The Inversion Principle

Triangle Mult : Div Flashcard

The ‘inversion principle‘ is a key indicator for mathematical success.

The ability to understand that 8 + 7 = 15 so 15 – 7 = 8 and the reversible thought process “can

potentially enhance students ’ability to perform calculations.”  Young students, ages 5 – 8, who

use concrete materials can more readily understand the concept.   Teaching and using fact families 

is essential to reinforcing the inversion principle concept.

Fast forward to grades 3 and 4, where the inverse of multiplication / division is introduced. We often hear

students complain that ‘division is hard’ when they KNOW their multiplication facts. Perhaps they

need more practice with the inverse principle.   Using flashcards to learn multiplication facts is a tried and

true method for success.  Instead of using the traditional (and one dimensional) flashcards, let’s apply

the inverse principle.   Triangle flashcards are perfect for teaching and learning BOTH multiplication and

division facts and drives home the inversion principle concept with students.   And yes, you can use

addition / subtraction triangle ‘fact family’ flashcards as well for the younger students!

Inversion Multiplication Division Flashcards

Multiplication Division Flashcards Inversion Principle


Addition Subtraction Inversion Principle Flashcard

Addition Subtraction Inversion Principle Flashcard


Fast forward again to pre-algebra, as inverse operations are essential to solving multi-step equations.

Lastly, “improving inversion understanding improves children’s mathematical knowledge in general

and is a good predictor of children’s mathematical success later.”

So simple, yet so powerful!


Source:  Psychology Today, December 2023