Page 168 - Math Course 2 (Book 2)

Inductive Reasoning and Conjecture
Mo. 12

Lesson 1
Let’s Begin

KEY CONCEPTS:

1. Make conjectures based on inductive Patterns and Conjecture
reasoning.
2. Find counterexamples. Example

Make a conjecture about the next number based
MO. 12 - L1a on the pattern. 2, 4, 12, 48, 240

Conjectures Based on Find the pattern:
Inductive Reasoning 2 4 12 48 240

Vocabulary A-Z x2 x3 x4 x5

Let us learn some vocabulary
The numbers are multiplied by 2, 3, 4, and 5.

conjecture Conjecture: The next number will be multiplied
is an educated guess based on known information. by 6. So, it will be 6 • 240 or 1440.

Answer 1440

Geometric Conjecture

Example

Inductive reasoning
is reasoning that uses a number of specific For points L, M, and N, LM = 20, MN = 6, and
LN = 14. Make a conjecture and draw a figure
examples to arrive at a plausible generalization to illustrate your conjecture.
or prediction.

Given: points L, M, and N; LM = 20, MN = 6,
and LN = 14. Examine the measures of
2..4..6..8...? the segments. Since LN + MN = LM, the
points can be collinear with point N
between points L and M.
counterexample L N M
It takes only one false example to show that a Answer
conjecture is not true. The false example is called 14 6
a counterexample. 20

Associative Property of Subtraction? Conjecture: L, M, and N are collinear.
(1 – 2) – 3 = 1 – (2 – 3)
–4 ≠ 2

160