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

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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. 

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

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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?

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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

Regrouping

Division in base x

Division in base 10 and base x

Multiply by base 10 and x

Standard index form

Rounding

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