The purpose of this activity is for students to identify objects that are longer or shorter than a given object. Students find two objects that are longer and two objects that are shorter than an unsharpened pencil. The students use the language of “longer than” and “shorter than” and record their findings in complete sentences so that indirect comparison can be discussed during the Activity Synthesis.

• Display the T-chart with headings “longer” and “shorter.”
• “What objects are longer than an unsharpened pencil?” (a book, the ruler, the height of the desk)
• Record responses.
• What objects are shorter than an unsharpened pencil?” (a marker cap, a crayon, a toothpick)
• Record responses.
• Display previously identified objects that are close in length.
• “How do the lengths of the two objects compare?” (The book that is shorter than the pencil is also shorter than the block because the block is longer than the pencil.)
• “Because we compared the lengths of objects to the pencil, we know that some objects are longer or shorter than others without lining them up.”
• Emphasize that since we know the book is longer than the pencil and the crayon is shorter than the pencil, we know that the book is longer than the crayon. If needed, use this framework with other examples: I know A is longer than B. I know B is longer than C. Therefore, I know A is longer than C.

The purpose of this activity is for students to use a third object to compare two lengths that can't be lined up by endpoints. Students compare the length of a side of their desk to the length of one of the legs of their desk indirectly using a string. This lesson helps students use a familiar object in their classroom and encourages them to mathematize their environment (MP4).

Since the side of the desk cannot be easily compared to the leg of a desk directly, students need to determine how to use the string to compare. For example, they may mark where the length of the side reaches on the string and then compare that to the length of the leg. They may cut the string to be the length of the leg and then lay the string on the side of the desk to compare. Throughout the activity, when students reflect on the language they use and revise it to describe the attributes of objects, the lengths they measure, and how they use tools, they attend to precision (MP6).

If students sit at furniture that is significantly different than the desk pictured in the Task, the teacher can adjust what students measure. For example, if students sit at a table, identify one side of the table that is near the same length as one of the table legs for students to measure.

• Invite previously identified students to share.
• “How was the string useful in comparing the lengths?” (We could put the string next to each part of the desk to see which part is longer.)