Unit 2 Lesson 1 Patterns and Inductive Reasoning
Unit 2 Lesson 1: Patterns and Inductive Reasoning
Lesson Overview
Patterns
What You Will Learn
- To recognize repeated patterns.
- Make conclusions based on these patterns.
Additional Resources
Overview
In this lesson, you will learn how to make conclusions based on patterns. You will show your understanding by writing conjectures using patterns.
Essential Understanding
Inductive Reasoning is Reasoning based on patterns you observe. You can observe patterns in some number sequences and some sequences of geometric figures to discover relationships.
This course is based on a textbook that is viewable by clicking on the textbook icon. Keep the textbook open while you go through the lesson so that you may refer to it throughout the lesson.
Lesson 1: Patterns and Inductive Reasoning
Additional Resources (Patterns and Inductive Reasoning)
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Prepare for Application
Instructions
You have now studied points, lines, and planes. It is now time to demonstrate your learning.
Try the activities below on your own. You should be able to answer these before beginning the practice.
Do these activities in your journal.
Find the following two terms in each sequence.
- 45, 40, 35, 30
What conjecture can you make about the twenty-first term in R, W, B, R, W, B, ....?
What conjecture can you make about the sum of the first 30 odd numbers?
Use the graph to the right for questions 1-2.
- What conjecture can you make about backpack sales in June?
- Is it reasonable to use the graph to make a conjecture about sales in August? Explain.
Find a counterexample for each conjecture.
- If a flower is red, it is a rose.
- One and only one plane exists through any three points.
- When multiplying a number by 3, the product is divisible by 6.