1) The document discusses different types of reasoning used in mathematics including inductive reasoning, deductive reasoning, and estimation. 2) Inductive reasoning uses specific examples to derive general conclusions, while deductive reasoning uses general statements to arrive at specific conclusions. 3) Estimation is used to find approximate answers by rounding values and checking for reasonableness. Problem solving employs inductive reasoning, deductive reasoning, and estimation to work through problems systematically.

1. Proof and Critical Thinking in Mathematics Mathematical Ideas Week One

2. Read pages 2 – 4 of your textInductive Reasoning Inductive reasoning is the process of reasoning to a general conclusion through the observation of specific cases. This general conclusion is not to be assumed to be correct for all cases. It is a conclusion made based on examples explored. (Read the bottom of p 4 for more information)

3. Have a look again at Example 1 and 2 on page 2 of your text. How many examples do you think is enough for you to induce a solution?

4. Read p 5 of your textDeductive Reasoning Deductive reasoning is the process of reasoning to a specific conclusion from a general statement. Deductive reasoning results in PROOF of conjectures being true or false

5. Read p 9 - 13 of your textEstimation The process of arriving at an approximate answer to a question. The symbol ≈ means is approximately equal to. When making an estimate ensure you check your value for reasonableness.

6. Estimation Contd. Example: What is the value of purchasing 9 plates at $3.99 each? Solution: We could round each value. We can work out the value of 10 plates at $4.00 each ($40). This solution is reasonable. So we can say: 9 plates at $3.99 each will be approximately $40.00.

7. Read p 20 - 29 of your textProblem Solving Inductive/Deductive Reasoning and Estimation are useful skills when it comes to problem solving. The last set of this chapter looks at methods of problem solving, and putting those methods to practice.

8. This Week: This week we’ve looked at how mathematics can allow use to read patterns, and predict eventualities. We’ve used reasoning methods and estimation to solve problems. We’ve also looked at problem solving methods which specifically articulated how we work through problems to arrive at a solution.