The Decimal System

Question

Each person participating in this activity needs a bunch of toothpicks or other small objects, such as coffee stirrers. Each person should have less than 100 toothpicks but enough so that they can't see right away how many toothpicks there are. Each person also needs either several small plastic snack bags, or some rubber bands, or both. The purpose of this activity is to help you understand the development of our way of writing numbers. 

1) Determine how many toothpicks you have without counting them all one by one. Do this by arranging your toothpicks so that you can visually see how many toothpicks you have. Use your plastic snack bags or rubber bands to help you organize your toothpicks. Describe how you arranged your toothpicks. 

2)Does the way you arranged your toothpicks in, above, problem 1 correspond to the way you write the number that represents how many toothpicks you have? If so, explain how. If not, try to arrange your toothpicks so that you can visually see how many toothpicks you have and so that this way of arranging the toothpicks corresponds to the way we write the number that stands for how many toothpicks you have. 

Answer 1

O.K., here is how many toothpics I have:

|||||||||||||||||||||||||||||||||||||||||||||||||||||| 

    How many are there?

 

Since that is not easy to count, I grouped them like I count cars passing on the highway:

†††††  †††††  †††††  †††††  †††††  †††††  †††††  †††††  †††††  †††††  ||||

    (note: these are groups of five with a hash mark when five are completed)

     Now, how many are there?

 

Since the problem asks you to write this in a way that can be read in decimal, I re-wrote this:

††††† †††††

††††† †††††

††††† †††††

††††† †††††

††††† †††††

||||

  (note: I used lines rather than rubber bands or snack bags)

  O.K., quickly now:  How many are there?