# The Mathematical Fusion Machine

This is another take on James Tanton’s Exploding dots.

In kindergarten, when students are shown 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and THEN the crowd of students should all looked shocked and say things like “WHOA, what just happened there!!!!” BUT instead this HUGE mathematical idea goes unnoticed. So, this activity will make students ooh and ahhh as they should, as well as deepen their understanding of our base 10 system which is foundational to understanding our number code, addition, subtraction, decimals and more.

# Day 1 – base 2 fusion machine

download paper copy of machine here: fusion machine paper copy

Powerpoint for the lesson: Part 1 of the fusion machine

# Video description of student work

# Day 2 – other bases

Powerpoint for the lesson: Part 2 of the fusion machine

# Day 3 – base 10 fusion machine with blocks

Download paper copy of machine: Base 10 fusion machine only

Download coding sheet for the machine: Base 10 fusion machine to 114

## Extension

There are many different directions you could choose to go from here. You could look at addition, subtraction, multiplication, and division to see how you could calculate using the fusion machine (Division is especially nice).

Another very **fun extension** is to have the students code for a base that is higher than 10, which would require them to make up their own symbols for the quantities 10 and up.

A great question to pose to the students would be:

What would be the largest base that could be used on a computer (considering the limitations of a keyboard)?

Base 16 uses A B C D E F as symbols for 10, 11, 12, 13, 14, and 15 respectively, but what is the highest base that could be used on a computer and there still be unique symbols for each number higher than 10?