Rationale for teaching with a task:
After I have worked directly with the students on a skill, I like to use a task. A task gives the students more practice on the skill while working in groups. Allowing the students to work in groups gives the students different perspectives from their classmates. Students can learn from each other. As the students work on a task, I am the facilitator, walking around monitoring and questioning the students to lead them to the solution.
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 have private work time to think about and plan how to solve the task. Next, the students work in groups to explore the concept of the lesson. Finally, the students share/analyze/and discuss the task as a whole class. Each student has a copy of the task at their desk and a place value chart. We have already learned how to use place value to add.
In today's lesson, the students use their understanding of division and using multiplication to help with the division problem. They will be guided to the answer through questioning by me as they work in their groups. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors (4.NBT.6).
I give the students about 5 minutes of independent time to read and plan to solve this task (MP1). The students should have a multiplication chart at their desk. The students can use the multiplication chart at this time to plan how to solve the task (MP5). The multiplication chart will help the students with dividing their problem. After the 5 minutes of independent planning, the lesson goes to the next phase of group exploration.
Kim, Paul, & Tammy all worked on a project for Kim’s dad. Kim’s dad said that he will pay them a total of $954.00 to share equally. How much will they each get?
Find the amount that each person will receive. _______
Tell which clue word(s) helped you decide which operation to use.
Extension: Each person decided that the payment was too much. They enjoyed working on the project and did not want Kim’s dad to spend so much money to pay them. They asked Kim’s dad to take away $50 each from the amount of money he was going to pay. How much will they each receive now? __________
During the group exploration/discovery phase, the students work in pairs. Each group has a copy of the task and Multiplication Chart.pdf. The students must work together to complete all requirements of the task. The students are required to find out how much money each person will receive. The students reason abstractly and quantitatively by decontextualizing the information from the task and representing it symbolically. During this phase, the students do not receive direct instruction. In this lesson, they apply skills previously learned. The students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and agree upon the possible ways to arrange the chairs. This takes discussion, critiquing, and justifying of answers by both students. As the groups discuss this task, they must be precise in their communication within their groups using the appropriate math terminology for this skill. Each pair has a multiplication chart to help them with their real-world problem. As I walk around, I am listening for the students to use "talk" that will lead to the answer. For example, in one group I hear a student ask his partner to show him the answer with the counters. I am holding the students accountable for their own learning.
During the phase, I monitor and assess the students' progression of understanding through questioning. Possible questions to help lead to the solution are as follows:
1. What is the total amount of money that dad paid the children?
2. How can the multiplication chart help you?
3. What clue words let you know which operation to use?
4. How many people will share the money?
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.mathplayground.com/ASB_DemolitionDivision.html
During this phase of the lesson, student solution paths are shared. While the students were working in groups, I was walking around questioning, as well as identifying 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 know how to add according to place value. 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.
During this phase, I like to organize the sharing of the solution paths in a strategic manner. I begin with a group that has identified the correct clue words that help determine the operation. From there, I go to the division problem and multiplicaiton problems that help solve the division problem (Student Work 2). Last, we hear the solution to the extention of the task (Student Work 1).
I feel that this is a well rounded lesson on using multiplication to help solve a real-world division problem because the students are responsible for their own learning. They have been given the tools and resources necessary to accomplish solving the task.
In the Video - How Much Will They Get.mp4, you hear me discuss the sample of student work. This sample of student work shows how the pair of students used the algorithm to solve the division problem. The students checked their answer with multiplication. Clue word(s) were identified to help solve the problem.
After the share/discuss/analyze phase of the lesson, close the lesson out by having the students do an exit ticket. This will enable me to see how well the students understood how to use multiplication to solve a division problem.
The students receive an Exit Ticket 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.