Base ten, or the digital number system, the number system used in modern society, is based on grouping numbers in multiples of 10. It is important that children begin to understand place value if they are to eventually understand regrouping across places, decimals and exponents.
Our digital system uses ten different digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. By placing in different positions, from right to left, on either side of a decimal, we can increase the value (or decrease the value.) Primary children need to be able to identify 20 as two tens, 30 as three tens, etc. Children with disabilities need lots of concrete and visual experiences with numbers. Some of the activities that will support this understanding include.
One Hundred Days: This activity is pretty typical of most pre-school and kindergarten programs. You add a popsicle stick or stirrer to bundles of ten, and write the number names, ie. 52 days is five bundles of ten and two individual sticks for the ones. On the hundredth day, you celebrate.
Hundred's Charts: A hundreds chart, both a large classroom chart and smaller individual charts can be used in a number of ways to help children understand the base ten number system. The chart can be cut into "tens strips" (i.e. 11-20, 31 to 40, etc.) and then students can order them and paste them in the correct order. The chart can be used to teach skip counting by 5's and 10's, also an important part of understanding place value as well as counting coins in the decimal system (U.S. dollars, Canadian dollars, the Euro and the English pound.) The hundred's chart can be used as a giant bingo card, and it will give children experience both in reading numbers and matching them on the hundred's chart.
Base Ten Blocks There are several manufacturers of base ten blocks, which consist of 1 centimeter square cubes, 10 by 1 centimeter rods (10's), 10 X 10 X 1 squares (100's) and 10 X 10 X 10 cubes (100's.) The rods can be used for measuring, the square can be used to help students understand area, and the cubes for teaching volume. A printed template can also help support teaching students place value for tens and ones, using the Base Ten Blocks.
Cuisenaire Rods Cuisenaire rods are system build on the concept of one equaling a white centimeter cube, and rods of differing lengths and colors (a 2 is a two centimeter rod, 4 is a four centimeter rod, etc.) They can be used not only to teach operations, addition, subtraction, multiplication and division, they can also be used to help students understand numbers larger than ten, since the sets will include hundred squares and thousand cubes. Because the Cuisenaire Rods are also centimeter based, they can be used in conjunction with Base Ten Blocks.
Regrouping: Regrouping is the term that is interchangeable with "carrying" and "borrowing." Regrouping across ones and tens is the first step in understanding operations across the base ten system, and often the key to future success with long division and multiple digit multiplication. It is important for children with disabilities to understand how we can gather ten ones into a ten, and add it to the tens, or to break a ten into ten ones in order to subtract a number. It is good to actually have students create the numbers with base ten blocks, and do the regrouping, either for addition or subtraction: i.e. for 24 + 37, the child counts out four tens and two tens, and seven ones and three tens, combine the four ones and seven ones to make eleven, which the child converts into a ten rod and a one block, and then counts the ten rods, to write the sum (61.) Subtraction is done in a similar manner.