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.
If nǁm, find x.
10x - 27
5x + 12
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
the process of
GEOMETRY the generalization is called
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”
The rule that gives the nth term
for a sequence is called the function rule.
Intercept form y = b + mx (OR y = mx + b )
of a linear
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)
IF f(n) = 3n – 2, find:
1) f(1) = 3(1) – 2 = 3 – 2 = 1 (substitute 1 for n)
5) f(20) (or 20th term in a sequence)
6) f(100) (or 100th term in a sequence)
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 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?
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.
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
Which model for the handshake problem makes most sense to you? Why? How did it help you think about the problem?