Laura Wolff

Partitive Division: Sharing Cookies

(Adapted from “Sharing Cookies”  Activity 8.6, page 315, in Guiding Children’s Learning of Mathematics, Tenth Edition, by Leonard M. Kennedy, Steve Tipps, and Art Johnson.    

Content Areas: Math: division

Grade Level: 3rd grade

Materials Needed:  bag of 18 cookies (made of construction paper), manipulative materials for student demonstrations (small objects, i.e., beans, pennies, candies, pencils, etc,) paper and pencil for each student

Key Concepts: partitive division, remainders


·        show understanding of whole number operations using manipulatives,

·        recognize, create, and extend patterns of objects and numbers using a variety of materials such as beans, toothpicks, cubes, etc.

·        use standard notation in reading and writing open sentences,

·        define problems in familiar situations,

·        interpret and compare information in familiar situations,

·        identify the unknowns in familiar situations,

·        reflect on and evaluate procedures and results in familiar situations,

·         organize and clarify mathematical information in at least one way- reflecting, verbalizing, discussing, or writing

·        express mathematical ideas to familiar people using everyday language  

Goals:  work in cooperative groups, students create real life math problems using manipulatives and everyday language to describe the operations of the problems.

Objectives:  Given brief teacher instruction and demonstration on partitive division, students will be able to work in pairs to create their own division problems that will be performed in front of the rest of the class.  Other student pairs will observe and record their description of what happened in the demonstrations and a class discussion will take place following each team demonstration. (Note: group sizes can vary with class size, but groups should be no bigger than four.)

Procedures:  Students will sit in a circle in front of the chalkboard while the teacher reviews vocabulary and concepts and demonstrates the activity.  Teacher has students bring a piece of paper and a pencil with them to the circle. 

“We have been working on division in math these last couple weeks.  Who can raise their hand and tell me what division is the opposite operation of?  (multiplication).  We’ve also talked about the two ways we go about division, either through repeated subtraction or sharing.   Yesterday we talked about repeated subtraction where we stared with a known number of objects and a known number of how many of those objects we wanted in a group.  We used repeated subtraction to find out how many groups to make.”  Teacher demonstrates on the board.  He/she draws out 20 dots in a pattern of a 4x5 grid.  “If we have 20 students and we want to make groups of 4 students, how many groups will we make?”  The teacher starts circling groups of 4 from the dots on the board.  While he/she is circling, he/she says, “Here is one group of 4 students, two groups of 4 students, three groups of 4 students, four groups of 4 students, and five groups of 4 students.  We made five groups of 4 students.  Today, instead of asking how many groups can we make, we are going to ask how many are in each group.  This is called partitive, or sharing division. (Teacher writes How many are in each group? on the board.)   “Using the same example, (teacher erases the grouping lines from the same problem on the board) we have 20 students, and we want to make five groups.  How many students will there be in each group?”  Teacher draws 5 circles on the board.  “Here are our five groups.  I will start diving the 20 students into the 5 groups.” (Teacher puts a dot in each group circle and after he/she draws the dot, he/she crosses one of the dots out in the group of 20 students.)  After all of the dots are divided out, he/she asks, “How many students do we have in each group?”  (4 students). 

Right now I’m going to quickly divide everyone into groups of four.  (Teacher divides class into groups of four students.)  “I have here a bag of cookies.  I am going to act out with one of you and your group how four friends could share this bag of cookies.  (Student name) (Student name) (Student name) and (Student name) would you come up here and help me?”  Teacher hands the pair the bag of cookies and asks, “ I’d like you to, with out talking, act out a way to the divide the cookies so that all four friends have a fair share of the bag.  I want the rest of you to pay close attention and then when they are done you and your group will write down on you paper what happened.”  Students work together and the rest of the class observes.  Students should start pulling the cookies out of the bag making 4 piles.  The piles will end up with 4 cookies in them each, with 2 cookies left over.  “Who would raise their hand and explain to us what you just observed?”  The class discusses the event. 

“Now I’d like each group to get together and create a story about sharing things, and answering the question I have written up here, “ How many are in each group?”  I have some materials up here that you can use as props.  Be creative.  After everyone is done creating their situation, each group will have a chance to act it out and the rest of us will write down what we observed.  Does anyone have any questions about what you are going to do?”  “I’ll give you five minutes to come up with your situation.” 

Students work on demonstrations for 5 minutes. 

“Who would like to go first?” 

Each group presents in a similar fashion to the bad of cookies situation and while the rest of the class observes and records their description of the situation.  A class discussion follows each demonstration.  After all groups present, the teacher reviews the lesson.

“Today we practiced partitive, or sharing division where we found how many objects went into each group.  This is different than yesterday’s lesson of repeated subtraction where we already know how many objects were in each group and we wanted to know how many groups there were.”  

Assessment:  Students will be given 2 problems each of repeated subtraction division, and partitive (sharing) division and will be asked to draw a picture to demonstrate their explanation of their answers to the problems.