Three students share their methods for soliving the Similar Triangles on the Same line task, one using translation and dilation, one using similar rectangles, and the other presenting parallel lines. tranversal and equal angles.

# Implement Tasks That Promote Reasoning and Problem Solving

## Launching a Discussion

Debra (the teacher) launches the Pool Border task in her class. During this whole class discussion, several students share their initial thoughts on how they would go about solving the Pool Border task.

## Discussing 5 by 5

Debra (the teacher) asks students to consider how many 1 x 1 tiles would be needed to create a border for a 5 x 5 pool. The class then discusses the different approaches students took to counting the tiles, both correct and incorrect.

## Debra’s Question

After small groups share three different equations to determine the number of 1 x 1 tiles needed to form a border for a square pool with side length x, Debra asks, “Are these equations the same?”

## Comparing Logos

After discussing several equations for Regina Logo (linear function) and Schemel’s Logo (quadratic function), students consider how the two tasks are similar and different. As the lesson closes, the teacher asks them to do a journal write on how the graphs of the two functions compare.

## 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.