MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C90752.756F7040" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C90752.756F7040 Content-Location: file:///C:/EA33A238/T101Lesson1.2aF'08.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Lesson 11

Lesson 1.2 F08

DAY 1

Objectives:      1. To explo= re patterns.

2.&n= bsp;  To use indu= ctive and deductive reasoning.

3.&n= bsp;  To find the= term of an arithmetic, geometric or other sequence.

 

NCTM- Standards page = 22

 

The World’s Lar= gest Pizza Par lour offers a pizza that is 3 feet in diameter and comes with any combination of 40 different toppings.  In its advertisement the establishment boasts that its mushroom and cheese toppings are so good that every customer will order at least those t= wo toppings.  The ad also says th= at even if every person in the world ordered a different combination of toppin= gs, assuming cheese and mushroom were always chosen, there would still be many unordered combinations of toppings.  Is the ad truthful?

How can we solve this problem?

 

MAKE A TABLE

# of additional top= pings

# of pizzas

Rule

1=

 

 

2=

 

 

3=

 

 

4=

 

 

…<= /span>

 

 

40

 

 

The world population = was 6,715,046,511 on 8/14/08

Math is a study of pa= tterns.

 

Example 1, 4, 16, 64,= …

 

Is there a pattern?

 

 

What are the next thr= ee terms?

 

 

Describe the pattern = in your own words.

 

 

 

Example             1 x 10 + 2 =3D12<= /o:p>

            =             =   12 x 10 + 3 =3D123

        =             &nb= sp;   123 x 10 + 4 =3D1234

        =             &nb= sp; 1234 x 10 + 5 =3D12345

       

Use inductive reasoning to determine the next line in our pattern.<= span style=3D'mso-tab-count:1'>      =

  

 

 

 

 

Inductive reasonin= g-is the method of making

            =             &nb= sp;       generalizations based on collected data.

 

 

Assign Activity 11= page 18 in Dolan.

If you put 5 cents in= the bank on the first day of September, 10 cents on the second day of September= and continue this pattern, how much would you put in on the 15 day of September= ?

 

Conjecture-a statement thought to be true

 

Day

CASE 1 (arit= hmetic)

CASE 2(geome= tric)

1=

 

 

2=

 

 

3=

 

 

4=

 

 

5=

 

 

6=

 

 

n=

 

 

 

       

 

 

Find the amount on th= e 30th day.

 

 

 

Are the following seq= uences arithmetic, geometric or neither?  Find the twelfth term.

 

= 1.&n= bsp;  1,4,9,16,25= ,…        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;   a12= =3D ____

 

= 2.&n= bsp;  10,7,4,1,&#= 8230;        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;        a12= =3D ____

 

= 3.&n= bsp;  2,6,18,54,1= 62,…        &= nbsp;           &nbs= p;            &= nbsp;           a<= /span>12= =3D ____

Recursive Formula-pag= e 31

 

Deductive reasoning-once we have accepted certain statements as true, the truth of cer= tain other statements may follow by logical reasoning.

 

 

Find a formula for= the nth term of an arithmetic sequence.

 

 

Number of term (n)

Term

Rule

1=

a1<= /sub>

 

2=

a1 + d

 

3=

a1 + d += d

 

4=

a1 + d += d + d

 

5=

a1 + d += d + d + d

 

6=

a1 + d += d + d + d + d

 

n=

 

 

 

 

 

Example-Use deductive reasoning to find the 7= 31st term

            =      of this sequence.   

2,9,16,23,30,…

 

 

 

 

 

 

 

Find a  formula for the nth term of a geom= etric sequence.

 

Number of term (n)

Term

Rule

1=

a1<= /sub>

 

2=

a1x r

 

3=

a1xr x r=

 

4=

a1x r x = r x r

 

5=

a1x r x = r x r x r

 

6=

a1x r x = r x r x r x r

 

n=

 

 

 

 

 

 

Example-Use deductive reasoning to find the 8= th term of

            =      this sequence.   How many terms ar= e in this

            =      sequence?           &nb= sp;           1, 3, 9, 27, … 531,441

 

 

 

 

 

 

 

 

 

 

 

Assign Activity 12= page 20 in Dolan 

Homework Start Math XL for Lesson 1.2 and book work 1.2 start #1a-c, 5, 6, 7, 8, 10, 11, 13, 19, 20, 21, 27, 36= -38

DAY 2

Example= :  = Find the first four terms of a sequence whose nth term is given by the follow= ing formula, then determine if the sequence is arithmetic, geometric or neither.

 

1.  6n + 7            = ;             <= /span>                =          2. 

 

a1=3D____<= span style=3D'mso-tab-count:7'>        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;     a1=3D____

 

a2=3D____<= span style=3D'mso-tab-count:7'>        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;     a2=3D____

 

a3=3D ____=         &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;    a3=3D ____

 

a4=3D____<= span style=3D'mso-tab-count:7'>        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;     a4=3D____

 

 

How many terms are th= ere in the following sequences?

 

1.&n= bsp;  10, 20, 30, 40,…. 3110.

 

 

 

 

2.&n= bsp;  2,4,8,16,&#= 8230;,2048

 

 

 

 

 

 

Example: 

In an arithmetic sequence , ,  find the first three terms.

 

 

Example:  Steve’s annual income has be= en increasing each year by the same amount.&n= bsp; The first year his income was $32,000, and the eighth year his income was $42,500. in what year will his income be $51,500?

 

 

 

 

 

 

 

Other sequences<= /b>

 

Fibonacci Sequence     

1, 1, 2, 3, 5, 8, 13,= 21, 34, 55, 89, 144, …

 

 

 

What is the sum of th= e first three numbers? 

 

What is the sum of th= e first four numbers?

 

What is the sum of th= e first five numbers?

 

What is the sum of th= e first six numbers?

 

What pattern is there= in the sum of the remaining numbers in the Fibonacci Sequence?

 

 

 

Figurate numbers-numbers that can be represented by dot arranged in the shape of certain geometric figures.

 

 

= 1.&n= bsp;  Triangular numbers ( page 33)

 

 

 

 

 

 

 

 

Find the 11th term

 

 

 

 

Diff= erences

Assuming the pattern continues, find the seventh term in the following sequence.

 

        &= nbsp;           &nbs= p;       5,  6,  14,  29,  51,  80, …

First Difference

 

 

Second difference

 

 

 

 

Is there a pattern when you multiply a two digit number by 11?  (counterexample)=

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Assign Problem Solving Worksheet

Homework Finish Math XL for Lesson 1.2 and book work 1.2 #1a-c, 5, 6, 7, 8, 10, 11, 13, 19, 20, 21, 27, 36-38

DUE BY ____________________=

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