triangle formulas

Adapted 3-Variable Formula Triangle

Hands-on activity for students who are blind or visually impaired to use formula triangles to solve 3-variable equations.

Formula triangles are commonly utilized in math and science classrooms to help students solve 3-variable equations.

Most commonly this tool would be used in physical science classes.

For example, the equation:   velocity = distance/ time  



  1. Please refer to the picture as you follow these directions.

Draw an equilateral triangle on a piece of copy paper.  The sides should be 8 ” long and the triangle should take up most of the page.

See picture

Draw a horizontal line from one side of the triangle to the other 3″ above the bottom side of the triangle.  Draw a perpendicular line from the bottom of the triangle in the middle to the horizontal line just drawn.  Draw an X in the middle of this line (to represent multiplication).  Place a dot above and below the horizontal line in the middle of the triangle on the left and right sides of the line.  This represents the division symbol.

  1. Using a PIAF, produce a raised line image.  If a PIAF is not available, a hot glue gun may be used over the dark lines.   See Use of a PIAF machine to produce tactile graphics for science.
  2. Attach  a piece of velcro to the 3 areas of the triangle approximately in the middle of each section.
  3. Write the variables from the equation using a Perkins brailler leaving enough space to cut each out and write the print letter below the braille (See picture.)
  4. Attach each variable to one of the  pieces of velcro on the formula triangle as per the procedure.


Explain to the students that they should attach the variable from the left side of the equation to the bottom left quadrant of the triangle.  Next,  attach the variable in the numerator on the right side of the equation to the top quadrant, and the variable in the denominator to the the bottom right quadrant.  

The  horizontal line = division; the vertical line = multiplication

Instructions for students:  
  1. Cover the variable you are looking for. For instance, if you are trying to solve for (D) distance, that leaves V(velocity) and T (time). In this case, you would multiple the two variables (since the vertical line means multiplication). If you were looking for Time (T), you would cover up the T leaving D (distance) and V (velocity). In this case, you would divide distance by speed to solve for time since the horizontal line means to divide.
  2. Work with the student until he/she is comfortable solving equations using the formula triangle.
  3. Students should practice using the formula triangle independently to solve for all variables. 


3- variable raised line formula triangle of a different equation.
3- variable raised line formula triangle of a different equation

NGSS Standards

High School: Forces and Interactions

This activity was designed by Mr. Jim Clark, science teacher at TSBVI.

Pictures by Ditmar Hospitál

Reference :

By Laura Hospitál

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Collage of adapting a 3-variable formula triangle for braille students