Welcome to I Love Math 2013
Welcome! I Love Math Day is coming up on February 14. In the weeks between now and then, Middle School students will work in small teams to solve challenging problems. They will be given one week to solve each problem and prepare a solution to submit to the judges.
By way of this blog we encourage all school families to read the problems and join in the fun. We hope parents and students at all grades will find ways to talk about these problems, puzzle over them, and enjoy the pursuit together. The first problem for this year asks students to recognize and ponder patterns that emerge when specific strings of numbers are added together. You can read the problem below.
By way of this blog we encourage all school families to read the problems and join in the fun. We hope parents and students at all grades will find ways to talk about these problems, puzzle over them, and enjoy the pursuit together. The first problem for this year asks students to recognize and ponder patterns that emerge when specific strings of numbers are added together. You can read the problem below.
Feel free to peruse older posts to see what went on last year as part of Mustard Seed School's I Love Math tradition. You will see some of the creative solutions to problems students worked on last year.
The problems will be made available to the school community with a small lag. Middle School students have already begun their work and will be turning in their submissions shortly. Parents and school families are invited to work on these problem too, and turn in a solution if they like. Please email Mr. Lawrence with any solutions. Also please email Mr. Lawrence with any questions or comments (glawrence@mustardseedschool.org).
The problems will be made available to the school community with a small lag. Middle School students have already begun their work and will be turning in their submissions shortly. Parents and school families are invited to work on these problem too, and turn in a solution if they like. Please email Mr. Lawrence with any solutions. Also please email Mr. Lawrence with any questions or comments (glawrence@mustardseedschool.org).
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The Sums of
Sequential Numbers
When you add up sequential numbers, something interesting
seems to happen:
1 = 1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 = 9
1 + 2 + 3 + 4 + 3 + 2 + 1 = ________ (you
do the math)
1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = ________ (well?)
Check 3 or 4 more. Can you predict each sum in advance?
Go ahead and do the sums.
What do you notice?
Make as many observations as you can.
For a sequence like this, what will the sum always
be? Will it always be a square number? Find a way to show that it will always work (in other words, find a way
to convince a skeptic.)
I look forward to hearing from you! Enjoy. Mr. Lawrence
