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Cogito

Integrated Math 2 · Chapter 7 · Lesson 1

Practice Worksheet

Reasoning and Proof

What counts as an argument.

12 problems · about 20 minutes · G-CO.C.9

NameDate

Figure — use these to answer the problems

Measuring one angle is evidence. Proving something about every angle needs an argument instead.
030609012015018060°
Angle in degrees60
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. How many counterexamples disprove a general claim?

    Answer

  2. Why is inductive reasoning not a proof?

    • The next untested case could still fail.
    • Because the examples are usually wrong.

  3. Generalising from examples is which kind? 1 inductive, 2 deductive.

    Answer

  4. Deriving from accepted facts is which kind? 1 or 2?

    Answer

  5. Do 100 confirming examples prove a general claim? 1 yes, 0 no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Every prime is odd. Which number disproves it?

    Answer

  2. Every square number is even. Which of 4, 9 or 16 disproves it?

    Answer

  3. Is the converse of a true statement always true? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each activity by the kind of reasoning it uses.

    Write each item under the heading it belongs to: Measuring several triangles and noticing a pattern · Guessing a rule from a sequence · Deriving a result from known theorems · Writing a two-column proof

    Inductive

    Deductive

  2. Every multiple of 3 is odd. Which of 6, 9 or 15 disproves it?

    Answer

  3. The Counterexample

    Every number ending in 1 is prime. Which of 21, 31 or 41 disproves it?

    Answer

  4. The Count

    How many counterexamples are needed to disprove a general claim?

    Answer