Counting to 10 and recognizing and identifying numbers is the first mathematic skill a Montessori child learns. By age 4 or 5, the child is familiar with the idea of 10 numbers because of math materials such as the brown stairs and the pink tower, both of which have 10 blocks or rods of increasing size. Around age 4 or 5, he can begin to use more complex materials such as the red and blue rods. The red and blue rods are 10 rods of increasing size that alternate in color. The smallest rod is "1" and the largest rod is "10." The different colors help the child distinguish among the sizes, and counting the rods helps the 5-year-old develop a concrete understanding of the difference in value among different numbers. He also learns to write and recognize numbers by tracing and reading sandpaper number cards.
A Montessori child begins to learn the concept of decimal places around age 4 by using the gold bead materials. The gold bead materials include single gold beads, strings of ten gold beads, squares of 100 gold beads and cubes of 1,000 gold beads. By age 5, a Montessori child can identify the number of beads in the different units, can recognize the names of different units and can form units by combining others. For example, he can combine 10 strings of 10 beads into a square to make a 100-bead square.
A Montessori child begins to add, subtract, multiply and divide with the gold beads around age 4 or 5. Most Montessori children will master these concepts by age 5 or 6. Addition and subtraction are often taught as group activities. Two children both bring a number of gold beads, and each child counts how many beads he has. The children then combine their beads in the center and count how many beads they have together. Subtraction is taught the same way, but with the children taking beads out of the center instead of adding beads to the center. To teach multiplication, three or more children all select the same number of beads and count how many they have together. To teach division, the teacher begins with a number of beads and divides them equally among three or more children.
A Montessori child begins to learn fractions between the ages of 4 and 5. The materials for fractions are a series of trays with circles. One circle is whole; the rest are divided into different numbers of equal parts, from two parts to 10 parts. At age 4 the child begins by exploring the fraction trays, taking them apart and putting them back together like puzzles. By age 5 he is learning to name the different parts of fractions such as 1/2 or 1/8. He then learns to write the fraction names and then to perform operations with the fractions.