Pattern Blocks, Attribute Blocks, Tangrams, and Pentominoes are popular manipulatives that teach reasoning, logic, planning, visual/spatial skills, geometric concepts, and other mathematical concepts. I've often been asked if you need all of these materials and what is the purpose of each one. This will be a short description of each and their intentional use; however, there are many support materials, such as reproducible books of worksheets and cards for each of these manipulatives that can help teachers better utilize them for varying ages.
PATTERN BLOCKS come in six shapes and six colors–yellow hexagons, orange squares, green triangles, red trapezoids, blue parallelograms, and tan rhombuses. Pattern blocks are used to teach geometric shapes and their relationships. They can be used to make linear patterns that allow students to extend, copy, or vary the provided guide. They fit together to make large triangles or hexagons. I find these are the best manipulative for beginning math geometric concepts because of their simplicity and versatility.
ATTRIBUTE BLOCKS come in five shapes, three colors, and two thicknesses and sizes. The shapes are rectangle, square, circle, triangle, and hexagon. Each of these shapes comes in red, yellow, and blue. They also are thick and thin, as well as large and small. By combining four attributes, students can learn shapes, classification (sorting) skills, congruent vs. similar, fractions, proportions, patterns, comparison/contrast, patterning, and many other mathematical concepts and thinking skills. I have found attribute blocks to be the most versatile manipulative, although not as popular as pattern blocks. Attribute blocks can be used with very young students through middle school. Additional support materials add to the flexibility of attribute blocks.
TANGRAMS are geometric puzzles that include 2 large triangles, 1 medium triangle, 2 small triangles, 1 square, and 1 parallelogram. Together these shapes form a large square. Tangrams are most useful for elementary students through adults in building spatial sense. Each puzzle comes in 1 color, although classroom sets can include a variety of colors. Again, many support materials make tangrams more interesting to use. I find that tangrams can be quite difficult for students who have difficulty with visual/spatial skills. Often these students benefit from pattern blocks and simpler activities before advancing to tangrams.
PENTOMINOES are 12-piece puzzles that are scored in 1-inch sections. They combine to fit together to form a rectangle and are used to help students visualize area and perimeter, as well as other math concepts. Pentominoes now come in 3-D pieces with two-tone coloration to provide visual clues to puzzles. The 3-D pentominoes are similar to color cubes.
Finally, does a math teacher need all of these materials? The answer is–that depends. If you are in a tutorial situation, working with 1 or a small group of students, I would suggest attribute blocks because of the versatility in both concept building activities and age-range of usefulness. Pattern blocks are my personal favorite because they are a fun way to build visual/spatial skills and teach strategic thinking. For older students, I would skip the pattern blocks and use tangrams–they tend to be more challenging and are less expensive. If you are teaching in a classroom, I would recommend having all of these manipulatives on hand due to the variety of students' needs and the demands of manipulative-based curricula.
I hope these descriptions and suggestions have been helpful in selecting appropriate manipulative materials for your students. If you have further questions, please feel free to e-mail or call us, and we'll be happy to post more information or help you individually.