Effect of Increasing Length and Width on Area
Emily and Mauricio compare the areas of two home offices. One office was formed by increasing both the length and width of the other office. The students create a visual representation of the area of the new office that breaks the room into four parts. They write arithmetic equations that express different ways to find the area of the new office.
Episode 1: Making Sense
Mauricio and Emily make sense of floor plans that architects use to represent rooms in a house.
Episode 2: Exploring
The students make a drawing to find the area of a home office and explain its meaning.
Episode 3: Reflecting
Emily and Mauricio reflect on the meaning of multiplication when finding the area of a rectangular room. They show multiplication as “groups of” in their drawing.
Episode 4: Making Sense
Mauricio and Emily make sense of a situation in which both the length and width of a rectangular office are increased by 3 feet. They make a prediction about how these increases will affect the area of the new room.
Episode 5: Exploring
The students create a drawing to explain why increasing the length and width of a room increases the area so much more than they predicted in Episode 4.
Episode 6: Exploring
Emily and Mauricio create a drawing that splits the area of the new room (from Episodes 4 and 5) into four parts. They determine the area of each part.
Episode 7: Reflecting
Mauricio and Emily reflect on their drawing from Episode 6 and write equations to express different ways to find the area of the new room.
Episode 8: Repeating Your Reasoning
The students apply what they learned in the previous episodes to explore a new situation in which the length of a media room is increased by 3 meters and the width is increased by 2 meters. They make a drawing and write equations to find the area of the new media room in different ways.