Creating Definitions
A 'Zorblax' is a 2D shape with exactly 3 sides and no right angles. Would a right triangle count as an example or non-example?
What is non-example
This type of reasoning relies on observing specific patterns, examples, or past occurences to make a general statement.
What is inductive reasoning
In this statement "If an angle measures 90°, then it is a right angle," what is the phrase "an angle measures 90°" called?
What is the condition (or hypothesis)
This type of reasoning uses facts, definitions, accepted properties, and rules of logic to reach a guaranteed true conclusion.
What is deductive reasoning
An example that shows a general claim or statement is false is known as this.
What is a counterexample
When writing a good geometric definition, your goal is to make it so precise that there is none of this among people.
What is room for debate (or disagreement)
What is the next term in the sequence: 3, 7, 11, 15, ...?
What is 19
In the conditional statement "If two lines intersect, then they share one point," what is the conclusion?
What is "they share one point"
True or False: If your initial hypotheses are true, deductive reasoning guarantees that your conclusion is 100% true.
What is True
How many counterexamples do you need to prove a statement is false?
What is one
Based on the examples (114°, 150°, 91°) and non-examples (90°, 35°, 180°), what is the definition of an obtuse angle?
What is an angle with a measure greater than 90° and less than 180°
An unproven statement or educated guess based on observations is called this
What is a conjecture
How do you form the converse of a conditional statement?
What is swapping the condition and the conclusion
Identify the type of reasoning used: "All right angles measure 90°. Angle A is a right angle. Therefore, Angle A measures 90°."
What is deductive reasoning
Provide a counterexample to the claim: "If a shape has four right angles, then it must be a square."
What is a rectangle
Why is "School is a place where children and adolescents go every day" considered a bad definition?
What is children don't go to school every day or it includes places that aren't schools
Look at the pattern: 1, 3, 6, 10, 15, ... What is the 7th number in this sequence of triangular numbers?
What is 28 (6th is 21, 7th is 28)
Write the converse of this statement: "If a shape is a square, then it has four sides." Is the converse true or false?
What is "If a shape has four sides, then it is a square" (False)
Identify the type of reasoning used: "Every Friday for the last two months, the school cafeteria served pizza. Therefore, the cafeteria will serve pizza this Friday."
What is inductive reasoning
Provide a counterexample to the claim: "If a number is divisible by 4, then it is divisible by 8."
What is 12 (or 20, 28, etc.)
When creating a definition for a new geometric term, what two groups of images or items should you compare to figure out what to include and exclude?
What are examples and non-examples (or counterexamples)
Find the general (nth) term rule for the sequence: 2, 5, 8, 11, ...
What is 3n - 1
Provide a conditional statement whose original form is TRUE, but whose converse is FALSE.
For example: "If you live in Dallas, then you live in Texas"
Explain the main difference in how Inductive and Deductive reasoning arrive at conclusions.
What is inductive uses specific examples/patterns to guess a general rule, while deductive uses facts/rules to prove a specific logical point
A student claims, "If you multiply any two numbers together, the product will always be greater than both numbers." They test 3 x 4 = 12 and 5 x 6 = 30. Explain why testing these examples does NOT prove the claim.
What is testing examples only supports a claim; to prove a statement, it must work for all numbers, and a counterexample (like 1 x 5 = 5 or 0.5 x 4 = 2) shows the claim is false