Improper Fractions and Mixed Numbers

Suppose you are planning a pizza party. How many pizzas do you need to buy? And how much will be left over? The Improper Fractions and Mixed Numbers Gizmo represents fractions as circular area models (or pizzas) so it can help with important investigations like this. The Gizmo allows anywhere from 2 to 10 pieces per pizza, but let’s use the traditional 8 pieces. This means each piece is one eighth. Three pieces is 3 eighths, and a whole pizza would be 8 eighths (8/8 = 1).

Let’s say you’ve invited 16 people to a party, and each person will get one piece. How many pizzas do you need? Model it in the Gizmo and students can see that 16 pieces is really just 2 pizzas (16/8 = 2).

If extra people show up and now you need 21 pieces, the Gizmo helps translate 21 eighths (21/8), into 2 whole pizzas plus 5 eighths more. Thus, the improper fraction 21/8 equals the mixed number 2 5/8. So in this scenario, you would need 3 pizzas, and with 3/8 (3 pieces) expected to be left over.

What if there were 6 pieces per pizza instead of 8? What about 10 per pizza? Hopefully this Gizmo offers a fresh way to approach improper fractions and mixed numbers.