| 2.4 Apply Mathematical Reasoning to Make Mathematical
Connections with Other Disciplines |
2.4 Grade 3
(Mathematical Reasoning and Connections) |
2.4 Grade 5
(Mathematical Reasoning and Connections) |
2.4 Grade 8
(Mathematical Reasoning and Connections) |
2.4 Grade 11
(Mathematical Reasoning and Connections) |
| A. Using inductive and deductive reasoning |
A1. Make, check, and verify predictions about the quantity,
size, and shape of objects and groups of objects. |
A1. Draw inductive and deductive conclusions within mathematical
contexts. |
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A1. Use direct proofs, indirect proofs, or proof by contradiction
to validate conjectures. |
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A2. Make conjectures based on logical reasoning and test conjectures
by using counter-examples. |
| B. Validating arguments (if-then statements, proofs,
etc.) |
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B1. Use models, number facts, properties, and relationships
to check and verify predictions and explain reasoning. |
B1. Combine numeric relationships to arrive at a conclusion. |
B1. Construct valid arguments from stated facts. |
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B2. Interpret statements made with precise language of logic
(i.e. all, every, some, or, many). |
B2. Construct, use, and explain algorithmic procedures for computing
and estimating with whole numbers, fractions, decimals, and integers. |
B2. Determine the validity of an argument. |
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B3. Use statistics to qualify issues in social studies. |
B3. Use measurements and statistics in family and consumer science. |
B3. Use if . . . then statements to construct simple valid arguments. |
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B4. Explain the concepts of prime and composite numbers. |
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B4. Use truth tables to reveal the logic of mathematical statements. |
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B5. Explain multiplication and division algorithms. |
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B5. Demonstrate mathematical solutions to problems in the physical
sciences. |
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B6. Select a method for computation and explain why it is appropriate. |
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B6. Distinguish between inductive and deductive reasoning. |
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B7. Describe the relationship between the size of the unit of
measurement and the estimate of the areas and volumes. |
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B8. Connect, extend, and generalize problem solutions to other
concepts, problems, and circumstances in mathematics. |
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