Manipulatives can play an important role in helping kids learn. Not only because they offer hands-on learning experiences and can give a visual to abstract math concepts, but because they can make learning fun. Below are some of the many manipulatives available, some of which are available in printable form here.
Transparent Color Chips, Cuisenaire® Rods
There is an unlimited number of different items you can use to help with adding, subtracting, multiplying, and dividing operations--LEGOs, macaroni, acorns, you name it. To visualize place value and the process of regrouping, we recommend using base ten blocks. They come in units, tens, hundreds, and thousands. Cuisenaire® Rods, varying in length from one centimeter to ten centimeters, can help develop basic number, pattern, measurement, and fraction concepts. Color cubes are perfect for visualizing area and volume and for building basic 3-D structures.
As your children get older, try using dice for practicing basic operations, such as adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Take a couple of numbered dice (any number of sides) and a set of operation dice, roll them, and calculate. Dice are also great for practicing greater than and less than activities and for exploring probability concepts. Place value dice are helpful in introducing writing numbers in expanded form.
There are many products available to help children add, subtract, compare, and learn the equivalencies between fractions, decimals, and percents. If you use fraction circles (found at most Walmart stores and school supply stores), we highly recommend purchasing a set of fraction rings. They fit standard fraction circles perfectly and include rings to illustrate not only fractions, decimals, and percentages, but also degrees and time. Interlocking tower cubes can also double as a means for demonstrating simple bar graphs.
You'll find a variety of manipulatives helpful for teaching geometry concepts. Pattern blocks and polygon tiles are great for exploring tiling, area, and angles. Geoboards, available with square, isometric, and circle pins, can help children visualize area and perimeter. Use three-dimensional shapes, such as GeoModel Relational Solids, for identifying shapes and volume. Pentominoes and Tangrams (not pictured) are also great for visualizing area and perimeter and can help children develop problem solving skills.
You'll find manipulatives at EAI Education, Learning Resources, ETA Cuisenaire, eBay and Amazon, to name a few. It pays to shop around, as retailers frequently put manipulatives on sale, and you can oftentimes find discontinued ones for sale by resellers. If you would like to learn more about using manipulatives in your homeschool, we recommend Rosamond Welchman-Tischler's Start with Manipulatives. This binder is full of activities and is designed to help you explore the mathematical potential of manipulatives.