I let the students know that today we will do a task. I remind the students of the structure and routine of a task. First, the students will have private work time to think about and plan how to solve the task. Next, the students will work in groups to explore the concept of the lesson. Finally, the students will share/analyze/and discuss the task as a whole class. Each student should have a copy of the task at their desk. The students have already learned how multiplication can help with division. The students must use what they have learned about division to solve this task.
In today's lesson, the students will use their understanding of the relationship between division and multiplication to solve this task without direct instruction. They will have to find the whole number quotient when dividing by a one-digit divisor (4.NBT.6).
Each student gets a copy of the task (Baseball Card Task (Let's Share Equally).
Peter owns several baseball cards. He has so many that he wants to share them equally with his 3 friends. Peter wants to give away 228 baseball cards. How many cards will each of his friends receive?
1. Draw a model to represent the problem and shows how many cards each friend will receive.
2. Write an equation that represents the number of cards that each friend will receive.
3. Write to explain how you solved the problem.
I give the students about 5 minutes of independent time to read and plan to solve this task (MP1). As the students work quietly, I walk around to monitor what the students are writing. I do not interject at this point because I want to see what the students are going to do on their own. After the 5 minutes of independent planning, the lesson goes to the next phase of group exploration.
During the group exploration/discovery phase, the students will work in groups of 3. Each group will have a copy of the task. The students must work together to complete all requirements of the task. The students will have to reason abstractly and quantitatively by decontextualizing the information and representing it symbolically (MP2). During this phase, the students will not receive direct instruction. In this lesson, they should apply skills previously learned. The students will be guided to the conceptual understanding through questioning by their classmates, as well as by me.
The students will be required to find the whole number quotient with up to four-digit dividends and one-digit divisors (4.NBT.4). The students will draw a model of their problem (MP4). The students must communicate with each other and agree upon all components of the lesson. This will take discussion, critiquing, and justifying of answers by all 3 students (MP3). Once they have come up with their equation, they must give the quotient, as well as explain the steps in which they came up with their solution. The written answer must be precise in explaining their steps (MP6).
During the phase, I will monitor and assess the students' progression of understanding through questioning. Possible questions to help lead to the solution are as follows:
1. What were the total number of cards Peter gave away?
2. How many groups do you need to divide the cards into?
3. What strategy can you use to divide the cards in even groups?
4. How can drawing it out help you?
5. How can you check to see if your quotient is correct?
Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.funbrain.com/cgi-bin/mb.cgi
During this phase of the lesson, student solution paths are shared. While the students were working in groups and I was walking around questioning, I identified solution paths to be shared as a whole class for this phase.
I call groups to the front to share their solutions. This is a teaching opportunity for the few students who may still not have mastered the skill. This part of the lesson is lead by the teacher through asking assessing questions. The students may also have questions that they would like to ask. I use a document camera to display the student work on the Smart board for all students to see.
For this particular lesson, I organized the sharing of the solution paths in a strategic manner. First, I have a group of students share their models. I am looking for 3 groups with 76 in each group. I feel that if the students can draw out the problem, then they understand division. Next, I have a group to share their equation. The students must realize that when the task asks for an equation, that all equations have an equal sign. It is okay for the students to set the problem up in another way, but once they find their answer, they need to write it as an equation (if this is part of the task). The equation that the students should have is 228 ÷ 3 = 76. Last, I have a group share their written response. The written response if very important because it shows how well the students understand the process they use to solve the problem. From the written response, I can tell if the students strictly use procedures of if they have a conceptual understanding.
After the share/discuss/analyze phase of the lesson, I close the lesson out by having the students do an exit ticket. This enables me to see how well the students understood how to divide a multi-digit number by a one-digit divisor.
The students receive an Exit Ticket Let's Share Equally to complete their answers. I collect these exit tickets to evaluate the students' understanding. Those students who need remediation will work with me in small group the next day.