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.
In today's lesson, the students learn to evaluate expressions containing one variable to find possible problem solutions. In today's lesson, the students use their understanding of variables and expressions to solve this task without direct instruction. They will be guided to the answer through questioning by me as they work in their groups. The students are representing problems using equations with a letter standing for an unknown quantity (4.OA.A3).
Give the students about 5 minutes of independent time to read and plan to solve the Task on Smart board (MP1). After the 5 minutes of independent planning, the lesson goes to the next phase of group exploration.
Tammy wants to purchase a gift for her mother. She's just not sure what to get. She knows that she will buy a watch for $125. Her other options are a ring for $236, a pair of shoes that cost $75, or a new television for $628.
Write an expression that shows the amount of money Tammy will spend if she buys a watch and any of the other gifts (g) for her mom.
1. Make a table with the information.
2. Write the expression.
3. Evaluate the expression.
What if Tammy only had $375 to spend? Which gift could she get along with the watch?
Some of the students did not understand how to get started. So after about 5 minutes of Private Work Time, I let the students talk in their groups for about 2 to 3 minutes explaining what strategy they would use the solve the problem. After that, they went back to their private work time for another 5 minutes.
During the group exploration/discovery phase, the students work in pairs. Each group has a copy of the Variable Task. The students must work together to complete all requirements of the task. The students are required to write an expression, then solve (4.OA.A3). The students reason abstractly and quantitatively by decontextualizing the information from the task and representing it symbolically (MP2). 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 expression and solutions. This takes discussion, critiquing, and justifying of answers by both students (MP3). As the groups discuss this task, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6). As I walk around, I am listening for the students to use "talk" that will lead to the answer. These are some of the comments I hear as I walk around: "That's how I got my answer," "She can't buy a television because it costs too much," and "Let me ask you something." 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 does the variable represent?
2. What numbers did you substitute for the variable? Why?
3. How do you find the answer?
As I walked around, I noticed the students working together to find the items that Tammy could by along with the watch. At first, the discussion between the students focused around how to set up the table. The students had to work together to come up with a variable. After agreeing upon the variable, the students worked together to come up with the expression. Because the students knew that Tammy would buy a watch, they knew that they must add 125 with the variable. A few groups had no idea how to begin. I sat down with these groups to ask questions to lead them to the expression. After getting the expression, the students could plug the other numbers in to find out the amount Tammy would spend if she purchased the items.
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.
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. From the Video, you hear the students walk the class through their answer. This is a teaching opportunity for the few students who may still not know how to solve expressions. 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. From the Student Work, you can see how the students made a table and wrote the expression for the task. Also, the students used calculations to figure out what other item(s) could be purchased for $375.00.
I feel that this is a well rounded lesson on how to add multi-digit numbers using place value because the students are responsible for their own learning. They have been given the tools and resources necessary to accomplish solving the task.
After the share/discuss/analyze phase of the lesson, I close the lesson out by having the students do an Exit Ticket Variables. This will enable me to see how well the students understood writing expressions and evaluating them.
The students will receive an exit ticket to complete their answers. I will collect these exit tickets to evaluate the students' understanding. Those students who need remediation will work with me in small group the next day.
From example 1 of the Student completed exit ticket, you can see that this student understood clearly. Even though she did not complete the expression in the table by writing x + 78, you see from her math problems that she knows to add 78 to each of the numbers. From example 2 of the incorrectly completed exit ticket, this student is completely lost. This is one of my lower level students. As I review his exit ticket, I do not see any reasoning for his answer. The student did label the top part of the table correctly with the numbers representing "x." Other than that, it appears that he just wrote down numbers for his answer. I will have to work with him 1-on-1.