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Geometry 8 October 2012PowerPoint Presentation

Geometry 8 October 2012

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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………

functions m = 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…”

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

Read page 111.

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

See handout “solving quadratics”

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

Tables? Sketches? Shared parts?

2) Table- find DIFFERENCES!

2nd difference constant? => quadratic!

3) Try n2 ± ???

4) Look for patterns in the FACTORS of the values

debrief

Which model for the handshake problem makes most sense to you? Why? How did it help you think about the problem?

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