The purpose of the discussion is to notice that equations that have been multiplied by the same value have the same solution.

Consider asking students to explain why their solutions might be the same for each row.

For each row, the two equations are equivalent. Sample responses for each row:

1. The equation in column B is 2 times the equation in column A.
2. In each column, one side of the equation is the distributed form of the same side of the equation in the other column.
3. The equation in column B is of the equation in column A.
4. The equation in column B is of the equation in column A.
5. The equation in column B has added to both sides of the equation from column A.
6. The equation in column B is of the equation in column A.

While there may be other valid ways of connecting the equations (for example, in row 4, dividing the equation in column A by 3 and dividing the equation in column B by 2 result in the same equation), encourage students to recognize that there is a single multiple of one equation that results in the other equation.

The mathematical purpose of this activity is for students to get a chance to follow through on a plan of how someone might reason through a contextual situation that can be modeled by a system of linear equations. As students come to understand solving equations as a process of reasoning about equivalent statements, they benefit from getting to interpret the reasoning of others.

This will benefit students when they attempt to solve systems of linear equations on their own in their Algebra 1 class.

In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).

The purpose of this discussion is to help students synthesize and generalize what Jada and Priya were doing as they explored different combinations of objects whose weights they could determine, which would help them find the true weights of the objects.

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response explaining Jada and Priya’s processes by correcting errors, clarifying meaning, and adding details.

• Display this first draft:
  Jada and Priya found out the weight of each object by making it so the amount of one of the objects was the same on each scale and then adding the scales together.
  Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.
• Select 1–2 students or groups to slowly read aloud their draft. Record for all to see as each draft is shared. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Here are some questions for discussion:

• "When did they add or subtract what was on the scales? Why?" (When they knew the weight of the same number of items as are on the scale, they could subtract to find the weight of the remaining items.)
• "When did they multiply what was on the scales? Why?" (When they knew the weight of some items and multiplying would make it match the number of items on the other scale. This would let them subtract the weights to find out the weight of the remaining items.)
• "What does this have to do with solving systems of equations?" (There are two situations with two unknown weights of objects.)
• "Can you think of a move that Jada or Priya could have made that would not have helped them?" (Adding the weights at the beginning to find the combined weight of all the items would not have been useful.)

If time allows, ask students to pick one of Jada's or Priya’s moves that they thought was crucial, and to explain why it was so helpful in finding the weight of one object on the scale.