My youngest granddaughter just turned 4 in November and is very interested in how numbers fit together. She'll tell me "1+1+1 = 3 and 2 + 1=3 and 1+2=3." She tries to analyze every number and has even figured out that 4 has 2  2 s in it as well as four 1s. How can I encourage this. Her teacher says none of the other kids do it as much as she does it. Her mother and  have bought her counters, but want to know how else we can encourage her gift or pregift.  And she wants to add and count everything such as dirty dishes and carrots.

                                                   Kathy

Play games with her that include numbers.  I don't have any on the tip of my tongue but there are many places you can look for these kinds of games.  You could even make your own games with an old table cloth and a bean bag.  Mark the table cloth anyway you want with numbers, have her throw the bag at the numbers.  She can add them, tell you what numbers are in the ones she hits, she can also subtract, mult or divide.  Go for it and even let her think of games.  We drew squares on the sidewalk and my daughter became a frog jumping from one square to another working on whatever we needed to work on.

Hope this helps even a little bit.

My son (now 11) was the same way with numbers -we must have read "The Reeses Pieces Counting Book" about 500 times! Just type in "counting books" here on pbs and there are tons of books.  She may love the M & M one or the Cheerios one -they're really neat.

My son was like this.  I got him a set of cuisennaire rods.  Big hit.  It is super easy to see how numbers work together with the rods, and they are pretty good for free play as well.

I agree about the "candy" books, and the manipulatives.  She might like some linking cubes (can do more than Cuisenaire).  Ours are a set of 100, in 10 colors, and each side has a different shape (but round "peg").  She might like a balance scale with some gram cubes, and other math manipulatives.  Teacher-Created Resources has some great books.

There's the Math Mat - an electronic math pad that you jump on your answers and it has sound.  You can also take a cheap shower curtain or liner and write numbers on it (letters, too) and have her step on the numbers - or play twister, etc.

In a year or two (she may be gifted!) she might like the Theoni Pappas "Penrose" books.

There are a lot of great math sites online, too, for playing games.

JC

At that stage of development counting of items and concrete things is the best way to set the foundation. It is wonderful when a child grasps the actual concept instead of learning abstract number operations only and never really gets what math is about.

There are inexpensive sets of little objects, sometimes teddy bears, out of rubber or a plastic, they are different colors. You can count those and group into sets by color and count them.

Another thing to do is to start counting by 2's, grouping objects and counting off 2, 4, 6, 8.

Next up can count by 3's, 4's, 5's etc.

Also to identify the number 3 (the shape is memorized) is three (when verbally said) and is used to count 3 objects. After the base number shapes/symbols are memorized count above ten and teach to read left to right. That 17 is seventeen not seventy-one. My younger son used the car's digital outdoor temperature thermometer to discuss it. "Look, today it is 33 degrees outside!" Also that car had a digital clock that he could see from his booster seat and we'd (in normal conversation) talk about the time, "we're driving to the appointment at 10:00 and look now it is 9:52." Then later he'd say, "Look the time changed to 9:53...".

My boys both really loved dot to dot books. In educational stores for teachers (local retail stores) and through onlien companies you can get ones that are differetn groupings. Like 1-10, 1-20, 1-50, 1-100 and 1-150. I used those in progression as my kids learned numbers.

All that can be done before the child ever sees a worksheet with operations listed out on it and is told to do the operations.

Have fun. Breathe easy that she seems to be a natural learner of math. Unless something goes terribly wrong at school she is on a road to easily grasping math. Hooray for that.

I second the cuisinaire rod suggestion. My son loved these, and it really helps to see how the numbers fit together. I loved mine when I was little. We also used to do dinosaur math, with a bunch of plastic toys from the dollar store. There were about 20 of each color, and he could sort them and put the groups together. Yahtzee is fun, but if she's interested in the sequencing, you might try rummikub.

hi ho cherrio is a good counting game too :)