discovering geometry - chapter 2 … · 17/02/2014 · discovering geometry - chapter 2 lessons...
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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
Warm-Up
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
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
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?
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!
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!
What is inductive reasoning?
Inductive Reasoning = making predictions based on experience of past events.
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.
Let’s Try One…
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.
Using inductive reasoning and conjectures in
mathematics…
Try these…
Use the rule below to generate the first 5 terms
of a sequence.
3n – 2
Lesson 2.2: Finding the nth term
In this section we will answer…
How can I develop a mathematical statement
which describes a pattern?
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
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
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.
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.