Subtraction Problems, Russian Style
A stick has two ends. If you cut off one end, how many ends will the stick have left?
This pre-kindergarten math problem was given to me by Maxim Kazarian who lives in Moscow, Russia. That got me thinking about math education in the US. Actually, just about anything can get me thinking about education in our country. One of our math education patterns is to provide simplified templates and to train kids to plug numbers into them without thinking.
Math education should be about thinking. We need to give kids a lot of math problems that do not fit into standard templates, in order to encourage creative thinking. Here is another puzzle from Maxim:
A square has four corners. If we cut one corner off, how many corners will the remaining figure have?
I invite my readers to invent additional problems that sound as if a subtraction by one is needed, when, in fact, it is not. Here is my contribution:
Anna had two sons. One son grew up and moved away. How many sons does Anna have now?
I recently trimmed my mustache. This morning when I kissed my wife, she asked, “How long will your hairs remain so prickly?”
Inspired by the stick problem in your blog post, I offered to cut off the sharp ends immediately!4 April 2009, 6:26 am
She said this would not be necessary…
There’s the American classic: 10 crows were sitting on a fence. A farmer shot one. How many were left?11 April 2009, 3:41 pm
My friend Yulia Yelkhimova gave me the following puzzle:16 April 2009, 9:37 pm
Jonh had four candles and lit them all up. Then he changed his mind and
blew out one of the candles. How many candles has he left?
One of my favorites: a 100 pounds of mushrooms, that were 99% water, got a bit dehydrated, and became 98% water. What is their weight now?17 April 2009, 4:56 am
Math Teachers at Play #5 « Let’s Play Math!:
[…] Khovanova poses a few Subtraction Problems, Russian Style. […]17 April 2009, 6:15 am
Tanya Khovanova’s Math Blog » Blog Archive » Multiplication Problems:
[…] many people liked the puzzles I posted in Subtraction Problems, Russian Style, that I decided to present a similar collection of multiplication and division puzzles. These two […]17 April 2009, 1:07 pm
If there are five apples, and you take away one, how many do you have?23 April 2009, 10:03 am
A rancher has 30 head of cattle standing in a field, when suddenly a bolt of lightning kills all but 1 of them. How many head of cattle are left standing?23 April 2009, 10:05 am
Zdravstvuiyte, Tanya23 August 2009, 1:46 pm
I really enjoy your blog. Being a mom of 3 kids, I am very concerned with a level of math education my kids get in school. In desperation, I started a math circle for young kids( 6-9 years old). They seem to enjoy it, as we do a lot of non-standard problems. I wonder, however, what makes a problem non-trivial? Given a problem,( that does not require specific skills), how do we determine if the problem is standard or not? Do you happen to know people who enjoy generating this type of problems, and who figured out the specific features of these problems?
Subtraction and Multiplication Problems by Tanya Khovanova « Konstantin’s Weblog:
[…] presents on her blog. It would be interesting to know how high school kids perform on the Subtraction and Multiplication Problems now compared to 50 years […]27 September 2009, 8:35 am
hello19 September 2010, 12:12 pm
please send me free ebook and problems and guestions exams ( of coure with solutions ) about real analysis , abstract algebra , functional analysis , probability theory and toplogy
very very very thank a lot
@misha, I did the math. The mushroom weight M is 1, the water weight W is is 99. The weight of the mushroom is constant as the water weight decreases changing the percentage. through some algebra we can show that 2% of the new weight must be 1lb, and therefore the total weight is 50 lbs.13 January 2011, 12:22 am
A pond contains 100% goldfish. I take one goldfish out of the pond. How many % goldfish does the pond contain now?22 March 2011, 12:29 pm