• Observe and ask questions during the brownie activity to help determine students’ level of understanding.
• Use the think-pair-share fraction activity for further evaluation of student mastery.

“Today I will read a book to you. At the end of math class, you will complete an activity in your math journals.”

As an introductory activity, read the book Give Me Half by Stuart J. Murphy to your students. If this book is unavailable, Go, Fractions! by Judith Stamper, Apple Fractions by Jerry Pallotta, or The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Pallotta and Robert C. Bolster are good alternatives. Look at the pictures and talk about what is on each page.

“Before I give you a problem to solve, I would like to read a book to you. Let’s look at the cover. What do you think our book will be about?”

Take student suggestions and predictions about the book.

“The title of the book is Give Me Half by Stuart J. Murphy. As we read the story I want you to notice the strategies the children in the book use to solve their problems.” Ask students questions about the book and groups of items on each page as you read. Sample questions could include:

• “What did you learn from the book?”
• “What was the problem at the beginning of the story?”
• “What does it mean to share?”
• “When we share something do we always get the same amount?” (Review the fact that fractions of a whole are equal in size.)
• “Give an example of equal sharing in the book. Explain.”
• “What happened at the end of the story when it came time to clean up?”

Paper Fair Share Activity

Begin an activity in which each student will end up getting one piece of paper, showing that everyone has a fair share. Say to students, “I have a stack of papers here.” Ask a student, “Will you please pass them out so there are no extras? Everyone needs to have the same amount.” (Each student should receive one.)

The student passes out one piece of paper to every student. The student does not have any extra papers. “Everyone hold up your papers above your heads. How many sheets of paper did you get?” (Students say, “We all got one sheet of paper” or “We all got the same.”)

“That’s right, everyone has a fair share of the paper.” Talk about how they know everyone got a fair share. “Please place that paper in the top left corner of your desk. You will need it at the end of the lesson.”

Brownie Fair Share Activity

“I need your help solving a problem. I brought a plate of brownies hoping you could help me. I’m meeting with my book club tonight. I made some brownies and put them on a plate yesterday after school. My family ate some while I was shopping. My problem is that there will be six people at my house and I have only three brownies left. What should I do?”

Students may suggest ideas like making a new batch of brownies, buying some at a store, or “Maybe some of your friends won’t want a brownie.” “But what if everyone wants a brownie? I have to have enough so everyone who wants one can have a fair share of the brownies.”

A student may say, “I think you should cut one of the brownies into smaller parts and then you would have enough.” “Can you come to the board and draw what you mean?” The student comes to the board and draws three brownies. The student then divides the first brownie into four parts.

The student says, “Now you have six brownies. I would take one of these because it’s bigger.” “You are right. There would be six brownies if I cut them the way you drew it on the board. But would you be happy if I gave you one of the first pieces?”

“Talk with a partner at your desk. Use the paper from the corner of your desk and draw how you would divide the brownies so everyone would get a fair share.” Ask students to share their thinking with a partner and share with the class. Highlight appropriate strategies for solving the problem. Ask groups to show possible solutions to the brownie problem.

Possible Solutions:

The relationship between the number of things to be shared and the number of people sharing can be easy (paper-sharing activity) or more difficult (brownie-sharing activity) based on the numbers used.

After the brownie-sharing activity, allow students to continue solving problems.

“You did a great job helping me solve the brownie problem. Now you are going to use the Brownie Problems worksheet (M-3-3-1_Brownies on Paper and KEY.docx) to work on solving other brownie problems. Let’s look at the directions and complete the first problem together.”

(Model how to solve the problem. The first problem says there are 6 brownies to share with 2 children. This means that each child gets 3 brownies. A model may look like this:

Ask students if there are any questions and clarify the directions if necessary.) “Now that we have completed the first problem together, continue with the next problem. When you think you have found a solution, continue with the remaining problems. I will be coming around to check your work.”

After students finish the Brownie Problems worksheet, use the think-aloud strategy to model the problems below. The problems can be found on the Fraction Practice Problems worksheet (M-3-3-1_Fraction Practice Problems and KEY.docx):

• 5 brownies shared with 4 children
• 2 brownies shared with 4 children
• 4 brownies shared with 8 children
• 3 brownies shared with 4 children

When students who are still using a halving strategy try to share five things among four children, they will eventually get down to two halves to give to four children. For some, the solution is to cut each half in half; that is, “each child gets a whole and a half of a half.” Others will slice each of the five things in half and distribute the halves. The solution to this problem is “each child gets two halves and a half of a half.” After modeling for students, have students complete the Fraction Practice Problems worksheet (M-3-3-1_Fraction Practice Problems and KEY.docx) independently or with a partner.

You will have opportunities to assess students while they are solving the brownie problems and through discussions and questions. Students may need to be pulled into small groups to further clarify understanding, or you can assess student learning at another time.

Some sample questions might include:

• “Why did you cut the brownies this way?”
• “Explain how you solved this problem.”
• “When you solved multiple problems, did you notice anything similar about finding the solution?”
• “What do you find challenging about this problem?”

Ask students to record the fraction and explain their thinking. When students share their answers, it is important to emphasize the equivalence of different representations. Students will need many experiences with fraction problems in order to understand fully the relationship between fractions and real-life experiences.

Extension:

• Routine: To practice these concepts or as a warm-up for the next day or throughout the school year, use this think-pair-share fraction activity. Have students find a partner. Then give each student a half sheet of paper. Write a fraction problem on the board, e.g., “Six students want to share four licorice whips equally. Write down how many licorice whips each student will get.” Give students about 30 seconds to think about how to solve the problem. They may use any strategy. Give students about a minute to solve the problem and write their answer on the half sheet of paper. Students should show their partner their answer. If answers differ, students should discuss why they think their answer is correct.
• Small Group: Students who require additional practice can be given 2-inch x 4-inch pieces of paper to represent the brownies. This would allow students to cut and lay the pieces on top of each other. Solutions can be glued to a piece of paper, or students can represent their solutions with a drawing. Some students will need to have the brownies already drawn in order to keep the sizes the same. Use the Brownie Problems worksheet for this purpose (M-3-3-1_Brownies on Paper and KEY.docx). Ask students to record the fraction and explain their thinking.
• Expansion: For students who master the concepts quickly, have them divide nonrectangular shapes equally into parts, i.e., an equilateral triangle, a circle, or an isosceles trapezoid. Or have students divide simple fractions into equal parts, i.e., “Jane has half of a pizza (could be a circle or a rectangle). She wants to divide it into three equal parts. What fraction of the whole pizza will be in each part?” Suggest that students draw pictures or use manipulatives to model the problems.