With a pile of hearts, Eli had to figure out how many each of us would get if he divided the group into fair shares. He had to decide what to do with the leftovers, too.
We practiced the ABC’s by finding each letter printed somewhere on the hearts.
We love making concrete graphs! Eli has practiced many times with bar graphs, so this time I made sure to introduce making a circle graph.
To begin transferring concrete bar graphs to written graphs, I asked Eli to make a bar graph with his candy hearts. Then, I asked him to draw his own graph on a chalkboard. Why a chalkboard? Both because we had colored chalk to match the colors of the candy and because chalk encourages a more tactile experience than pencil and paper.
Middle and High School Lessons
This was a fun twist on measuring area. Instead of placing candy on a prepared heart to determine the area, I gave my children a small pile of candy and said, “Take a look at the pile and cut out a heart that you estimate has the correct area.” We did this a few times with different sized piles of candy to improve estimation skills.
The next several pictures show a variety of graphing and probability activities. Bar graphs, stem and plot graphs, histograms and more were created.
We also had fun placing several different numbers of each color in a bag to predict and test the probability of drawing each color.
Our day wasn’t all math related. We had fun with some science experiments, too. In the first two pictures, we experimented with the rate candy hearts dissolve in various acid and base mixtures.
The final picture shows the results of an erosion experiment (disclosure: link to my book.) We placed one heart in water and let it stand still. The second heart was placed in the same amount of water, but we shook the container for three minutes. In the end, we talked about how this models why jagged rocks eventually become small, smooth pebbles.
We literally could have gone on for a week learning with candy hearts. Look at the list of ideas we came up with at co-op!
Whether you use candy hearts or another variety of colored candy, make it a fun day once in a while!
Sadly, the formal study of economics is left out of most of the curricula I’ve run across in my 11+ years of homeschooling. An understanding of economics is EXTREMELY important as our children grow up to care for a family, learn to tithe and give, and become the financial leaders of our country.
Unless we took an economics course specifically in high school, or more likely college, I venture to say most Americans today don’t have more than a surface understanding of managing our own money – much less how the government officials (who are supposed to be accountable to their well-informed citizens) are managing our money in the larger scheme of things.
Is economics something that can only be understood and taught at the high school or college levels? No way! We should begin teaching economics principles as soon as our kids understand the worth of money.
And just how to we go about this? Homeschool Economics!
During the elementary years, we use literature to help us demonstrate some more formal economics concepts in a laid back way. I’ve shared about one of those lessons in this post about productive resources. We also try to plug in at least a few field trips that lend themselves to economics discussions – factories, a bank, a grocery store, farms, having a good conversations with any business owner. Really, just about any trip can be turned into an economics-themed trip – even a trip to a pioneer fort where you discuss trading goods.
In my quest to raise economically smart children, I’ve used many tools and come across others that are waiting in the wings for the right time. I’ve included all of them below. The * indicates those that are tried and true resources.
Math is so much fun and means so much more to little ones when it concretely builds understanding. So many times, we skip over “the tough stuff” because we think our little people can’t handle it. Below are a few activities I have done with my five-year-old to begin building two of those “tough” concepts - division and logic.
Division: The Doorbell Rang
Here’s very simple, engaging early math activity for understanding fair shares and beginning division concepts using The Doorbell Rang by Pat Hutchins.
Gather a pile of 12 “friends”. These could be bear counters (like we’ve used), stuffed animals, plastic people, or whatever other toys you have handy.
Gather 12 pieces of food. We’ve used M&M’s (because they were handy), but you could use anything – cookies, cereal pieces, crackers, grapes, popcorn – ANYTHING that your child will enjoy as a snack after the activity.
Read the story again. This time, stop each time a fair share is made in the story and act it out with your “friends” and food. For example, when the brother and sister are given 12 cookies, allow your child to fairly share the food with two of the “friends.”
When the doorbell rings, add two “friends” to your group and have your child rearrange the food for fair shares.
Keep reading and rearranging in this manner until the book is finished.
Depending the age/ability of your child, you might consider figuring how the children could continue fair shares if more children were to show up with only 12 cookies on the table. (Fractions)
You might also count the additional cookies on grandma’s tray and make a new set of fair shares with the larger number.
This is just one of many, many concrete lessons you can teach younger (or older) children using literature books. And literature is just one of many methods to make math more “living” or real. Whether you have a preschooler or older children and would like to learn more about how to add “real”, concrete and/or creative lessons into your homeschool, check out Loving Living Math.
Logic: Primarily Bears
Speaking of living math, I consider logical-mathematical activities to be part of solid math instruction. Logic can start way earlier than you think! In fact, while we had the M&M’s out, I let my 5yo use them as manipulatives in some beginning logic activities from Primarily Bears (which has logic activities using bear counters appropriate for grades K-6.)
Since logic puzzles at this age can require lots of trial and error, it gets frustrating erasing mistakes all the time. What better way to make those errors seem like no big deal (and save paper), than using manipulatives in place of a pencil!
Above left photo: Eli had to determine which colored bears sat in which part of the caves based on a logic pattern.
Above right photo: Using clues from the top of the page, he had to determine which bear played which sport. The red and green M&M’s we had been using with The Doorbell rang, served another purpose – the red meant “no” and the green meant “yes”.
Quite simply, you put a picture board in front of your child with a pile of some sort of manipulative. You read clues one by one and your child uses logical visual discrimination to determine which pictures don’t fit. He covers the pictures that don’t fit to show it’s “out”. By the last clue, your child should have all but one picture covered, showing which picture fits all the clues. Eli loves these!
In case you’re super-interested in early logic, another of my favorites is Lollipop Logic.
Snap cubes are great for teaching perimeter, area, and volume in a hands-on way. This lesson focused on volume and understanding the formula for finding volume.
Before jumping into the subject of volume, we reviewed the formulas for finding perimeter (p = 2l + 2w, or perimeter = 2x the length plus 2x the width) and area (a = l x w, or area = length times width.) If you’d like some hands on ideas for teaching perimeter and area, check out these previous posts:
After reviewing perimeter and area, I asked my son to build a 3-D rectangular structure using the snap cubes. Then I asked, “Do you think there’s a way to determine the number of cubes in your structure without counting all the cubes individually?”
“Consider that you already know how to figure out the area. Knowing the area is 2/3 of the answer!”
Of course, he figured it out quickly, but couldn’t explain the exact formula that might be used to determine rectangular volume. Out came the handy white board – yes, it’s very well-used preschool easel we’ve had for years and years. All it took was a little drawing to define the new term “height” and he came up with the formula easily (v = l x w x h, or volume = length times width times height.)
I asked my son to tear apart his structure and count each and every piece to see if his new formula worked. It did! Then, I asked him to make a few more rectangular structures using the snap cubes, working the formula, then counting each and every piece to make sure the formula works every time. It does!
Finally, I asked him to collect several boxes from around the house. Using a ruler and the formula, he had to determine the volume of each box. Guess what? He “gets” rectangular volume now and isn’t soon to forget.
Skills Covered: reading, addition/multiplication, calculator skills, problem solving, charting data
The King’s Chessboard by David Birch is a fantastic book – both for math and character training. In it, the king foolishly agrees to doubling a gift of rice everyday for the number of days on a chessboard. Because he doesn’t know about the power of doubling, he loses A LOT of rice.
Reading the book is a great way to start off a lesson on the power of doubling.
After reading, ask your child, “What if I offer to pay you 2¢/day for doing the dishes every night for 20 days? How much money would you make?
(Hint: 2¢ x 20 days = 40¢. Yes, ONLY 40¢!)
Now ask, “What if I offer to pay you 2¢ the first day and double that each day for 10 days? Would it be worth it to you?”
(Hint: Make a chart like the one pictured above and allow your child to use a calculator to double the amount each day. Remember – on the 10th day, add each day’s wages together to get the total earned over 10 days.)
“Hmmm…You think $20+ is fairly worth your effort for 10 days, huh? Well, what if I continue doubling your money until 20 days are up? Would you care to dishes nightly then?”
(Hint: Keep doubling on the chart through 20 days. Again, add all the days wages together to get the total earned over 20 days.)
“Yes? Yes? You’d like to make that deal? Let me know when you find someone willing. We’ll both go to work for him!”
A Similar Lesson
You might be interested: We did a similar lesson a few years ago using another fabulous book, One Grain of Rice.
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