# Let's Test That Conjecture: Odd and Even Numbers, Parity and Constructive Proofs

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Okay, you covered “odd” and “even” number with your students and they now know that all even numbers have a 0, 2, 4, 6 or 8 in the ones place (they don’t “end” with those digits, because numbers don’t have a “beginning” or “end,” they have “places”) and are odd if they have the digits 1, 3, 5, 7 or 9 in the ones place. All good!

But let’s ramp this up a bit: your students now know one of the basic concepts of mathematics, better known as “parity,” which gives them an opportunity to conduct an investigation: what happens when you start adding and subtracting odd and even numbers. There are “simple” investigations in this set (“Odd + Odd = Even”) or more complex ones (“Odd - Even - Even = Odd”) or just souped-up complicated statements (“Adding an odd number of even numbers equals an odd number.”) So, you hhave lots of room here to challenge kids at all levels of mathematics and linguistic sophistication.

Central to this investigation is the concept of “proof” by using examples that either support or disprove the conjecture. This is called a “constructive proof.” If the statement says “Odd + Odd + Odd = Even,” then a child creating a constructive proof would find examples that support or disprove this. In this case, the statement is incorrect, which can be proven by using the examples 1 + 1 + 1 = 3, 1 + 3 + 3 = 7 and 1 + 3 + 5 = 9. Of course, there an infinite number of examples you can construct to prove this statement false.

Comes with 40 different statements for your students to test AND complete teaching instructions!
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