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. 

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!

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!

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!

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.

Scarecrow Measurement Man

Candy Corn Triangular Number Pattern

Insect and Spider Problem Solving

And these are on our to-do list….

~Area and Perimeter of Leaves  (I’m thinking of tying this into a nature study day??)

~Coordinate Graph Jack-o-lantern

Go have some fun with math this month!

1.) Living math really is thoughtful, meaningful math.

2.) Living math isn’t hard to implement at all.

Here are a few of our January/February activities with links…

This Grab the Candy Game allows the kids to practice coordinate graphing and record keeping.  Valentine Battleship is another version of a coordinate graphing game.

How Many Different Ways Can You Make the Word Snow? is a quick activity to encourage problem solving and critical thinking.  This Heart Paths sheet is similar, but requires an extra “rule” to make the kiddos think a bit harder.

These Candy Heart Patterns are a little harder than they first seem.  I gave these to my 5th grader as “fun filler” and she realized half-way through that she hadn’t thought the pattern through completely!

Glyphs are pictures children make based on a legend or key of codes.  Not only does it reinforce problem solving, critical thinking and organization skills, but mapping as well.  Here’s a link to the Snowman Glyph activity we used.

These Symmetrical Heart Masks reinforced the concept of symmetry, as well as creativity.

This President’s Day activity is going to require charting and creating a graph.

Even this worksheet of Valentine Word Problems is a fun, seasonal way to change the pace from a textbook.

There are a few more activities we’ve done or have planned to do, but I’ll let you find them for yourself at MathWire – an awesome site for living math ideas!

When the activities are quick, I’ll do several in one day.

As for living literature, we’ve checked out this series of books from the library to go along with our Medieval Unit.  Some of them are better than the others, but they’ll go along well with our unit.

Sir Cumference and the First Roundtable: A Math Adventure

Sir Cumference and the Sword in the Cone: A Math Adventure

Sir Cumference and the Great Knight of Angleland

Sir Cumference and the Dragon of Pi

Sir Cumference and the Isle of Immeter

I’d love to hear about your living math learning!  If you share on your blog, please let me know so I can come visit!  Happy math times!

I hated math when I wad a kid.  Hated it.  It didn’t make much sense to me, I had a hard time memorizing facts, and my teacher’s didn’t spend much time helping me to understand.  I used to nearly have anxiety attacks in middle school when the teacher put this sort of problem on the board.  “If a train from NY is traveling 60 mph……”  You probably didn’t care much for those problems either, did you? 

I remember my poor Dad spending countless hours trying to teach the concept of fractions to me in third grade, only to have every lesson end in tears and me leaving the table saying, “I just don’t get it!”  Surprisingly, I made very good grades in spite of the disdain for math.  And even though I hated every minute of it, I survived.

Fast forward to my early twenties when I started teaching.  What was one of the subjects I had to teach?  Math!  But, I wasn’t afraid.  I could handle elementary math, couldn’t I?  Imagine my surprise (and my Dad’s) when math actually became one of my favorite subjects to teach!!  You see, I had learned to teach with manipulatives, something my teachers had never given me.  What a difference it made!  I was finally able to understand fractions AND I was able to teach someone else to understand them!  Wow!

So, needless to say, I’m a big believer in teaching math with manipulatives.  There’s a connection made in the brain that allows children (and adults) to “see” math and to understand the why’s of math rules.  I believe teaching math with manipulatives is a key element to making math a living subject. And just why would math need to be a living subject?  The same reason we try to make history or science living subjects – because “living” subjects draw people in.  They give a relevance to learning that means more than facts on paper.  They make heart and mind connections so that we hopefully love what we’re learning.  And they give whole pictures of a topic so the “pieces” fit together better.

Besides manipulatives, what else makes math living?  A Charlotte Mason education certainly includes good books, right?  Math can include living books, too!   There is so much wonderful math literature out there!  I’ve started a  small library for myself (some of which I pictured below),  but most of the books we’ve used have been easy to find at our library.  Below are three websites that list many titles you might like to check out.

List of living math books

Penny Gardner’s List of Living Math Literature

Living Math Books Sorted By Mathmatical Concept

Including literature during a math lesson is very easy.  I wrote a post not too long ago about using One Grain of Rice for a lesson in doubling numbers.  Some other very simple ideas would be…

*Reading The Doorbell Rang then using manipulatives to make fair shares.

*Reading How Big is a Foot and comparing measurments based on your feet and your child’s feet.  Then talking about the necessity of a standard unit of measurement.

*Reading Alexander, Who Used to be Rich Last Sunday then working on a skill like money subtraction with real coins.

The ideas are endless, but well worth the thought  because your children will thrive on such exciting activities.  The greatest part is that you probably don’t have to really work that hard.  Doing a Google search on “(name of book) activities” will most likely place activity ideas right in front of you.  Here are some great websites to get you started.

Mathwire Literature Connections

Winter Math Activities – great ideas, with a couple tied to literature

NCTM Ideas

Linda’s Learning Links

Math and Literature Idea Bank from Math Cats

Finally, another way to make math living for your children is to give them real tasks to do.  Let them be part of budgeting, coupons, planning the garden plot, balancing the checkbook, deciding how much grass seed to buy, recipe conversions, bill paying, measuring air in the tires…………..As my children get older, I give them just a bit more responsibilty with real-life tasks in hopes that they will be fully able to do them on their own before leaving my house.  They appreciate being included and I reap the benefit of capable helpers!

Am I advocating never opening a math workbook or never working on math drills.  Absolutely not.  My philosophy is “varied learning makes for well-rounded kids”.  I’m simply suggesting that math doesn’t have to be boring and it doesn’t have to come from a workbook.  I have friends who worry about skipping lessons in the math workbook, so they might add living lessons to the hour of math the workbook requires.  Please promise me that if you plan to try some living math, you’ll tear up that day’s worksheet and pitch it in the garbage.  (Gasp – it really is okay to throw workbook pages away.  I promise.)  Living math won’t be nearly as exciting if it’s on top of “regular” lessons.  

May you and your children find math to be exciting and worthwhile!  I would love to hear some of your favorite math books and how you used them in your homeschool!!

Have you ever read One Grain of Rice by Demi?  Good book!  We read it again the other day and my 5th grader did some fun math activities to go along with the story.

I found the activities and worksheets at this site.

After reading the story, Mahayla had to chart the number of grains of rice the raja gave away.  Since the numbers became huge, I let her use a calculator.

Next, she had to determine how many cups of rice were given away on a few of the days, as well as the weight of the rice and number of people it would feed.

Fun math, real-world type stuff, and lots of computation!  Who could ask for more?