Problem Description Sheet:       Pizza Pieces             

Introduction: When you order most pizzas, they already come cut into pieces. Usually these pieces are about equal in size. In this problem, our pizza will come as a whole circle and we will have to cut it into pieces. Our pieces don’t have to be equal in size. Each time we make a cut, the cut must be straight and go across the circle (but it doesn’t have to go through the centre of the circle).

Problem:

  1. Draw two straight lines across one of the pizza circles to show two straight cuts. How many pieces of pizza are made?
     

  2. A pizza with two cuts is shown in the Hints area at the bottom of this page. Show how you can make a third cut on this pizza to make seven pieces of pizza.
     
  3. What is the most number of pieces you can make by making four straight cuts across the pizza circle? Show these cuts on a pizza circle.
     
  4. Make a chart (like below) showing the most number of pieces of pizza you can make using one, then two, then three, then four, then five, then six, then seven straight cuts.
     

      Number of Cuts

      Most Number of Pieces

      1

       

      2

       

      3

       

      4

       

      5

       

      6

       

      7

       

  5. Look at the chart you made. Can you see a pattern that helps you predict how many extra pieces are made with each new cut? Describe the rule for this pattern. Use the rule to predict the most number of pieces you could make by making ten straight cuts.

Materials: pencil, paper, ruler, sheet of circles to represent pizzas, calculator

Topic(s):

Numbers and patterns
(N11-12; D-1c,d; P-4b),
critical and creative thinking, communication   

Activity Type:

  Group  Individual 

Assessment:

  Scale:      Levels 1-5        

  Self  Peer  Teacher 

  Include in your portfolio?
  Yes  No  Optional 

  Toward your marks?
  Yes  No  Optional 

 Hints: