Teaching Math: Grades 9-12: Reasoning and Proof


	Exploring Reasoning and Proof


	Introduction \| Triangular and Square Numbers \| Conjecturing with Algebraic Symbols \| Proving the Conjecture \| Reflection Questions \| Summary \| Your Journal

Here is our conjecture, n (n + 1) / 2 + (n + 1) (n + 2) / 2 = (n + 1)².

Now work on your own to prove this conjecture, when you are ready, select "Show Answer" to see our response.

1. Evaluate the expression.

Sample Answer: n (n + 1) / 2 + (n + 1) (n + 2) / 2 = (n² + n + n² + n + 2n + 2) / 2

2. Simplify.

Sample Answer: = (2n² + 4n + 2) / 2

3. Divide by 2.

Sample Answer:

= n² + 2n + 1

4. This can be written as (n + 1)(n + 1) or (n + 1)², which is a square number.

We have proven our conjecture.




		Teaching Math Home \| Grades 9-12 \| Reasoning and Proof \| Site Map \| © \|

| | | | |