Counters don't have to be expensive or come from a teacher supply store. Counters can be dry beans, plastic animal shapes, matchbox cars, real or play coins or even something edible like cookies. A brightly-colored abacus can also help a child with simple number skills. According to Marilyn Burns, author of "About Teaching Mathematics," using counters "helps children build mental models that they can then translate to the abstract idea." Because they can be grouped and regrouped, counters are ideal for teaching numbers and operations concepts like counting and sorting, adding and subtracting and multiplying and dividing.
Children can use pattern and attribute blocks to develop early algebraic and geometric thinking. Pattern blocks come in six shapes and colors -- yellow hexagons, orange squares, green triangles, red trapezoids, blue parallelograms and tan rhombuses. Pattern blocks are used to sort and identify shapes and extend patterns. They can be positioned to make larger shapes. Attribute blocks have four attributes -- shape, color, size and thickness. Students can sort and classify them according to these attributes. They can work on fractions and learn the difference between concepts such as congruent and similar with attribute blocks.
Base 10 blocks are blocks that come in units, or ones, 10 sticks and flats that have 100 units on them. They are ideal for teaching students regrouping when adding and subtracting. They are also a visual representation of multiplication and division.
Geoboards are grids with pegs used to teach students about geometric shapes, area and perimeter. Students stretch rubber bands around the pegs to make shapes. They can draw the shapes they made on geoboard dot paper. Geoboards can be made with a square piece of wood and some nails, or plastic ones can be purchased at teacher supply stores.
Fraction strips are slips of paper divided into fractions that can be cut apart. There are also durable, plastic versions of fraction strips that can be used permanently. Fraction strips are used to show part-to-whole relationships and equivalent fractions. For example, a student can use a strip with four-fourths to cover a fraction strip with two halves. Fraction strips can also be used to add and subtract fractions and find common denominators.
Dice or number cubes can be used to teach probability with older elementary students. They can find the probability of rolling a certain number. Dice are versatile because primary students can use them for addition by adding the two numbers they roll together. Or they can subtract the lower number from the higher one. The numbers on the dice can be multiplied or divided.