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!
Multiplication Division Flashcards Inversion Principle
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!
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Source: Psychology Today, December 2023
