Today we used the digits 1,2,3,4,5, and 6 to complete the equilateral triangle so that all legs had equivalent sums. We then examined the number arrangements and searched for patterns.
- Work through the Fascinating Triangle Handout/Prompts again, but this time use the digits3,5,7,9,11, and 13.
- How might you arrange the patterns to create equal legs of the triangle?
- What sums were you able to create?
- Were you able to apply the patterns discussed in class with the new digits? Explain why and how.
- Try1, 2 , 4, 8, 9 , 11…. ? What conjecture (algorithm/rule) might you generate to explain the patterns found in Fascinating Triangles?
HINT: If you are struggling here is a review from class=
What do 1, 3, 5, 7, 11, 13 have in common with 1, 2, 3, 4, 5, 6 and 2, 4, 6, 8, 10, 12? Six consecutive numbers can be arranged on the legs of the triangle with each leg having the same sum. There will be four solutions.
We determined Monday evening that the conjecture for 1-6 is H1 + H2 + L1 (6,5,1=12) is the highest sum possible and that L1 + L2 + H1 = (1,2,6 = 9) is the lowest sum possible.