Cards and Counters is a traditional Montessori material that is used early on in the math curriculum. Very specifically, it is usually the third math material presented to young children, following lessons with the Red and Blue Rods, the Sandpaper Numbers, and the Spindle Box.
In my Montessori training, I was particularly amazed and impressed by the Montessori math materials. A perfect example of the ingenious way in which Maria Montessori designed her materials is these first three math lessons. Typically, in a non-Montessori setting, young children are introduced to the concepts of number and quantity by being asked to count loose objects. As those of you who work with very young children know, a child's ability to use one-to-one correspondence (i.e. point and count at the same time without losing track, recounting, etc.) develops gradually and is often difficult for the child at first.
In Montessori education, the child's first introduction to quantity and one-to-one correspondence is with the Red and Blue Rods. This material was designed specifically to address a young child's difficulties with this skill by making the quantities fixed. Instead of counting "loose" objects which are easier to miscount or recount, the child counts "fixed" objects by touching the red and blue portions of the rod and counting.
After the child has mastered this material and learned to pair the quantities with the corresponding numerals (through use of the Sandpaper Numbers), he is introduced to the Spindle Box. This material is the reverse of the Red and Blue Rods in that the numerals are fixed (i.e. they are already printed on the box in correct order) and the quantities (spindles) are loose. NOTE: In addition, the Spindle Box is designed to introduce the concept of "zero".
After the child has mastered the Spindle Box, he is ready to put it all together with the Cards and Counters. In this material, both the numerals and the quantities are "loose". The child must first place the numerals in correct order, then use correct one-to-one correspondence to count the appropriate number of items for each quantity represented by the numerals.
In addition to the traditional Cards and Counters, I like to put out many variations of this activity throughout the year. Oftentimes, these variations are seasonal (i.e. counting snowflakes on numbered mittens in January). Below is a photo of my Cards and Counters On the Rocks. As soon as I saw the bags of smooth stones at my local discount store, I knew I would use them to create a counting activity. I think the children will enjoy the weight and feel of the stones. Below are a few photos of this finished work.
On the left is a photo of the activity as it will be presented on the shelf. I really wanted all parts of this work to be from natural materials, thus the two baskets and the wooden bowl. The photo on the right shows a set of number cards I considered using. They are (obviously) very bright yellow and made from plastic. I rejected them in favor of the wooden number tablets pictured at left. I will admit, however, that I am not completely happy with those either. I am seriously thinking about making a set of laminated number cards using natural colors of cardstock cut into stone shapes.
Here is the activity laid out on a floor rug, just like the children will do. A built-in control of error is the fact that there are exactly 45 stones.