Manipulatives are valuable resources for accelerating and deepening students understanding of math, yet its use is almost non-existent in high school. In every decade since 1940, the National Council of Teachers of Mathematics (NCTM) has encouraged the use of manipulatives at all grade levels (Bellonio), yet many high school teachers are reluctant to use this type of resource. It could be that they didn't learn with them and don't know their power in learning. It could be that it seems hard to manage them in the classroom.Need more encouragement to use math tools and manipulatives in your classroom? The Common Core State Standards Math Practices clearly state that students need to be able to use them to help them to gain insight into problems and make sound decisions. Here is Math Practice #5.

5. Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
Until you see students beam with understanding, you could be a disbeliever. However, they can make a difference in the classroom with the material that you are teaching!
Manipulatives: The Missing Link in High School Math by Marilyn Curtain- Phillips, M. Ed. -
View and contribute to Hands-on Lessons - some examples.

Measurement Tools
  • Rulers
  • Protractors
  • Compasses
  • Trundle wheel
  • Meter/yard sticks
  • 25'-50'-100' tape measures
  • Clinometers (measures angles of elevation and angles of depression)
  • Carpenter's ruler

Manipulatives- Teacher/student-made or commercially produced
  1. 3-D models
  2. Algebra Tiles
  3. Alpha Shapes (
  4. Anglegs (
  5. Balance Scales (commercially developed Hands-on Equations)
  6. Base Ten Blocks
  7. Coins to flip
  8. Cuisenaire Rods
  9. Deck of Cards
  10. Dice
  11. Dominoes
  12. Fraction Circles
  13. Geoboards (5 x 5 or 11 x 11)
  14. Geofix Shapes ( )
  15. GeoLegs (
  16. Hundred Chart
  17. Miras (also known as GeoReflectors or GeoReflectas)
  18. Mirrors (flat and/or hinged)
  19. Pattern Blocks
  20. Pentominoes
  21. Power Polygons - an extended set of pattern blocks (
  22. Random Number Generator (available on the Smart Board and on your calculator)
  23. Spinners (also available on the Smart Board)
  24. Square Tiles
  25. Tangrams
  26. Thermometers
  27. Timers (available in the Gallery in Smart Board)
  28. Two color counters
  29. Unifix Cubes
  30. Versatiles (

Virtual Manipulatives
  1. A great site for virtual manipulatives can be found at: the National Library of Virtual Manipulatives -
  2. More e-manipulatives:
  3. Math Concepts and manipulatives that can make connections:
  4. Interactive Activities:
  5. (ES) Dilation Manipulative:

  1. Tape - scotch/masking/painters' tape
  2. Scissors
  3. Colored pencils
  4. Toothpicks
  5. Glue sticks/glue/rubber cement
  6. Brads
  7. String
  8. Patty Paper
  9. Notecards
  10. Card stock
  11. Manilla folders
  12. Grid/graph paper
  13. Playdough
  14. Personal whiteboards/markers/erasers