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.

# Pool Border

## Revisiting 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.

## Siri & Tiffany

Siri & Tiffany’s group share how they approached the Pool Border task, decomposing the border into four “side plus corner” pieces, the equation for which they write as n = s4 + 4

## Pascal, Adam, & Tammy

Pascal, Tammy, and Adam to go to the board and show their equation, n = (s + 2)4 – 4, explaining that each of the pool’s 4 sides is s + 2, giving you (s + 2)4. They add that since they counted each of the 4 corners twice, they needed to subtract them out (– 4).

## Lulu’s Group

Lulu shares her group’s equation, n = (s + 2)^2 – s^2, explaining that it describes finding the area of the larger square (side length s + 2), then subtracting the area of the pool (side length s). Debra (the teacher) asks another student to paraphrase Lulu’s group’s approach.

## 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.

## Different Equations

After Debra’s class has determined y = 4x + 4 as one equation for solving the Pool Border task, Debra asks them to work in small groups, exploring visually to find as many other equations as they can.

## 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?”