This presentation is the property of its rightful owner.
1 / 11

# Geometry 8 October 2012 PowerPoint PPT Presentation

Geometry 8 October 2012. Place binder and text on desk. Warm up: (New paper- top front) If nǁm , find x. n. 10x - 27. m. 5x + 12. Objective. Students will use mathematical modeling to find the rule for the nth term.

Geometry 8 October 2012

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### Geometry 8 October 2012

• Place binder and text on desk.

• Warm up: (New paper- top front)

If nǁm, find x.

n

10x - 27

m

5x + 12

### Objective

Students will use mathematical modeling to find the rule for the nth term.

Students will take notes, do an investigation and work collaboratively.

DUE TUESDAY: 2.3, pg. 112: 1 – 4, 6, 9, 10, 20

DISTRICT INTERIM TEST on Chapters 1 and 2

Wednesday and Thursday

BRING COMPASS TO CLASS on Wed/ Th

### Inductive Reasoning

the process of

OBSERVING

FINDING PATTERNS

MAKING GENERALIZATIONS…

GEOMETRY the generalization is called

A CONJECTURE!!!

If……then………

Linear y = mx + b

functionsm = slope=

b = y-intercept

(y value when x = 0)

FUNCTION f(x) = mx + b

notationread as “f of x equals m x plus b”

Function rule

The rule that gives the nth term

for a sequence is called the function rule.

### linear equations

Intercept form y = b + mx (OR y = mx + b )

of a linear

function

y = b ± mx

y = b + mx

Slope goes with the x

1. where does it start?

y-intercept, value when x = 0

2. increasing or decreasing?

3. By how much?

(add or subtract repeatedly x times)

### CW: function notation

IF f(n) = 3n – 2, find:

1) f(1) = 3(1) – 2 = 3 – 2 = 1 (substitute 1 for n)

2) f(2)

3) f(5)

4) f(10)

5) f(20) (or 20th term in a sequence)

6) f(100) (or 100th term in a sequence)

### using your rule to predict

Write your rule in function notation

linear equation: y = 3n – 2

function rule: f(n) = 3n – 2

To predict the value of the 20th term,

you can substitute 20 for n

f(20) = 3(20) – 2 = 60 – 2 = 58

“the function evaluated when n is 20 equals….”

“f at 20 equals…”

DID YOU FIND THE RULE??

Mathematical models used for the “# of handshake” problem:

a table

a set of points w/ connecting line segments

sum of integers

triangle of dots

rule or formula

WHICH MODEL is most useful for solving with

any number of students?

WHICH gives the most insight into the situation?

WHICH leads to a formula using inductive reasoning?

### rectangular numbers

Strategy– if n is the number of the term in a sequence, use n for one dimension and try to express the 2nd dimension in terms of n.

### Methods for solving quadratics from tables

1) Try models- rectangle? points w/ segments?

Tables? Sketches? Shared parts?

2) Table- find DIFFERENCES!