUNE

What are they supposed to be choosing?

Learning Goal & Do NowLearning 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…

ARTINA DANIELS

Ask class if they want to do an activity of ask questions and practice. (May be do a split class thing. Have people who want more help sit closer to front and have people who want to do individual practice sit in back, put a worksheet on edmodo for individualers.

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: ak=16+7 a1=2

Ex: a1=67 ak=1675(5)

Common ratioRecursiveArithmetic

Term number

Geometric

Explicit

Activity

DRAKE MCCUNE

What are you trying to teach them about?

BYRON GAINES

I'm trying to teach them about the whole 1st term for recursive thing but I can't word it right.

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

HomeworkReview previous lessons on edmodo*Have study guide completed by tomorrow*Quest = TOMORROW


List the 4 types of functions from this unit.1. Recursive function for geometric2. Recursive function for arithmetic3. Explicit function for geometric4. Explicit function for arithmetic

Peer feedback and comments1 2 3 4 5 6 7 8 9 10

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 comments1 2 3 4 5 6 7 8 9 10

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

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