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DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

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Page 1: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

DISCOVERING GEOMETRY - CHAPTER 2

Lessons 2.1 and 2.2

Lesson 2.3

Lesson 2.4

Lesson 2.5

Lesson 2.6

Chapter 2 Review

Page 2: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Warm-Up

Page 3: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Homework Review

1. 35, 40, 45

3. 9, 9, 11

5. 13, 21, 34

7. 25, 26, 27

9. 12, 6, 3

11. 17, 9, 0

13. x + 4, x + 5, x + 6

15. x, y, x

17. x8 + 8, x10 + 10, x12 + 12

2. 64, 128, 256

4. 40, 47, 54

6. 25, 33, 42

8. 50, 40, 30

10. n - 4, n - 5, n - 6

12. 32x5, 64x6, 128x7

14. 25, 36, 49

16. n5, n6, n7

18. 4x - 8, 3x - 6, 2x - 4

Page 4: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Homework Review

19. x12, x14, x16

21. 12a - 5, 9a - 5, 6a - 5

22. 8m - 2, 8m - 1, 8m

23. m + 19, m + 22, m + 25

24. 5x + 25, 6x + 30, 7x + 35

25. 82, 92

26. 57.7, 56.5, 55.3

20. 17, 13.5, 10

Page 5: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Lesson 2.1: Inductive Reasoning

In this section we will answer…

What is inductive reasoning?

How can I use inductive reasoning to predict

future terms in a pattern?

Page 6: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Test Review

How Can I Reassess?

If the word YES is circled on your test, you must

complete the practice pages attached to your

grade sheet.

Once ALL practice problems are CORRECT, you

may retake the test during tutorial or prep.

PLEASE set up an appointment – DON’T just show

up!

Page 7: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Test Review

What if the word NO is circled?

CONGRATULATIONS! You are keeping your Not

Proficient scores.

DON’T take a chance and skip homework

assignments in the future!!!

If you do your homework, you are less likely to earn

Not Proficient scores!

And if you do earn one, you may fix it!

Page 8: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

What is inductive reasoning?

Inductive Reasoning = making predictions based on experience of past events.

Page 9: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

How do I use Inductive Reasoning?

1. Make observations.

2. Notice similarities or patterns of repeated outcomes.

3. Make an educated guess or conjecture, about what will happen next time.

4. Test for a counterexample.

Page 10: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Let’s Try One…

Page 11: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

WHICH IS THE BEST EXAMPLE OF INDUCTIVE

REASONING?

[A] A scientist observes during many tests, that a certain bacteria colony doubles in size within an hour. The scientist concludes that this bacteria colony will always double in size within an hour.

[B] A student measures the angles of one square and finds they are all 90 degrees. The student concludes the angles in every square are 90 degrees.

[C] A math student observes that the number 132 is divisible by the number 4. The student concludes that any even number is divisible by 4.

[D] A scientist observes on Monday that it takes a certain material 2 hours to decompose. On Tuesday, the scientist observes the same material takes 3 hours to decompose, and on Wednesday it takes 2 hours to decompose. The scientist concludes that it will always take 2 hours for that type of material to decompose.

Page 12: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Using inductive reasoning and conjectures in

mathematics…

Page 13: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Try these…

Page 14: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Use the rule below to generate the first 5 terms

of a sequence.

3n – 2

Page 15: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Lesson 2.2: Finding the nth term

In this section we will answer…

How can I develop a mathematical statement

which describes a pattern?

Page 16: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Step 2:

Can you spot

the pattern?

Step 3: Does

this generate

the correct

answer?

How can it be

fixed so that it

works?

Step 4: Check

Page 17: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

How can I find the nth term?

1. Set up a table of values.

2. Find the difference between terms. That’s the number that

multiplies n.

3. Does that get you each term?

If not, you need to choose a column to find a number to add

or subtract which will give the desired term.

4. Find the value for the term you are interested in.

Term

Value

Page 18: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review
Page 19: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review
Page 20: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Ticket Out the Door…

Work INDIVIDUALLY on your Ticket Out the Door.

When you finish, put it in the folder up front

and pick up a homework assignment.

Page 21: Discovering Geometry - Chapter 2 … · 17/02/2014  · DISCOVERING GEOMETRY - CHAPTER 2 Lessons 2.1 and 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Chapter 2 Review

Almost Finished…

Clear your calculator and turn it off

2nd + 7 1 2 2nd On

Copy down due dates

Standard Checks

Tests

Re-test Deadline

Homework

Section 2.1

Section 2.2

Do NOT pack up until you are told to do so.