Oni's Equation Adventure- Day 11
Lesson 11 of 15
Objective: SWBAT solve real-world and mathematical problems leading to two linear equations in two variables.
For today's Warm Up assignment, I have provided students two systems problems, one that I want them solve with substitution and one that I want them to use elimination. Because it has been several days since working with substitution, I knew it was important to bring the strategy back for review. In today's lesson, students will be tackling word problems and they can use any strategy they would like to find the solution. Some problems lend themselves to a solution using substitution, while other to using elimination. Although either strategy will yield the solution, I want students to think about efficiency when selecting a strategy.
As students work on the problems, I move through the room asking guiding questions and encouraging students to look back in their journals at examples if they unsure of their work. Once the timer sounds, I select volunteers at random for the names cup to share their answers. Rather than ask for class confirmation, I instead ask how we might prove the solution provided is correct. I want students to be in the habit of checking their solutions, which they are reminded about with this question. Once we prove the solutions, I move on to today's learning objective.
With today's Learning Objective I include a sample word problem. I want students to see an example of the types of problems we will be solving during today's work because they will require students to create linear systems by analyzing the text.
Tackling Word Problems
After introducing students to word problems, I remind them of a previously learned tool that will help us analyze them: CUBES, a close reading strategy. CUBES is an acronym for C, circle the numbers; U, underline the important words; B, box the question; E, eliminate the extra information; and S, solve. If students are weak in reading, this strategy helps them to focus on the important words when solving word problems.
I ask students to help me use CUBES on the first problem of Tackling Word Problems. I explain that once we have boiled the problem down into parts with our coding, we can more easily tackle the math. I then remind the students of our learning objective, which means we should be creating a system of equations to solve. I ask students to identify the common elements and pick a variable to represent each one. I then record on the Smart board: x = adult ticket; y = student ticket. I ask students to think about what equation we would write for the first sentence. I ask them to record their ideas in their journals. After about 15 seconds, I ask for a volunteer (whose answer I have already verified) to give me their equation. I ask the student to explain how they decided this would be the equation. I then ask all students to write the equation for the second day's ticket sales in their journals. I again select a volunteer to share their equation. I reiterate the math by "reading" the equation while pointing to variables: "9 adult tickets plus 7 student tickets equals $127. And 5 adult tickets plus 2 student tickets equals $46."
Next, I explain that now that we have the system of equations recorded, we are ready to solve. I ask students to choose a strategy they have learned (graphing, elimination, or substitution). Most students will choose the one that is most comfortable for them. I want to encourage them, however, to consider efficiency, so I ask, "Is the strategy you picked the most efficient one for solving this system? Be sure to think about this when solving." I encourage the students to solve the first system, ask for a student to volunteer his/her answer, and confirm with class before repeating the process with the second example.
I reveal the Work Time slide and ask students to read the instructions to themselves while I distribute envelopes with Systems Word Problems cards to them. I explain that they have 20 minutes to solve at least 5 of the problems and they can use whichever strategy they would prefer. I explain that I want the work recorded in their journals along with the solutions. I then start the timer.
Once the Work Time timer sounds, I call the students' attention back to the Smart board for Building Consensus. Although students were just required to solve 5 of the 8 problems, I seek student volunteers to model the process they used to solve each problem. After each student writes the equations and solves, I ask if any student used a different method for solving the system. I show these examples under the document camera to verify that any method can be applied and the same solution results. If no student selected a particular card, I skip it until the end for the class to solve as a whole. After we have solved all eight problems I preview the next day's lesson with students by explaining that we will be