1. MathOnMonday® Presents: Building Math Courage® Dirk M. Horton dirk@mathonmonday.com A program designed for Adults or Kids who have found learning math in the traditional classroom boring or difficult! Mental Math Problem Solving Building A Dog Pyramid

2. The Dog Pyramid Patte dreamed about being a dog trainer. When she was 1 she dreamed about seeing a dog stand on his paws.

3. The Dog Pyramid When she was 3 she dreamed about seeing a dog pyramid. Do you see a pattern? 1212 Total Dogs 1+2 = 3

4. The Dog Pyramid When she was 6 she dreamed about seeing a another dog pyramid. Do you see a pattern? “woof” I Ruv Ru! 123123 Total Dogs 1+2+3 = 6

5. Total Dogs = 1+2+3+4 = 10 The Dog Pyramid Patte dreamed about the last dog pyramid when she was 10. Predict how many dogs were in the dream? Patte When Patte dreamed about winning the ribbon and saw her own dog fluff holding all the dogs up, I knew she was going to be a dog trainer! 12341234

6. Pyramids With Abacus Patte decided to use the abacus to make pyramids of 3,4,5 height to see if she could discover the rule that would tell her how many dogs she would need for any height. Adding 1+2+3 = (1+3)x3 ÷ 2 = 6 1234512345 Adding 1+2+3+4= (1+4)x4÷2 = 10 1234512345 Adding 1 to 5=(1+5)x5÷2 = 15 1234512345 Using the abacus, Patte realized that the pyramid problem was the same as adding n consecutive numbers! She also found an easy way to add these numbers: Sum of N consecutive Numbers = Nx(first + last) ÷ 2 Patte was ready to take the 9 row problem! 1234512345

7. Sum N Consecutive Numbers= Nx(first + last) ÷ 2 123456789123456789 Sum 1 to 9 = 9x(1 + 9) ÷ 2 = 45 Pyramids With Abacus

8. High π, Patte! You learned a good lesson. Play-Ponder-Pattern works for you! Remember by visualizing the abacus, you can add consecutive numbers quickly. Can you add the numbers from: 1 to 100?