Monday, November 24, 2008

Marcus's new trick

Marcus heard about square roots, that they were tricky and hard. He wanted in. So I taught him a trick - if you know that a number is a square (16, 121, 5041), then it is not impossible to work out the square root in your head. Squares only end in 1, 4, 5, 6, 9, or 0. If it ends in 1, the square root ends in 1 or 9. If it ends in 4, the square root ends in 2 or 8. If it ends in 5, the square root ends in 5. If it ends in 6, the square root ends in 4 or 6. If it ends in 9, the square root ends in 3. And if it ends in 0, the square root ends in 0. He memorised this list more or less instantly.

So, if I say to him 5041, he knows it ends in 1 or 9. He can do 60 x 60, 70 x 70, 80 x 80 pretty easily, so he can find a range to look in. 5041 is between 4900 and 6400, so the root must be between 70 and 80. Its pretty close to 4900, so chances are that out of 71 or 79, the answer will be 71.

It takes me about five minutes (while driving) to work out a question for him. It takes him about 25 seconds to work out the answer. It only works with perfect squares, so it is not a particularly useful formula in daily life, but its a neat number trick.


Wendy said...

Wow, this is so cool. Marcus is so bright! I don't have tons of experience with kids, just use my own as a benchmark. My oldest is 5 and we're still working on counting by 10's. But the poor dear child is handicapped by his math-challenged mother who is a mental midget in that department.

Would you say Marcus has natural math skill or would you say this is a by-product of his learning environment? Or both?

chris rees said...

I think its natural. His home learning environment pretty much consists of Elf and I being prepared to take some time to answer questions, and also ask questions, and then listen to the answers, so that can only help. I was good at maths but not in a jaw-dropping way.

chris rees said...

Following up this post 9 years later; Marcus has proved to be genuinely jaw-droppingly good at Maths. He turns 16 in 5 weeks, and shortly after will start grade 11, already having completed Grade 12 maths. So he'll be doing maths at the university under their High Achievers Porgram [well we are waiting for conformation of that but the application is in. He got the highest possible award for Grade 12 maths, 'Exceptional Achievement'.