2A:  In this part of the lesson, the teacher is beginning with an example to show the students how they will be working with expressions in today\'s lesson. They begin by observing a pattern created with toothpicks. The students must correctly identify what the next three terms would be (fifth, sixth, and seventh terms) and then write an expression to show how the number of toothpicks is related to the term number in the pattern (the expression can be used to determine how many toothpicks are in any term). Once students have created an expression, the teacher asks if there are any other expressions that would represent the same thing:  equivalent expressions. This sets students up for their independent work.

3D:  In this part of the lesson, students are working on the introduction problem. Students are sitting in table groups where they are encouraged (by the teacher and seating arrangement) to talk about their thinking. The teacher is walking around asking questions and offering support to students who are struggling to find an entry point. Students are observed sharing their ideas with each other. One student can be overheard asking whether she should start with one or five, because of where her work with the pattern started. Two students are sharing the numbers they got and explaining how they got them.

3C:  In this part of the lesson, one student is at the board explaining her thinking behind the expression she wrote. Her expression is 2s + 2. She demonstrates by substituting the shape number into her expression and proves that the information is correct.

2B:  This video clip shows students working with grade-level problems for an extended period of time. The students\' task is to work with their table groups to determine which of the nine given expressions are equivalent to their original expression (2s + 2). Students are using different strategies they\'ve already learned to prove their answer (yes or no) is correct. The teacher is circulating during this work time and asking questions of students to determine understanding.

3A:  Here, the teacher is with a small group asking questions and prompting students in order to get them to share their thinking about the lesson.  For example, the teacher says, \"How do you know 3 is yes?\" and \"Give me an example of how that is different.\" One student who appears unengaged while his classmates are explaining is held accountable by the teacher as she asks him to restate what his peers said. When he unable to do so, she has the other students explain their ideas again.

2D:  Here, the teacher is checking on the understanding of one group of students. One student in the group says she does not understand this. A student proceeds to explain her thinking. The teacher adapts the lesson through the support she offers this struggling student. She refers to a handout that shows the Distributive Property and reminds students how it works. Then, she has the students continue with the remaining expressions.

2C:  As the lesson is wrapping up, the teacher asks the students if there is any expression they did not understand why it was or was not equivalent to the target expression. One student points out number 7. The teacher calls on a student to share how he solved expression number 7.  That student demonstrates how he used the table from the original graphic organizer to substitute a number in and determine equivalence. The teacher calls on another student who explains how she rewrote the expression to group like terms (Associative Property). A third student mentions simplifying but is unable to explain how. A fourth student shows how simplification can be used to show equivalence.

2E:  For the closure of the lesson, the teacher summarizes the mathematics of the lesson by having students share what strategies they can use to determine whether two expressions are equivalent. These include properties of operations (distributive and associative), simplifying, substitution (plug & chug), and like terms.