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MathOnMonday® Presents:
Building Math Courage®
Dirk M. [email protected]
A program designed for Adults or Kids who have found learning math in the traditional classroom boring or difficult!
Mental Math Problem SolvingBuilding A Dog Pyramid
The Dog PyramidPatte dreamed about being a dog trainer. When she was 1 she dreamed about seeing a dog stand on his paws.
The Dog PyramidWhen she was 3 she dreamed about seeing a dog pyramid. Do you see a pattern?
12
Total Dogs1+2
=3
The Dog PyramidWhen she was 6 she dreamed about seeing a another dog pyramid. Do you see a pattern?
“woof”I Ruv Ru!
123
Total Dogs
1+2+3=6
Total Dogs=
1+2+3+4=
10
The Dog PyramidPatte 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!
1234
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
12345
Adding 1+2+3+4= (1+4)x4÷2 = 10
12345
Adding 1 to 5=(1+5)x5÷2 = 15
12345
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!
12345
Sum N Consecutive Numbers= Nx(first + last) ÷ 2
123456789
Sum 1 to 9 = 9x(1 + 9) ÷ 2 = 45
Pyramids With Abacus
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?
