| Number Patterns | Problem Solving | Types of number patterns | Counterexamples | Number Patterns |
|---|---|---|---|---|
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10 and 20
The missing numbers: 5, ____ , 15, _____, 25, 30 . . .
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conjecture
When a statement is thought to be true but remains unproven, it is called a
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The spiral
What is a common pattern in nature?
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The process of forming conclusions on the basis of patterns, observations, examples, or experiments
What is inductive reasoning?
|
12
The missing number: 4, 8, ___ , 16, 20, 24, . . .
|
|
17, 15, 13, 11, and 9
The starting number is 17. The rule is Add 3, Subtract 5. What are the next four numbers in this number pattern?
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Understanding the problem
Devising a plan Carrying out the plan Looking back
Name a step in Polya's four steps of problem-solving
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Arithmetic Sequence
What type of number pattern is 1, 4, 7, 10, 13?
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Counterexample
What is an example that shows a statement to be false called?
|
Start at 18 and subtract by 3
The Pattern Rule for: 18, 15, 12, 9, 6, . . .
|
|
Add 10, subtract 5, add 10, subtract 5,...
What is the pattern rule for 10, 20, 15, 25, 20,...?
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12-inch bolts
James bought 16 bolts at the hardware store for a total of $6.00. Some were 3−inch bolts that cost 36 cents each and the others were 4−inch bolts that cost 42 cents each. How many 3−inch bolts did James buy?
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Geometric Sequence
What type of number pattern is 2, 4, 8, 16, 32?
|
7 and 4
Find two whole numbers for which the following statement is false: The sum of any two whole numbers is divisible by 2.
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Start at 30 and subtract by 5
The Pattern Rule for: 30, 25, 20, 15, 10. . .
|
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Multiply by 3 and then subtract 1.
What is the pattern rule for 1, 2, 5, 14, 41,...?
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79 ft
When two pieces of rope are placed end to end, their combined length is 128 feet. When the two pieces are placed side by side, one is 30 feet longer than the other. What is the length of the longest piece of rope?
|
1, 3, 6, 10, and 15
What are the first 5 numbers in a triangular sequence?
|
4 + 12 + 6 + 3 = 25
Give a counterexample for the statement the sum of any four whole numbers is divisible by 2.
|
Start at 200 and subtract 25
The Pattern Rule for: 200, 175, 150, 125, 100. . .
|
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20, 60, 180, 540, and 1620
The starting number is 20. The rule is multiple by 3. What are the next four numbers in this number pattern?
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36 tiles
Ramon took a collection of colored tiles from a box. Amelia took 14 tiles from his collection and Keiko took half of those remaining. Ramon had 11 tiles left.
How many did he start with? |
0, 1, 1, 2, 3, 5, 8, and 13
What are the first 8 numbers in the Fibonacci sequence?
|
8 + 9 + 10 = 27
Give a counterexample for the statement the sum of any three consecutive whole numbers is divisible by 2.
|
95 and 80 (Start at 100 and subtract by 5)
The Missing Numbers: 100, ____ , 90, 85, _____ , 75, ...
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