Inductive Reasoning in Geometry Patterns

This video tutorial by Mr. Banker Work covers lesson 2.1, focusing on describing patterns and using inductive reasoning. It explains how to make conjectures based on evidence and observations. The video includes examples of identifying patterns in diagrams and number sequences, exploring connections between collinear points, and making conjectures about sums of consecutive integers. It also discusses the use of counterexamples to disprove conjectures, providing a comprehensive understanding of inductive reasoning and pattern recognition.

What is inductive reasoning based on?

• Hypotheses

• Assumptions

• Evidence

• Intuition

Tags

CCSS.HSS.IC.B.3

What is a conjecture?

• An unproven statement based on observations

• A proven fact

• A mathematical theorem

• A hypothesis

If a circle is split into 6 pieces with one filled in, how many pieces will the next circle have?

• 10

• 7

• 9

• 8

What is the pattern in the sequence: -7, -21, -63, -189?

• Adding 14

• Subtracting 14

• Dividing by 3

• Multiplying by 3

Tags

CCSS.HSF.BF.A.2

What is the next number in the sequence: -189, -567, -1701?

• -8505

• -6804

• -5103

• -3402

Tags

CCSS.HSF.BF.A.2

How many connections can be made with 3 collinear points?

• 4

• 3

• 2

• 1

Tags

CCSS.4.G.A.1

How many connections can be made with 5 collinear points?

• 12

• 6

• 10

• 8

Tags

CCSS.4.G.A.1

What is the sum of the consecutive integers 4, 5, and 6?

• 12

• 13

• 14

• 15

What is the conjecture about the sum of three consecutive integers?

• It is the middle number minus three

• It is the middle number plus three

• It is the middle number times three

• It is the middle number times two

Tags

CCSS.6.EE.B.6

Which of the following is a counterexample to the conjecture that the value of x squared is always greater than the value of x?

• x = -4

• x = 0.5

• x = 3

• x = 2