Using Percentages (Investigation)

Objectives

• To visualize and estimate percentages using everyday objects.
• To practice converting fractions into percentages.
• To explore percent of a quantity.

Materials

• Several types of the same object (ex. a variety of different crayons or shoes)
• Paper
• Pen

Procedure

1. Work on your own or in small groups. Think of at least 3 objects around you that you have a lot of.
2. Pick the object you have at least 10 of. For example, I may choose crayons.
   Helpful Hint!

   You want to choose an object that comes in a few different colors, designs, or sizes (ex. Shoes, shirts, etc.).

3. Once you decide on an object, collect 10 of this object.
4. Pick a category that applies to one or more of the objects you have collected.
5. For each one you choose, count the number of objects you have collected that are in this category and record it.
6. For example, if I have collected these 10 crayons:
   

   My categories could be: blue (5 crayons) and extra large (2 crayons).

Investigate!

For each category:

1. Estimate the percentage that the number recorded in procedure step 3 represents of the total number of objects. Record it.
   Helpful Hint!

   It may be helpful to rearrange your objects here so that objects in the category are next to each other.

2. Calculate the actual fraction that the number recorded in procedure step 3 represents of the total number of objects. Record it.
3. Convert this fraction to a percent. Record it in simplest form. How close was the actual percent to your estimate?
4. Applying these percents, what number of objects would you have if the total number of objects you had increased to 100?
5. What about if it increased to 500?
6. What do you notice happens to the the number of objects in each category as the total number of objects increases? Why do you think this happens?