Introduction: Algebra Manipulatives

About: I've been a teacher/learner/maker of Math since 1994. I am also a Milken National Educator & NYS Master Teacher Emeritus. Lover of family, music, DIYing, and the great outdoors. Life is good! Also please …

As digital resources and instructional practices become more common with today’s students, I still find great value in the use of analog materials. This includes the use of manipulatives in the algebra classroom.

In preparation for working with Algebra 1 students in the fall, this set of plans allows students to transform a single sheet of card stock into a set of manipulatives that become powerful instructional tools.


One sheet of white card stock




Markers or colored pencils (blue, green, yellow, orange, purple, red)

Step 1: Setting Up the Card Stock

Using the ruler and pencil, divide the sheet as shown.

Large squares = 2” x 2”, medium squares = 1” x 1”, small squares = ½” x ½”, rectangles = ½’ x 2”

Step 2: Coloring the Cardstock - Front

On the bottom row of medium squares, number each tile 0 - 9.

Color the other three rows of medium squares orange.

Color the large squares blue.

Color the small squares yellow.

Color the rectangles green.

Step 3: Coloring the Card Stock - Back

Cut the sheet into the sections as shown.

Number the back of the number squares with 0 and -1 through -9.

Color the back of the orange squares purple.

Color the back of the blue, green and yellow shapes red.

Step 4: Cutting the Shapes

Cut the shapes following the grid lines drawn prior to coloring.

Step 5: Using the Shapes - Number Squares

The number squares can be use when exploring Open Middle Problems.

You can find additional Open Middle problems here:

The number squares can also be used to play with puzzles such as 1 to 9 Puzzles.

Step 6: Using the Shapes - Colored Squares

Visual Patterns are a powerful way to explore:

  • Functions
  • Arithmetic and Geometric Sequences
  • Perimeter and Area
  • _______________

The squares can be used to model the Visual Pattern.

You can find more Visual Patterns here:

Step 7: Using the Shapes - Algebra Tiles

Algebra Tiles are powerful manipulatives when exploring and modeling algebraic topics.

You can find out more about how to use Algebra Tiles HERE.

Step 8: Storing the Manipulatives

Use a plastic bag or an envelope.


You can also make an origami envelope following these directions:

The origami envelope has three pockets, one for each set of manipulatives.

Step 9: Printing Your Own Set of Manipulatives

While making their own set of manipulatives increases student ownership and buy-in, it may be easier to print the sheets with or without the coloring. Here are some templates that can be printed out.


Step 10: Feedback & Suggestions?

Thanks so much for checking out this Instructable! If you have any feedback or suggestions to pass along, I would love to hear from you!