The purpose of this activity is for students to use what they have learned about measuring angles to measure the angles of streets. Students measure the angle formed by a horizontal line that they create and the street in each image. A ruler or straightedge may be helpful for students to use as they create the horizontal line, and they might want to trace the line and extend the line that represents the street. This experience will be helpful in a later activity when students create steps for an angled street and determine what angle would make steps too hard to climb.

• Invite students to share how they measured the angle formed by the streets and a horizontal line.
• Invite students to share how living on a steep street might be different from living on a flat or level street.
• “Based on the angles you measured, which image do you think is of Baldwin Street, which holds the record for the steepest street in the world?” (Image A and Image E, because they are equal and formed the greatest angle between the street and the horizontal line.)

The purpose of this activity is for students to use what they have learned about angles to solve a problem involving steps. Students draw given angle measures formed by the ground leading from a parking lot to a playground and a horizontal line. Students create a drawing with an angle that they choose, and then determine at which angle the steps would become too hard to climb or too steep.

Students have to make many assumptions that are not described in the task, such as the horizontal distance between the parking lot and the playground and what it means for steps to be “too steep.” When students consider assumptions about information not given in a situation, model a situation, using a representation such as a drawing, and think about the real-world implications of their model, they model with mathematics (MP4).

• Invite previously selected students to share their drawings.
• “Why might different groups find different numbers of steps for the same angles?” (The measurement of the angles could have been a little off. They might not have counted a small step as a step. They might have used a different length for the horizontal line between the parking lot and the playground.)
• “How did you decide what angle would be too steep or too hard to climb up?” (We tried different angles and when we got past , the steps seemed like they would be hard to climb. We said because the steps were taller than they were long, so we thought it would be too steep.)