Carrying: Abacus...Hallelujah!

The first time my daughter and I made it through her math without fighting....

For a creative, math resistant, art-loving kid, I highly recommend a bead frame.  This one was $5 at Tuesday Morning.  To use it on normal math, you first need to do a lot of practice with her on simple addition so she can get used to "exchanging."

Example:  Put 8 on the frame, then add 4 more.  1, 2, exchange, 3, 4.  you should have one blue bead and six yellow.  

Do that until she can start bringing you the answer in another room.  "Go add 15 plus 7 and come back."

We use it for counting money, adding with carrying, skip counting, etc.

GLORIOUS.

Teaching 1, 10, 100, 1000 with beads

Of all the materials I've tried from the land of Montessori, this particular bead material is my favorite.  I got it for $15 from Alison's Montessori.  It contains nine unit beads, nine ten bars, nine hundred squares, and one thousand cube.  They are connect nylon beads, not near the same quality as the individual bead sets, but they are sufficient for me.  They are far superior to the base ten sets at Amazon due to the weight of the material.  A typical thousand block in conventional base ten material is hollow and doesn't FEEL like 1000.

My favorite Montessori album is the one at http://www.montessoriworld.org/.  I love the simplicity of the outline.  Montessori has such interesting ideas that it's a tempting to proliferate material in her style and clutter up the curriculum.  Montessori World does not make this mistake.

Decimal quantities is taught directly after the numerals and quantities of 1-9 are mastered.

Exercise 1:  Introduce the quantities 1, 10, 100, 1000.  Encourage the child to feel the quantities and say their names, hand them to you or move them around the mat when the names are said, and finally identify them when presented alone.  What is this?  Hundred.

Exercise 2:  Once the quantities are mastered (without numerals), demonstrate going to the next hierarchy every time one passes nine. Ten units is actually one ten bar.  Ten ten bars are one hundred, and following until we get to the thousand block.  The is repeated on subsequent days until the child has mastered it.

Exercise 3:  Naming Quantities:  I call this "fetching."  Hand me two hundreds.  Good, put them back.  Now go find eight tens.  

Numerals are not introduced until these three lessons are mastered.

Place Value: Base Ten Blocks

This is the FIRST time my daughter understood what ones, tens, hundreds meant!

To play this game, you need two boards (laminated paper) labelled as you see in the picture, preferably NOT the same color as your blocks.  You also need base ten blocks and three dice.

It's usually played as "Race to 100", but I found that we didn't get enough practice making change for that to help.  We race to three hundred, hence the third die.  With one die, we'd be there all day.

The first player rolls the dice, calculates how many one blocks to pick up, and then makes any necessary exchanges if he has too many blocks in a column.  Play continues until someone reaches 200.  We played this every day for a week.   She still couldn't "carry" on paper, but at least she got the place value idea.  And kicked my tail at this game, lots.

Variation:  When we started learning borrowing, we played this game BACKWARDS.  Start with three hundred and race to zero.

Carrying: Montessori Cards and Base Ten Blocks

Middle Kid, doesn't get carrying in addition AT ALL. We've been over it and over it and it's just not going in. She's already up to adding three digit numbers in Abeka, so I decided to try it with some manipulatives. So, I got a box of base 10 blocks and printed out some Montessori Large Numerals.

In the above and below pictures, you can see that the cards are made so that the child can build the number with its component parts and then stack them to read it as they would see on a page. I HEART this idea.

So, we built the numbers, and now we combine the piles.

Then we made the "exchanges" so that there weren't over ten in any column.

She "read" the new number on the mat and wrote it down.

Now, I will tell you, that this didn't solve our problems, but it did help. "Why can't I have 14 ten bars? I don't want to exchange. How many is the limit?" I think this will be one of those concepts that we're going to make head way little bit, by little bit.

One caveat, if I had a million dollars, I'd have bought these instead.

It's harder to tell on the plastic blocks that a ten bar is ten ones. It just looks like it's own thing. It's easy to go, "I have one block, one stick, and three cubes(113). That's more objects than just three blocks (300)." Montessori bead material has WEIGHT. You can tell that the thousand block is a thousand beads because you can FEEL it.

1 to 10: Tactile Cards

I've found tactile number cards indispensable for teaching numbers.

The tactile number set above is from The Knowledge Tree and the set below is a traditional sandpaper set from Montessori Outlet.

It seems that the Knowledge Tree set are his favorite and have the added benefits of going all the way up to 30 and directional visuals for tracing the numerals.

The set below is the traditional Montessori sandpaper numbers, but as you can see, if you want to go ahead and teach the number 10, you have to put the 0 and the 1 card together. I'm undecided on how much I like the traditional sandpaper numbers...I think if had I only intended to teach 1-9, then 10-19, I would like them better. But as it is, they kind of tripped me up by not having a "10" card.

They certainly are "prettier" and while that's really important in some activities with my kids, that attractiveness of these numbers didn't make this any easier.

Additionally, the Knowledge Tree cards can also be used with food counters...as long as your food item is non-greasy and small.