This lesson focuses on students solving systems of equations algebraically, building on the work they have previously done with graphing and using tables. Students are writing and solving equations based on information in real-world problems. This lesson strongly exhibits Core Action 1 and Core Action 2.
Solving Systems of Equations by Substitution (Redd)Download
Here, the teacher relates today's lesson to what the students have been working with in class and for homework over the last week. Students have worked with examples with three equations and also with making tables and graphs to solve systems of equations. Today, they are going to learn to solve the equations algebraically.
In this clip, the teacher is observed checking for student understanding. She uses questions to guide the students' thinking in order for students to be able to write an equation using two variables to represent the total number of items purchased. She does not tell the struggling students the correct equation; rather, she encourages them to talk to one another to come up with the correct answer.
In this part of the lesson, the teacher is asking questions (such as "Why do you have y there?" and "What does that mean?" and "Does it make sense to replace the y with 16?") to get students to share their thinking. Through these questions, the teacher is checking for understanding and determining how to best support each student.
Here, the teacher has asked a student to share the equation her group came up with. Although the equation is not correct, it appears to be a deliberate decision by the teacher, allowing the other students to think about and respond to the equation written. The teacher then calls on another student to share his equation. Since more than one group came up with the incorrect equation, this strengthened a number of students' understanding.
In this part of the lesson, a student is observed to be struggling with writing the equation. The student already knows the "answer" from the table that was completed at the start of the lesson. The teacher is trying to get the student to forget about that answer and write an algebraic equation, substituting what he knows from the first equation into the second equation. She does not provide the "right answer" and the student continues working.
Here, the teacher is checking for understanding of a student. When she realizes he does not understand what is being asked of him, she gets bags of candy to represent the problem (uses manilpulatives) so the student can connect a concrete representation to the abstract equation.
In this clip the teacher is working with a small group of students to guide their thinking. The students respond to the teacher's questions demonstrating their developing thinking. Students are observed elaborating both in response to the teacher's questions as well as unprompted.