Visualpatterns.org is a website that was created in 2013 by Fawn Nguyen, a California math teacher. I have been using these patterns with my 8th graders since I discovered them two years ago. For each pattern, students are given the answer to step 43 and are challenged to find the equation for the pattern. If your students have never studied a visual pattern before, you may want to check out this post by Fawn Nguyen about how she used a visual pattern with a class for the first time.
- I see the perimeter first, so step n has 4n for perimeter.
- Then I see 1 fewer columns than the step number inside, each column has n toothpicks, so n(n-1).
- The rows are the same as the columns, so I just multiply what I have for columns by 2.
- My equation is: T = 4n + 2[n(n-1)].
- I see the number of columns is always 1 more than the step number, and each column has the same number of toothpicks as step number, so I have n(n+1).
- This is true for the rows also, so I just multiply this quantity by 2 to get T = 2[n(n+1)].
- I used an input/output table to find the common differences to get T = 2n^2 + 2n