1.2 logical reasoning page 9. inductive reasoning: reasoning that is based on patterns you observe....

1.2 Logical Reasoningpage 9

• Inductive Reasoning:Reasoning that is based on patterns you

observe.

• Conjecture:A conclusion that is reached using

inductive reasoning.

Read and do #1 & #2

• Share your answers in your group. • 5 min

1. Five students attended a party……..

2. Use inductive reasoning to….

Read and do #3 & #4

• Share your answers in your group. • 5 min

3. Use the four circles…..

4. a) Describe any patterns you see….

4. b) Predict….

Algebraic Rule ?

Read and do #5

• Share and discuss your answers in your group. • 10 min

5. Use the circle……

5. d) Try to find a new pattern…..

5. d) Try to find a new pattern…..

5. d) Try to find a new pattern…..

Read and do #6 & #7

• Share your answers in your group. • 5 min

# 6&7.

Read and do #8 & #9

• Share and discuss the answers in your group. • 10 min

#8

#8c

9a) Each step in the pattern creates a large square in which the side length is one square greater than the previous square.

So, the total number of small squares in each large square is the next larger perfect square.

9b) The pattern is continued by adding n squares to the bottom row, n squares along the right column, and then one square to fill in the corner. This is a total of n+n+1 squares , or2n + 1 squares.

The expression 2n+1 is a way of representing odd integers.

Page 17, Read Aloud

• Deductive reasoning uses– facts– definitions &– accepted propertiesin a logical order to write a logical argument (proof)

Look for a pattern

Make a conjecture

Inductive Reasoning

Facts

Definitions

Properties

Proof

Deductive Reasoning

Read and do #10 to #15

• Share and discuss the answers in your group. • 7 min

Read and do #16 to #20

• Share and discuss the answers in your group. • 7 min

Odd IntegersEven IntegersConsecutive IntegersTwo consecutive Odd IntegersTwo consecutive Even Integers

#3, page 22

• Generate a sequence using the description:“ The first term in the sequence is 4 and

each term is three more than twice the previous term.”

Recursive RuleExplicit Rule

1) Write a rule to predict the total number of tiles for any step.2) Explain how your rule relates to the pattern3) Try to find a different rule

1) Write a rule to predict the total number of tiles for any step.2) Explain how your rule relates to the pattern3) Try to find a different rule

#4 , page 22

• Angela is tiling her bathroom with white and blue tiles. As she completes the project, a pattern emerges between the figure number and the number of blue and white tiles.

Write an equation that can be used to model the number of white tiles W for any figure number n.