Sums of Consecutive Numbers Puzzle (VIDEO!)

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?

Sums of Consecutives

• ON-LINE SHORT COURSES!

  QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

  Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)

  CHECK OUT: www.gdaymath.com

• Books

  • Thinking Mathematics! (TEN VOLUMES)
  • Solve This: Mathematical Activities for Students and Clubs
  • Encyclopedia of Mathematics
  • Geometry I & II

• Get in touch

  Email: tanton.math@gmail.com