# Math Explained Part 2

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More Lessons for Math Trivia

Math Worksheets

Sums of Consecutive Numbers Puzzle
7 = 3+4 and 30 = 9+10+11. Which numbers are the sum of two or more consecutive counting numbers? (For fun, try 12 and 15 and 32).
We answer this puzzle in this video using pictures of dots (though feel free to use algebra instead if you don't like pictures!) And then we can ask ... Which numbers are the sum of three or more consecutive counting numbers?
Fractions take up No Space: Rationals Have Measure Zero
How much space do the fractions take up on the number line? NONE! In this video we add up pieces of ribbon to prove that the fractions have "measure zero." It is all very easy and very perturbing because it is easy!
[This video does assume familiarity with the geometric series formula - so you might want to watch a video on that too. I do that with paper tearing!]

Fitting Exponential Functions to Data
A standard unit in an algebra II or pre-calculus course is to find a exponential function that fits two data points. There is a hard way to do this, and there is an easy way - just write down the answer! I show you how.
Two Surprising Fibonacci Puzzles
Here are two very different puzzles that seem to connect with the Fibonacci numbers in a surprising way: The language of ABEEBA and ordered parition numbers. This video just states and plays with the puzzles. The answer video gives the answers!

Fibonacci Surprise ANSWERS
Here are the answers to the two surprising Fibonacci puzzlers of the previous video. (Watch that first!)

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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