April 24, 2009 - Living Math with Area and Perimeter
Studying area is a great topic for comparing ways of teaching math. In the "old days" before my living math transformation, I would've breezed over the diagrams in the book as quickly as possible to get to the "real lesson" -- the formula A= l x w so we can work the problems.
But not the new improved living math Jimmie. No, I now realize that jumping too quickly to an abstract, albeit simple, formula does not foster true mathematical comprehension.
So we learned about surface area the hands-on way
with lots and lots of squares. It seems that doing living math in our house requires lots of colored squares. (It's a good thing that I have a real fetish for paper. I have all colors and thicknesses, so I'm never at a loss for something to cut up into manipulatives.)
Another great hands on tool was laminated graph paper and Vis-a-vis pens. We drew squares and irregular shapes and then counted the area and measured perimeter. We rolled a die for numbers of sides and then drew figures to see who could create the object with the longest perimeter or largest area. We marveled over shapes with identical areas but vastly different perimeters.
By the way, my favorite place for graph paper is Incompetech's PDF generaotor which you can set to whatever size you want. We chose 1 centimeter squares and 1 inch squares.
Living Math Hint --One thing I've discovered is that the "game" aspect doesn't have to be thoroughly planned out. Just spinning a spinner or dealing cards seems to make the math activity a lot more motivating.
I'm going to be honest with you. You and I know to multiply the number of rows and the number of columns to find out how many squares total. Well, I thought that would be painfully obvious to Sprite as well. But it was not immediately obvious to her. I let her count a gajillion squares until I tried to nudge her towards a simpler way than counting. It was still a bit hard to grasp. So do you know what I did? I stopped doing math that day before any frustration set in. And the NEXT day, we played a different game with the squares. She needed more experiences with the idea of area to really understand how length times width gives us the answer. And eventually she SAW the connection.
Later we used small boxes and traced all six sides onto the graph paper to determine, hands-on style, the surface area of a three -dimensional form.
Then we moved to circles a la lids. The green yarn was used to measure the circumference and diameter of each disc.
Can you see that Sprite's page has P = in front of the strand of yarn? Yes, that means perimeter. I told her to measure the distance around and to mark it on her paper. She used the word she had learned previously. And why not? Circumference is just the perimeter of a circle, isn't it? The technical word can wait.
This is living math in which we do not burden children with technical jargon unless the words are necessary or the child asks. Sprite asked me what to call the distance across the circle since she had no handy word for it. Thus she has D= on her paper for diameter.
Supposedly we could compare the ratios of the diameters and circumferences and get Pi, but I think our yarn was too stretchy and thus our figures were not accurate. So we left that for another lesson.
Comments
April 25, 2009 - Untitled Comment
Posted by Kris @ Weird, Unsocialized Homeschoolers
This is great! My younger two are just starting with area and my oldest is really starting to hate the word Pi. lol I think they can all get something useful from this post.
I was all about living math for awhile, then, I got lazy because, like you've said, it's certainly not as easy as pulling out a workbook. However, I can see where it is so much more meaningful. You're inspiring me to go more that direction again.
April 25, 2009 - Good reminder
Posted by Jennifer
Thanks for the good reminder of using manipulatives. I don't think we ever outgrow the need for that when learning a new concept. I know I sometimes need something to look at in order to understand something new.
Just yesterday my son told me he forgot his subtraction facts when working on a drill worksheet (he's only up to 4's). I know he understands the concept of subtraction from our kitchen math sessions. Something just got lost in the drill. So I went back to showing him on his fingers (or Easter Candy, which we still have a ton left over!).
http://onlychildadventures.blogspot.com/
April 25, 2009 - Untitled Comment
Posted by CherylinMA
Jimmie,
I love this hands-on math project! We enjoy the Sir Cumference books which go nicely with your lessons. Your reminder to be patient and wait for our children to "see" the solution for themselves is very encouraging to me. Thank you!!!
Cheryl
April 29, 2009 - Untitled Comment
Posted by Becky - Golden Acorn Homeschool
Great job! I love to see hands-on approaches to math that integrate it with real life. :-)
April 29, 2009 - Untitled Comment
Posted by Dana @ School For Us
Sounds like a GREAT hands-on math lesson!
Dana, www.alexml.blogspot.com
May 1, 2009 - Living Math
Posted by gowestx4
What a great way to teach math. I need to get better at these types of things. showing is better than telling any day.
May 1, 2009 - Untitled Comment
Posted by Denise
These are great ideas. I also like to extend the "squares" concept to include volume by using small cubic blocks. Around here, the cheapest area manipulative is a box of sugar cubes. Great excuse to have a cup of tea while we play around with math!
--Denise at Let's Play Math! blog
http://letsplaymath.wordpress.com/
May 2, 2009 - Untitled Comment
Posted by Anonymous
Love this. I've got it saved to refer back to, because I'm going to try to transition to more living math & you give great examples! ¢¾
Jamie
www.jamiescottage.com
May 4, 2009 - Untitled Comment
Posted by Anonymous
Because DD is so skilled in math and I frequently feel we get behind, I get so caught up in doing the quick textbook lesson that I neglect to make it hands-on. Thank you for the reminder of the importance of manipulatives!
Makita
4twinklingstars.blogspot.com
May 26, 2009 - Living Math with Perimeter
Posted by Anonymous
Thank you so much for this. Sometimes I find myself seeking the quickest option (especially if I think we're behind). I needed this as a reminder as to why I chose to homeschool!!
Di from Australia
