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DO NOW
DO NOW
Is this true or false? If it's false, find a counter-example.
If line segments AB, BC, and AC are congruent, then points A, B, and C are collinear.
DO NOW
DO NOW
Fold a paper in half. When you unfold it, the paper is divided into 2 rectangles. Refold the paper, then fold it in half again. This time when you unfold it, it's divided into 4 rectangles. How many rectangles would you get if you folded it in half 8 times?
LEARNING TARGET
LEARNING TARGET
I can define inductive reasoning, conjecture, and counter-example.
I can define inductive reasoning, conjecture, and counter-example.
I DO
I DO
What is inductive reasoning?
It's reasoning based on patterns you observe.
What's the next number in this sequence?
3, 9, 27, 81 ...
What's the next picture in this sequence?
What is a conjecture?
It's a conclusion you reach based on inductive reasoning.
Let's say you wanted to find the 100th term in a sequence. Counting all the way to that term would take forever. Making a conjecture helps you find it faster.
Let's look at some examples:
What conjecture can you make about the relationship between the number of diameters and the number of regions? How many regions would 104 diameters make?
What conjecture can we make about the sum of even numbers?
You often need to collect data to make a conjecture. It's helpful to do this in an organized way:
What is a counter-example?
It's an example that proves a conjecture wrong.
Let's look at some examples:
If the name of a month starts with the letter J, it's a summer month.
You can connect any three points to form a triangle.
When you multiply a number by 2, it's product is bigger than the original number.
WE DO
WE DO
YOU DO
YOU DO
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