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| What are the 5 Content Standards? |
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Definition
1. Numbers and Operations
2. Algebra
3. Geometry
4. Measurement
5. Data Analysis and Probability |
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| What are the 6 Process Standards? |
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1. Porblem Solving
2. Reasoning and Proof
3. Communication
4. Connections
5. Representations
6. Resources |
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Metacognition
not a practiced routine
build new knowledge by problem solving |
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justify why mathmatically
what strategy or proof was used to justify the answer is true? |
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furture math
other current subjects
real world |
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"Show me the Math"
Mathmatical ideas can be communicated using multiple representations. |
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georgiastandards.org
nctm.org |
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| What are the 6 ways a mathmatical problem can be represented? |
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Definition
1. Words
2. Symbolic Representations
3. Algebraic
4. Hands-on Models
5. Picture
6. Graphs |
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| patterns and relationships |
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| The movement from one mathmatical representation to another mathmatical representation. |
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| Drawing a general conclusion from specific examples. When we draw a generalization the result may or may not be true. |
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What are three ways we use inductive reasoning?
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1. extend patterns
2. learn math
3. show statements are false by counterexamples. |
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Definition
| This sequence is formed when a number pattern exists where there is a fixed difference between each number. |
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| When a number pattern is represented where there is a common ratio between each of the numbers in the sequence. |
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| Incorrect inductive reasoning leads to? |
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Definition
| misconceptions and malrules |
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| involves applying the rules of logic to true statements in order to draw conclusions. We use deductive reasoning to formally prove a statement is true. |
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| Fundamental Rule of Logic |
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Definition
IF P is true then not P is false.
If not P is false then P is true |
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Definition
| Written in if, then format |
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| when a conditional statement and its hypothesis are true. The conclusion must also be true. |
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| When a conditional statement is true and its conclusions are false. The hypothesis must be false. |
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| Is using the converse a valid rule of logic? |
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Definition
| No. The convere of p->q is q->p |
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| What is the inverse? Is it a valid rule of logic? |
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Definition
| The inverse is ~p->~q. It is not a valid rule of logic. |
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Term
| What makes up the contrapositive? |
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Definition
The contrapositive is made up of the converse and the inverse.
~q->~p |
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| What makes a conditional statement logically equivalent? |
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Definition
| If the conditional statement is true and the contrapositive is true the statements are logically equivalent. |
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| a^b is true only if both statements a and b are true. |
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| a v b is true is either a, b, or both are true. |
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