Download Geometry Day One! Let`s review a little Algebra... Simplify: (what

chap 1 day 1
Geometry Day One!
Let's review a little Algebra...
Simplify: (what does that mean?)
1) 32
1a) -32
2)
3) (-14)2
5)
6)
8) -(4x + 7)
1b) (-3)2
4) -62
7)
9) 6x - 4x + 8 - 5
chap 1 day 1
Solve: (what does that mean?)
10)
10n + 12 = 14n - 12
11) (7a + 3) + (-a - 5) = -16
12) 13c + 40 = 9c - 20 + c
13) 3x - 35 = 9x - 59
14) (x -3)2
Assign: WS on solving due in 15 min
chap 1 day 1
GEOMETRY
SECTION 1.1 Patterns and Inductive Reasoning
OBJ: To use inductive reasoning to make conjectures
Unknown terms: Inductive reasoning
conjecture
Let's make some patterns:
list the first 4 positive even integers
list the first 4 positive odd integers
list the first 10 perfect squares
list the first 7 powers of 2
list the first 5 powers of 3
chap 1 day 1
Now let's look at some patterns and make some predictions
based on the pattern
ex: 3; 6; 12; 24 ___; ____
ex: 100; 50; 25; ___; ___
ex: 1; 2; 4; 7; 11; ___; ___
ex: 0; 2; 7; 9; 14; ___; ___
ex: 8; 88; 888; 8,888; _____; _____
1
ex: 1 ; 1; 1 ; 1 ; ; ____; _____
3 5 7 9
chap 1 day 1
We have been using inductive reasoning to predict the
next 2 terms
Defn: Inductive reasoning: using patterns or several
examples to make a prediction.
Conjecture: a conclusion reached by using inductive
reasoning.
Counterexample: an example for which a conjecture
is false
chap 1 day 1
ex:
Make a conjecture about the sum of the first 30 odd
integers.
Pattern?
1
= 1
1+3
= 4
22
1+3+5
= 9
32
1+3+5+7
= 16
1 + 3 + 5 + 7 + 9 = 25
12
42
52
ex: Let's look at the first few odd prime numbers:
1, 3, 5, 7.
What conjecture regarding the pattern for odd
prime numbers could be made based on this pattern?
Our Conjecture: Odd prime numbers are two greater than
the one before.
True or false? If false explain why.
An example that proves the conjecture false is called the
conterexample.
Assign: Copy down problem, and fill in the blank with
the missing terms; write the pattern in words
pp 6-8 (2 - 12 even, 17, 18)
chap 1 day 1