Homemade Arithmetic Manipulatives for Homeschooling

I'm planning on homeschooling my kids. In fact, I say that I'm already homeschooling my children, as in my area it is nearly unheard of to have a child who is 2 or older be at home instead of in nursery/daycare. Having a 4 year old at home? Well, there is public school preschool already for children aged 3 and up, and keeping a 4 year old at home raises quite a few eyebrows, indeed, when people see him with me during normal school hours.
So yes, I consider myself to be homeschooling already, as I have a 2 and a 4 year old child at home with me full time; I am the one providing all their educational needs.
At this age, there isn't much schooling that needs to be done. Kids pick up so much just from their every day life; their head gets full of knowledge just from living life fully and the explanations about the where's, why's and how's that inquisitive children's minds are always asking every day of their lives. Formal schooling certainly isn't necessary during the preschool years.

A lot about the unschooling homeschooling philosophy speaks to me. Unschoolers believe that a child naturally is motivated to learn, and by forcing them to learn by having a rigid learning schedule, etc... a child's thirst to learn is quashed. Unschoolers believe in child led learning, not parent led learning. When the child expresses an interest in something, the parents provide the material and help to learn it, but not before. If the child doesn't show an interest in the subject, the parents won't require him to learn it.

I'm not completely in the unschooling camp; there are things that I'd require that my child learn, even if they weren't particularly interested in it, as I think there are some basics that must be learned in order to be a fully functioning adult in society, but the child led learning is something that I think is beautiful.

And so, for a while, Lee and I were learning the alphabet together, identifying and writing letters, learning the sounds the letters made, and beginning to put together basic words. But lately, Lee has shown that he really wants to learn arithmetic. I'd be standing there washing the dishes, the kids coloring pictures, and Lee would ask me "Mommy, how much is 4 and 2?" And I'd stop what I was doing, show him how to figure it out using his fingers, and then go back to washing the dishes. 5 minutes later- "Mommy, how much is 6 and 3?" And again, I'd show him how to figure it out.
At least a few times every single day, Lee has been asking me arithmetic questions. Even though some might say 4 years old is a drop young for teaching subtraction and addition, Lee has shown a strong interest in learning the subject, so I decided the time is ripe to teach him math.

Here is a tool that I made to teach my son arithmetic. It cost me absolutely nothing to make, and with its visual aids, is working wonders to teach my son basic arithmetic concepts.
What do you need to make these arithmetic manipulatives?
Cardboard- any kind will do. I used corrugated cardboard I found near the dumpster; old cereal boxes would also work fine.
Apricot, plum or peach pits, cleaned well. Or soda bottle caps, small pebbles, dried beans, etc...  Any small things that are a uniform size that you can get in large quantities cheaply or free. I used apricot pits because they come out cleanly from apricots, and I had a bunch saved from apricots I bought cheaply in season.
Colored markers. (I used markers I got for free from a family moving to Australia and emptying out their apartment; they gave me to sets when I came to pick up 30 canning jars they'd advertised on freecycle.)
A razor blade or scissors to but the cardboard.
Paper.

How to make the math manipulatives?
1. Cut out squares from the cardboard. Make a lot.
2. Write numbers 1 through 10, 15, or 20 on the cardboard squares, one number on each square. If desired, do this on both the front and the back of the squares. Ideally make more than one of each number to make the numbers easier to find.
3. Make a minus sign, a plus sign, and an equals sign on a few squares. Make a few of each, and ideally make them in a different color from the numbers to make it easier to find them and differentiate between them.
4. If using pits or pebbles, using a marker, color half the pits or pebbles one color, half another. You can use paint for this, but I found markers much easier to work with.
Thats it! Now you can use them to teach your child math.

How do you use these math manipulatives, and what is the purpose of doing so?
My purpose of using these math manipulatives with Lee is to make math more real so it is easier to visualize. I want him to be able to do addition without needing to count on his fingers. I want him at some point to be able do written arithmetic problems at some point. I want Lee to connect between visual amounts and numerals, and to learn what different math signs look like. I also want him to practice his writing numbers.
I know some people have an issue forcing a kid to use manipulatives in school when they can already do math without it, that manipulatives were "made for developmentally delayed children" and requiring kids to use manipulatives when they can do math without is just taking things a step backwards. I beg to differ. I think that if a child already knows how to do 3+4=7 on his own, he shouldn't be using manipulatives to figure it out, but if a kid is doing what Lee is doing, and constantly asking "Mommy, what is 2 and 8?" then these manipulatives can help him learn math better and improve his math skills.

How do I use these manipulatives with Lee?

First, I make two piles of apricot pits, one of each color.

I have Lee count how many apricot pits are in the first pile.

He then gets the numeral that matches the number of pits from the pile of numbers...

And places it beneath the pile of apricot pits that match the numeral.

He then counts the apricot pits in the second pile...

...finds the correct numeral in the pile of numerals...

...and places it beneath the correct pile of pits.

He then finds the plus sign...

...and puts it between both numerals...

...and then does the same with the equals sign.

We then say the equation together. 6 plus 3 equals what?

Lee then counts all the apricot pits in both piles...

...finds the correct numeral in the pile...

...and places it at the right side of the equation.

Because I'm working with Lee on learning to write his numbers (we've only worked on letters until now, so now we're starting with the basics of how to write numbers), I make dots to write out the same equation he just figured out with the manipulatives, and he traces over the dots to write his own equation. 

Once he does that, he writes his own numbers freehand.

At this point, I typically write out the equation underneath the two copies he just wrote.

If your kid already knows some basic addition with smaller numbers, you can put those equations together for him to figure out without the visual aids.

 Lee knew this was three, and found the three to put as the solution.

We then did the same thing that we did with the other equation. First he traced over the equation I wrote in dots.

Then he does it freehand. (Mistakes and all).

And then I write a copy of what he wrote underneath it.

I'm also using these manipulatives to teach subtraction. Subtraction works a bit differently.

I put out a pile of one color of apricot pits.

I then have Lee count them.

He finds the corresponding number from the pile.

He then finds the minus sign, and puts it next to the numeral.

I tell him how many we'll be subtracting from the original amount and ask him to find the number in the pile. He does, and then puts it next to the minus sign.

 After reading the equation, he takes away the number written. See Lee took 3 pits out of the pile.

We add an equals sign, then I ask him to see how many are left.

Lee sees that only 2 remain, so he finds the two from the pile of numerals, and adds that to the end of the equation, to the right of the equals sign.

  

Again, we write down the equation on a paper, first with him tracing along the dotted numerals.

  

And then he writes it free hand beneath it.

And then I write it out as well underneath it.

When we finish doing these problems and the papers get filled up, we hang them up on the refrigerator for Lee to see what he did and to be proud of himself.

Lee enjoys playing with these manipulatives so much, as does his little 2 year old brother Ike. Ike wants his own set, but I think he's still too young. Though when I asked Lee what two and one is, before Lee had a chance to respond, Ike chimed in "Fwee!" Not sure if that was just a fluke, or if he's also absorbing this by osmosis.

This makes math into a fun game for Lee, and when Lee asks me "Mommy, how much is 2 and 5?" I tell him "Do you want to take out the math game and figure it out yourself?" and he very excitedly says "Yes, Mommy! I love the math game!"

Sorry for the discolored fingers in the pictures. I had lost my first set of colored apricot pits and had to make a new one, and Lee wanted to play with the replacement ones that were freshly colored, before the marker had a chance to dry on.

If you've noticed that Lee isn't holding the marker correctly, it is something we're working on. He prefers to hold the marker in his fist, but I'm trying to teach him the proper way of holding a writing implement. He's getting there, but isn't there yet.

And no, his number writing skills aren't terrific yet. But hey, practice makes perfect! I believe in teaching kids the proper way to do things, but then letting them try it on their own and congratulating them on what they've done, even if it isn't perfect. With time, it'll get better. He's been writing numbers for a total of only a week so far, so I'm proud of what he's doing so far.

Are you homeschoolers or interested in homeschooling? What are your thoughts on unschooling? Do you believe in child led learning at all, or do you believe in having a rigid curriculum?

If you homeschool children, how do you usually teach arithmetic? With or without manipulatives? If with, do you use store bought or homemade manipulatives? 

If you think using manipulatives for teaching arithmetic is problematic, why is that? Where would be the specific issue in how I'm using them to teach Lee?

If you're a homeschooling mom, do you think you'd try out making and using manipulatives like this? Why or why not?

Sharing with WFMW, Frugal Friday.