October 19, 2008

Pictoral Subtraction

A couple ways to learn subtraction with pictures.

My second-grader's school is using Everyday Math "triangle fact cards" like this to review subtraction facts. You cover one corner and ask an addition or subtraction question depending on whether the dot is covered. One card tests three facts, and picking corners at random gives you a nice 2/3 bias toward drilling the harder subtraction facts. The triangle shows how addition and subtraction are related, so it's a nice drill.

Of course, there is only so much you can drill, so this morning over breakfast, we have been practicing addition and subtraction in-disguise while learning some geometry. Here is what we've been doing:

Draw any connect-the dot picture. The only rules are that anywhere a line begins, ends, or crosses another line, you have to have a dot. Here's a picture I drew.

This picture has seven dots and nine lines. It divides the paper into five regions (if you cut along every line, you would have five pieces), and there are two separate islands (components) of dots connected by lines.

We add the dots and regions, and subtract the lines and islands.

 +7 dots +5 regions -9 lines -2 components =1 total
.

The kids have been making crazier and crazier pictures all morning, adding up all the numbers. They are convinced that if they make a picture crazy enough, they can find one that doesn't come out to one.

They haven't found one yet, but they have practiced a lot of subtraction, and it is very easy for me to check their work, because if it doesn't come out to one, they have done something wrong, thanks to Euler's Law :-). Here are a couple more links on Euler's Law.

Posted by David at October 19, 2008 09:38 AM

David,

My feed reader showed me the complete contents of this posting. I'm assuming this is in response to my previous comment, so thank you.

--Samir

Posted by: Samir at October 19, 2008 08:00 PM

You're welcome! I changed it but hadn't tested it, so I didn't want to promise ahead of time.

Posted by: David at October 20, 2008 04:00 PM