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Activity Info
Title: Comparing Fractions and Partitioning Shapes
Learning Target: Students will be able to partition various quadrilateral shapes into equal shares for groups of two, four, and eight people.
Grade: 3
Math KCAS: 3.G.2
Partition 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.

Understand 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.

Read with sufficient accuracy and fluency to support comprehension.

Title: The Doorbell Rang
Author: Pat Hutchins
ISBN10: 0307755894
ISBN13: 9780688092344
Lexile Reading Level: 340L
Description: Each ring of the doorbell brings more friends to share the delicious cookies Ma has made. This terrific and suspenseful read-aloud picture book about friendship, sharing, and cookies can also be used to introduce basic math concepts to young children.
Activity Descriptors
Formative Assessment Strategy:

Students will complete the “fair share” brownie activity that can be used as an assessment. The teacher will also observe student discussion groups and will want to use an observational checklist to record which students partition the brownies equally and which students do not. The student journals could also be collected and serve as a formative assessment. 

  • Hutchins, P. (1986). The Doorbell Rang. New York: Greenwillow Books.
  • Brownie work mat sheet for each student
  • “Brownie” pieces for each student on brown construction paper


  1. Introduce and read aloud the story The Doorbell Rang by Pat Hutchins.
  2. After reading, invite students to have a discussion about the text, all while focusing on what they had to do to make sure they had enough cookies for everyone.
  3. “Imagine if you were making brownies, but I said that we had to make sure we all share the brownies equally. You would have to make sure that when you cut the brownie everyone was getting equal sized shares.” Draw a brownie pan on the board. “Sometimes, you have friends come over or have to share snacks with your family. You would definitely want to make sure each person gets an equal share.”
  4. Ask “What if you had to cut these brownies into two equal shares? You need to make sure you are cutting with straight lines, just like if you were using a knife.” Take a few student responses and have them come to the board to show how they could cut the brownies.
  5. Show at least three ways to cut the brownies into two equal pieces.
  6. Ask “What do you call the share of the brownie that each person gets (the fraction/part)?” “What fraction of the brownie does each person get (one half)?” “How do you know that your two pieces are equal? (we can measure them or fold them on top of each other to see that they are the same size)”
  7. Model how to measure the pieces or to cut and fold paper to prove that the pieces are equal. Discuss the vocabulary wall words fraction, equal, numerator, and denominator and make sure they are on an anchor chart.


  1. Give each student a copy of the “Let’s Share Dessert” activity.
  2. The students will cut, glue, and record fractions based on the prompts on their paper.
  3. They will need to work as a group and discuss the fractions they are making.
  4. Students will check one another’s work and discuss whether or not the pieces are cut fairly.


  1. Come together as a class and share work.
  2. Ask students to discuss how they knew that the ways they had partitioned the brownies was “fair”.
  3. Identify different partitioning strategies that the students used. Some students will say that they tried to fold the brownie squares and then cut them.
  4. Discuss as a class why just trying to fold may not be so easy when you are trying to split something into many pieces, such as when they had to share with eight friends (eights).
  5. Assess the students by examining their brownies and seeing who has correctly proportioned them.
  6. Students will end the class by writing in their math notebooks to explain what they learned about fractions for the day.
Variations, Connections, or Follow-up Suggestions

You can extend the lesson by introducing the fraction strip model and practice using rulers to partition the strips into various fractions. 


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