For an introduction to Exploding Dots, try the activity: Introduction to Exploding Dots


Arithmetic with Exploding Dots
Using Exploding Dots to model basic arithmetic operations
For decimal arithmetic a 1 ← 10 machine is used, and thus for any number dots are placed in each cell corresponding to its decimal digits. Each operation is then modelled as follows:
  • +  Put the dots corresponding to each term into the cells together, then apply all possible transformations.
  • −  Put the dots corresponding to each term into the cells together, using dots for the first term and anti-dots for the second term, then apply all possible transformations.
  • ×  Put the dots corresponding to the first term into the cells, and repeat the number times given by the second term. Then apply all possible transformations.
  • ÷  Put the dots corresponding to the first term into the cells, then select and mark off sets of dots in the cells in patterns corresponding to the second term (the divisor). Unexplode dots from cells to the right when more dots are needed to complete the pattern.
Choose an arithmetic operation using the buttons below, and use the Exploding Dots to calculate the answer.

About the activity

Good visual models illustrate mathematical concepts with clarity—bridging the concrete and the abstract. Exploding Dots are one such model, supporting interactive modelling and problem solving in arithmetic, representation of integers, and polynomial division. They provide an engaging and dynamic representation that is consistent across a broad range of concepts.

The development of these exploding dots activities was inspired by James Tanton's resources available at G'Day Math.