**"Numbers do not just evoke a sense of quantity; they also elicit an irrepressible feeling of extension in space."**

**Stanislas Dehaene,**

__The Number Sense: How the Mind Creates Mathematics__, pg. 69There's one hanging in every kindergarten...

first grade...

second grade...

and third grade...

classroom in my school. Yes, the ubiquitous "Class Number Grid". These grids hang out with big number lines on classroom walls:

Sometimes right next to each other! |

And are often seen in smaller versions going hand in hand on desks:

This type of name tag appears on student desks in many first and second grade classrooms in my school. It includes a hundreds grid on the left and a number line running across the top. |

The kids use number grids to do exercises like this:

Grade 1 |

Grade 2 |

Grade3 |

And to play games like this:

But most kids lose interest quickly. |

Last year I tried a small innovation:

Play on a blank grid and fill in the numbers as you go along. After three or four trips from 0 to 100 the grid begins to fill up. |

Turn the number grid into a number line by cutting the grid into strips and taping the strips together. Play on the number line. |

This student was on 76, rolled a 1, and jumped 10 to 86. How did he know where to land? One more than 85! |

We hung them from a clothesline in the room. |

I decided to try the experiment out in third grade with Capture 5:

First we gave them some time to get familiar with the game. |

Next, cut out a number grid into strips and glue together to make a number line. |

How long do you think the number line will be once we put it together?

Normally I would put these estimates on an open number line. |

Playing Capture 5 on a number line. |

I asked the kids to comment on the difference between playing on a number line as opposed to a number grid. Some reflections:

- "I had to use my my mind more because I couldn't go up and down."
- "I had to do more thinking, but it got easier the more I played."
- "I like the number line better. The grid is more confusing."

So what's next? Graham Fletcher has written about the potential benefits of "upside down" grids, another way for kids to conceptualize how numbers can be arranged. How about playing on a vertical number line? Could we adapt games like Capture 5 and the Number-Grid Game for play on a yardstick, tape measure or meter stick? A thermometer? Will this cause confusion or help build number sense? And is it possible that some of our students see numbers in ways we cannot imagine?

Number Forms |

**"Though a majority of people have an unconscious mental number line oriented from left to right, some have a much more vivid image of numbers. Between 5% and 10% of humanity is thoroughly convinced that numbers have colors and occupy very precise locations in space."****Stanislas Dehaene,**__The Number Sense: How the Mind Creates Mathematics__, pg. 71
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