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Consider the following ordering of numbers
Make a conjecture about what the next number is going to be, and why?
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Suppose we added one more number to the sequence:
What is your new conjecture?
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Suppose we added one more number to the sequence:
What is your new conjecture?
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At what point is there enough information to be confident about your conjecture? Why? This sequence has a special name can you do some research to figure out what it is? Is there anything interesting about this sequence?
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A diagonal is a line that connects a vertex to another vertex that it is not adjacent to it. A square has 2 diagonals, and a regular pentagon has 5 diagonals.
Draw all the diagonals in a regular hexagon:
Make a conjecture about how many diagonals a regular heptagon has (7 sides). Give your reasoning for your conjecture.
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Check your answer:
Fill in the following table
Sides/Vertices nNumber of Diagonals from each VertexNumber of DiagonalsdSquare412Pentagon5Hexagon6Heptagon7Come up with a formula for the number of diagonals d in terms of the number of sides/vertices n.
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Check your answer on the octagon:
Sides/Vertices nNumber of Diagonals from each VertexNumber of DiagonalsdOctagon8Which part of the table was the most helpful in figuring out the formula? Why?
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Describe in your own words the difference between deductive and inductive reasoning.
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Classify the following arguments as inductive or deductive. Is it a good argument? Why or why not? If it is a bad argument, how would you refine the argument?
All dogs hate cats. Rufus is a dog. Princess is a cat, therefore Rufus hates Princess.
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Jim, John and Joan are from Antarctica. Jim, John and Joan all like seafood, therefore everyone from Antarctica likes seafood.
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I have seen lots of cats. Every cat I have seen has a tail, therefore all cats have tails.
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All coins are made of metal. In my pirate pack kids meal I received a chocolate coin. I ate it. I ate metal.
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Consider the following statements. If a statement is true, provide a deductive proof. If it flase, provide a counterexample.
If m and n are even integers, then mn is divisible by 4.(Hint represent even numbers as 2n, and odd numbers as 2n+1)
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If a diagonal is drawn in a quadrilateral, then the two triangles created have equal areas.
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Consider 3 numbers, a,b and c, which are all integers. If ab = c, then c d" a.
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