K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will:

  • explore and investigate as many different ways that they can to create a completed circle (pizza) from the fractional parts. (pizza slices)
  • conclude and define equal fractions by comparing fractional parts to one another.
  • recognize “fair shares” as being equivalent fractions.
  • manipulate materials to show examples of equivalent fractions.
  • note the importance of fractions in everyday living.

Teacher planning

Time required for lesson

1.5 hours


  • paper plates or large construction paper circles to represent pizzas (teacher should pre-mark these into halves, thirds, fourths, sixths, eighths, and twelfths before passing them out to students.)
  • materials to add toppings (yarn or green paper shapes for green peppers, red circles for pepperoni, beige shapes for mushrooms, and anything else that would look like pizza toppings)
  • Glue and scissors
  • Two Hershey Candy Bars or any other candy bar that can be divided equally.
  • Pizza box containing circles divided in 3rds, 4ths, 6ths, 8ths, and 12ths. (for the teacher)
  • Pizza Hut might even give small pizza boxes for students to store their pizza slices in after they have added toppings and cut them into fractional parts.

Technology resources

Computer with:

  • an internet connection.
  • a spreadsheet program (I use Data Explorer by Sunburst but Microsoft Excel or Works will work just as well).
  • a word processing program.
  • Kid Pix Studio Deluxe by Broderbund or other drawing programs will also work.


  • Read aloud the book Gator Pie by Louise Mathews. Make predictions as story is being read and discuss the concept of sharing equally or equal parts. Emphasize that it is very important that each is a “fair share.”
    • In this story, two gators, Alvin and Alice, find a pie. To share the pie fairly, each gator would get half. Then, more alligators arrive. Alvin and Alice must divide the pie into more pieces. As more and more alligators arrive, the piece that each gator will receive becomes smaller and smaller. The gators start to argue about sharing the pie. Finally, Alvin and Alice take the pie and sneak away.
    • The Doorbell Rang by Pat Hutchins and Eating Fractions by Bruce McMillan can also be used to illustrate this concept. In these books, you can also discuss how characters in the stories share and how in real life when you share things, it means that you must cut them in smaller pieces.
  • Use two candy bars to illustrate this point further. Break the candy bar into three pieces: one being small, another being larger, and the third being the largest. Ask the students whether these pieces of candy are “fair shares.” Of course the students will respond, “NO.” Get them to explain to you how you would break the candy into pieces so that it would be fair and each person would get the same amount or “fair shares.” Then divide the candy bar into equal pieces. Model how the pieces are equal and now can be distributed in “fair shares.” (You could even give these pieces of the candy bar to the children.)


  1. Pass out pre-measured and marked paper plates to students. (These plates should have been pre-marked or divided on the back into halves, thirds, fourths, sixths, eighths, and twelfths.)
  2. Have the students write their name on each piece of their paper plates on the back. Be sure they write their names on each section or slice of their pizza.
  3. Have the students use construction paper shapes for pepperoni, green peppers and mushrooms or any other pizza topping that they want to include on their pizza. Have them glue these shapes on their pizza. Let pizza toppings dry.(I usually do this before lunch on Pizza Day and then after lunch we complete the lesson.)
  4. Then have students carefully cut their pizzas into slices. Use the lines that are drawn on the back of the plates as their guide.
  5. Teacher will then model how 1/2 of her pizza is the same as 2/4 of another pizza. Then 2/4 is the same as 4/8 of another pizza.
  6. Establish ground rules for moving around the classroom with their pizza slices. Rules might include: No running, no grabbing another person’s slices, ask someone nicely to trade slices, etc. In other words: Use your best manners.
  7. Then have student move around the classroom and trade slices with at least one other person emphasizing that they should trade “fair shares.” Also emphasize that they should place the pieces on top of each other to ensure equal trading.
  8. After about 5 to 10 minutes, warn students that they have two more minutes to complete their trading and return to their seats.
  9. After students have returned to their seats, get volunteers to share their new pizza and explain how they made a new whole pizza. They should state what they traded. Make a list of these fractions on the board as students explain their trading procedures.
  10. As discussion occurs, students should begin to discover and infer what fractional parts are equal.
  11. Write the word equivalent on the board stating that this is a new word for some students. As if anyone thinks they know what “equivalent” means. Students hopefully will determine that “equivalent” and “equal” are synonyms.
  12. Then have students write in their Math Journals about what they did in today’s Math time. This will allow you to gain insight into each student’s thinking process. As a teacher, you will also be able to note how much each individual students knows and understands about fractions, noting which need additional practice with equivalent fractions. Note if the students can differentiate between equal and unequal parts.

Computer/Technology Integration

  1. Go to the Dairy Council of California website to explore the history of pizza. This site will also allow students to make their own online pizza selecting their preferred ingredients. It will also allow them to name their pizza, print the directions for making their pizza including their recipe and then will provide them with an ingredients shopping list. This site also provides nutritional facts about pizzas.
  2. Conduct a survey about the class’ favorite pizza crust. Solicit types of crusts from students. Use Data Explorer or some other Spreadsheet program to compile the data. Create line plots and graphs of the data. Have students analyze and interpret these graphs. Discuss the mean, median, mode, and shape of the data from the graphs. Students can use a word processing program to record their observations.
  3. Using Kid Pix Studio Deluxe, have students draw pizzas and divide them into fractional parts. Allow them to add toppings with the drawing tools. Then using the alphabet tool and the typewriter have them write the fraction stating how much of the pizza has been eaten and how much is left to eat. Included is an example of this activity. Students could also draw candy bars, dividing them, and following this same procedure.
  4. A great site to use with students is Cynthia Lanius’ site: Who Wants Pizza?


  • Class discussions and student explanations of their trading pizza slices.
  • Journal writing explaining equivalent fractions.
  • Kid Pix Slide of pizzas or candy bars divided into fractional parts. (A Class slideshow can be made by putting each student’s slide into the class slideshow.)

Supplemental information

Remember that additional time is needed to complete the computer activities that go along with this lesson.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 3

        • Geometry
          • 3.G.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
        • Number & Operations—Fractions
          • 3.NOF.1Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
          • 3.NOF.3Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent...

    • North Carolina Essential Standards
      • Information and Technology Skills (2010)
        • 3.TT.1 Use technology tools and skills to reinforce classroom concepts and activities. 3.TT.1.1 Use a variety of technology tools to gather data and information (e.g., Web-based resources, e-books, online communication tools, etc.). 3.TT.1.2 Use a variety...

North Carolina curriculum alignment

Computer Technology Skills (2005)

Grade 3

  • Goal 3: The learner will use a variety of technologies to access, analyze, interpret, synthesize, apply, and communicate information.
    • Objective 3.01: Recognize, discuss, and use graphs to display and interpret data in prepared spreadsheets; identify and cite sources. Strand - Spreadsheet
    • Objective 3.04: Identify, discuss, and use multimedia to present ideas/concepts/information in a variety of ways as a class. Strand - Multimedia/Presentation

Mathematics (2004)

Grade 3

  • Goal 1: Number and Operations - The learner will model, identify, and compute with whole numbers through 9,999.
    • Objective 1.05: Use area or region models and set models of fractions to explore part-whole relationships.
      • Represent fractions concretely and symbolically (halves, fourths, thirds, sixths, eighths).
      • Compare and order fractions (halves, fourths, thirds, sixths, eighths) using models and benchmark numbers (zero, one-half, one); describe comparisons.
      • Model and describe common equivalents, especially relationships among halves, fourths, and eighths, and thirds and sixths.
      • Understand that the fractional relationships that occur between zero and one also occur between every two consecutive whole numbers.
      • Understand and use mixed numbers and their equivalent fraction forms.
  • Goal 4: Data Analysis and Probability - The learner will understand and use data and simple probability concepts.
    • Objective 4.01: Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems.