The purpose of this activity is to give students a concrete experience of building the boundary of shapes and quantifying that length of the boundary, allowing them to conceptualize perimeter as a measurable geometric attribute. Students use -inch paper clips as the units for measuring the distances around four shapes. This prepares them to reason about equal-size intervals that can be marked on the sides of a shape to measure its length (as students will see in the next activity).

• Select previously identified students to share their responses and strategies for finding the number of paper clips. Record the different strategies for all to see.
• “In this activity, we found the length of the boundary of shapes. The boundary of a flat shape is called its perimeter.”
• “When we find the distance all the way around a shape, like we did with paper clips, we are measuring its perimeter.”
• “To find the length of the perimeter of a shape, we can find the sum of its side lengths.”
• “We can say that the perimeter of Shape A is 13 paper clips long.”
• “When we say ‘find the perimeter,’ we mean find the length of the perimeter.”

In this activity, students find the perimeter of shapes—first on dot paper, and then using the tick marks on the sides of the shapes. Students may need a reminder that when we measure length, we count the number of length-units, not the number of endpoints. While students may count the tick marks on all sides and add them, they may also observe that some side lengths are the same, especially on Shapes A and B, and use this structure and multiplication by 2 to find the perimeter efficiently (MP8).

• “How are you finding the distance around the shape?”
• “How could you keep track of the side lengths as you work?”

• Select students to share their responses and strategies. Start with students who counted individual units and move toward those who use operations.
• Record the strategies for all to see.
• “Which shape, C, D, or E, has the greatest perimeter?” (C, because its perimeter is 33 units and the other two are 30 and 32 units.)
• Consider asking: “Which shape has a greater perimeter: the rectangle in the first problem or the triangle?” (The triangle has 33 units while the rectangle has 22 units, but the units aren’t the same length, so we don’t know which perimeter is greater.)