This class discussion highights how two students, James and Danielle, interpret x differently. Another student, Matt, uses money (quarters) to explain the distinction between the two interpretations.

# Growing Dots

## Revisiting James & Danielle

Two students share their methods for solving the Growing Dots task, one describing recursive thinking (x + 4) and the other presenting an explicit expression (x4 + 1).

## Revisiting Angel’s Question

As students discuss a variation of the Growing Dots task in which the starting point is shifted, one student shares that when the first dot is at time 0, the rule is 4x – 3. Another student, Angel, asks, “Where is the –3 in the picture?”

## James & Danielle

Two students share their methods for solving the Growing Dots task, one describing recursive thinking (x + 4) and the other presenting an explicit expression (x4 + 1).

## Matt & James

This class discussion highights how two students, James and Danielle, interpret x differently. Another student, Matt, uses money (quarters) to explain the distinction between the two interpretations.

## Working Backward

After solving the Growing Dots task, students are asked to work backwards to determine at how many minutes they will have 25 dots, 73 dots, and 99 dots. In this clip, students share how they arrived at their answers.

## Angel’s Question

As students discuss a variation of the Growing Dots task in which the starting point is shifted, one student shares that when the first dot is at time 0, the rule is 4x – 3. Another student, Angel, asks, “Where is the –3 in the picture?”

## Casey & Irma

After working on a variation of the Growing Dots task in which the starting point is shifted to several different times, students share what their graphs look like for several different starting points, and the discussion moves on to focus on connections across the graph, table, and equation.