Posted by Cindy on January 29, 2009
Anyone remember Circumference = 3.1416 x diameter? We had such a wonderful math lesson to understand this yesterday. The lesson was inspired from Family Math, pg. 97.
Taking several sized lids, I asked the kiddos to trace five different lids on a piece of plain legal-sized paper. Using a centimeter tape measure, I asked them to measure the circumference and diameter of each lid and jot that down on their papers beside the appropriate drawing.
Using their measurements, I held my fingers on the tape measure to show the circumference and diameter of each lid. I asked them to think about what they noticed that was similar about each of the measurements. (The diameter is always about 1/3 of the circumference. You can show this by folding the tape measure in thirds each time.)
Once they saw this “almost 1/3″ measurement concretely, I told them there was a way to figure out the circumference accurately every single time. All they need to know is the diameter of the circle. I secretly held a calculator and asked them to give me the diameter of several of their lids. I would multiply the diameter by Pi (3.1416) and get their circumference measurement every time.
This, piqued their interest of course, and they couldn’t wait to find out the magic trick. So, I showed them the formula C = (Pi)d (I don’t know how to make the Pi sign on the computer!) and allowed them to use the calculator to find several circumferences around the house.
They were so excited to tell their Dad that they will be able to help him decide what size tire he needs to buy the next time a giant tractor tire needs to be bought. 
Posted by Cindy on January 2, 2009
I meant to put this post up before Christmas break – oops!
I hope you aren’t getting bored with all the fun math we’ve been doing from Hardhatting in a Geo-World. I just can’t help sharing what has been a GREAT math & science unit! If you are getting bored, you’ll be glad to know this is the last post! The other posts can be found here and here.
We did one last lesson on bridges. This demonstrated the importance of strong anchors for a suspension bridge to be strong. (Yes, that’s our art table. We needed to place thumbtacks somewhere and the art table did the job. Yes, those are baby feet standing on the art table. He wants to be part of every activity we do!)
We also did a couple of thought-provoking activities concerning geometric shapes. Do you know if you’re a square, tall rectangle or short rectangle? We do! Just measure your height and arm span to find out. Equal measurements mean you are a square. Longer height than arm span makes you a tall rectangle, while shorter height than arm span makes you a short rectangle.
And this activity involved predicting shapes when circles were attached and cut in various ways.
As of January 5th, we’re back on our regular math schedule – three days per week of textbook, two days of living math/problem solving/logic. I’ll continue to share living math ideas, but they won’t come quite as frequently. Until then, happy math lessons!
Posted by Cindy on December 5, 2008
We are having SO much fun with this book! A little break from the regular math schedule has turned out to include such exciting math and science that my kids are actually asking to do more.
Here are some photos from one of this week’s investigations….
Cylinder structures – Using various sized cardboard tubes and homemade paper cylinders, the kids had to estimate and find out how many books each cylinder would hold. Their estimations and actual results were kept on a data sheet provided in the book. We then went on to talk about why cylinders are so strong, why certain heights might be better than others and where in creation and the man-made world we find the use of cylinders.
I’ve also recently discovered a wonderful blog called Think! that offers weekly math/science/art related challenges for children. To go along with the math investigations, I gave the kids this challenge. Using only 12 straws, 12″ of tape and a pair of scissors, they had to create a structure that would hold an egg at least 1″ off the ground. No tape was allowed to adhere the structure to the surface or the egg to the structure. Fun!
Caleb’s structure.
Mahayla’s structure.
Today, math was in the form of a cookie baking day in preparation for our annual cookie baking and exchange party at my mom’s house tomorrow. I’ll probably post pictures and few recipes soon. Have a wonderful weekend!
Posted by Cindy on November 10, 2008
October/November = lots of falling leaves and lots of candy. What better to do with both of those things? Math, of course! 
)
Whether you have extra M&M’s, Skittles, Smarties, Runts, or just a big bunch of assorted candy bars, take a few minutes to turn those sweets into more than cavities. Even little bitty ones can sort candy, place the pieces on a blank grid, then color a bar graph. As the kiddos get bigger, all the more fun they can have graphing their candy. Here’s a post from last year about how we used M&M’s to do all sorts of graphs. This year, we did some candy graphing, but not quite as in depth as last year.
And don’t forget all those autumn leaves! Make a nature walk even more productive by collecting a sack of leaves to sort and graph.
Literal or concrete graphs are not only fun, but help younger ones understand better what a graph on paper represents.
After making the concrete graphs, my children jotted the information and used centimeter grid paper to design their own graphs.
Happy graphing!
Posted by Cindy on October 29, 2008
It was COLD in Central KY yesterday. The nature walk part of our study was rather short – a quick trip down to the creek bed to collect a variety of leaves. But once we got home – the learning and fun began!
We started with a review discussion about the purpose of leaves and why they change colors. After a bit of struggle getting everyone to pay attention during the discussion, I announced there would be a test later in the day. (Yep, that meant I had to come up with some sort of test on leaves! In all that spare time I have, you know. Lucky for me, I was able to find this quiz online.) I don’t do tests very often, but it was just the thing needed today to turn their attention back toward our discussion.
Math was next on the list. Using a few of the leaves each, the kids had to find the perimeter of the leaves in inches and centimeters. Then had to find the area in square inches, square centimeters and an unknown square unit. Yarn and a measuring tape made finding the perimeter easy.
The area in square inches was found using one-inch tiles. A one-inch grid could be used as well.
We used cemtimeter grid paper for finding the area in square centimeters. (Simply trace the leaf and count the full squares inside the leaf. We estimated the half and quarter filled squares to add more area. For instance, if there were two halves, we would count them as one. If there was a square about 3/4 full and another 1/4 full, we combined them as one.)
Graph paper was used to find an unknown square unit. We talked about smaller units making for more accurate measurments.
Finally, we used Melissa’s idea of creating leaf bursts for an art activity to add to the nature notebooks.
