In this part of the lesson, the teacher is walking the students through an example of what they will be asked to do with their small groups. They are using substitution to determine the values of variables in a system of equations. They are substituting values between 1 - 10. Students are observed talking with one another about their thinking and the teacher has students share their thinking after working with each of the four equations.

In this part of the video students are observed discussing their thinking about the problem they are solving. Students are using the shape names and numbers they believe could be the value of each. The teacher calls the class back to whole group and the students talk through their reasoning. The students refer to each others thinking in their explanation, including asking questions of one another's thinking in order to clarify their own understanding.

Here, the teacher is connecting precise mathematical language to the work students are expected to do. The teacher is explaining how the students will use substitution to self-assess whether or not their group has the correct solution, and demonstrating the language she wants to hear the students using in their explanations.

Here, the teacher is checking in with one group to see how they got their answer. Two students explain their thinking to the teacher and how they arrived at their answer.

This is part of the lesson near the end of the class period where the teacher calls on different groups/students to share their strategies about how they solved the problems. The students name their strategies as resourcefulness, working backwards, guess and check, counter balance, common sense, simple thinking, and logical prediction. The students don't all understand the explanation given for "counter balance" so the teacher has another student explain it in his own words to clarify the understanding for all students.

In this part of the lesson, the teacher summarizes the mathematics and reinforces the focus of the lesson by asking the students if they remember what it's called when they have equations where every value is the same in that group. The teacher connects systems of equations to the concept of algebra (future work).