Watch the video on the left and then try to figure out what comes next.  



Check out more exploding dots here


Exploding dots reveals the structure of different bases and allows students to use all four operations in base 10 and base x using counters.

Below are examples of how I have adapted this using manipulatives from mathsbot

The following are examples of conceptual variation, using base blocks (make with multilink cubes) and place value counters. 

Stacking counters is a variation of exploding dots.  Every time you get two piles of counters the stick together and move one place to the left.  This method gives students a sense of the size of the numbers but quickly becomes unmanageable. 





Moving on to modelling with base blocks (mathsbot/multilink cubes) exposes the mathematical structure.



Autograph allows you add an image to your graph.  This is now free.

Base 2 to base x

Watch this video and try to figure out what comes next.  


What stays the same and what changes?


This exposes the structure of all bases and naturally moves to base x.  Base x leads to work with algebra tiles. 

Addition in base 10

Subtraction in base 10

Addition and subtraction in base x

Working with base x is exactly the same as working with base 10.

Replace subtraction with adding the opposite.

Multiplication and division


Division in base x

Division in base 10 and base x

Multiply by base 10 and x

Standard index form


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