Lesson 3

The purpose of this warm-up is to elicit the idea that we can compare objects when they are not aligned by using a third object, which will be useful when students compare the lengths of objects in a later activity. While students may notice and wonder many things about these images, comparing using a third object is the important discussion point.

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Which pencil is longer, A or C? How do you know?” (A is longer than B and C is shorter than B, so C is shorter than A.)

The purpose of this activity is for students to compare two lengths indirectly. Since a third object is not given, students choose a third object strategically and share different ways to use a third object to compare (MP5).

Students choose from a variety of objects: connecting cubes towers, pieces of string, and unsharpened pencils. As students compare the length of the paths, students may use a single tool, such as a piece of string to compare the two paths. They may mark or cut the string. Some students may choose the tower of connecting cubes and determine that breaking off or counting the cubes is a way to determine whether one length is shorter or longer than the other. Others may select and try different tools until they find one that has a length that is in between the length of the two paths.

• Each group of 2 needs:
  • Connecting cubes in singles and towers of 10
  • 6-inch and 10-inch piece of string
  • Unsharpened pencil
  • Scissors

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles, string, unsharpened pencils, and scissors.
• “Clare and Mai walk to school every day. You can see their paths on the map. Who has the shorter walk? Choose a tool to use. Be ready to explain your thinking so that others will understand.”

• 5 minutes: independent work time
• “Share your thinking with a partner.”
• 2 minutes: partner discussion
• Monitor for students who use a single tool to compare the two paths and mark the tool to show one length, such as bending string or breaking off cubes to compare the other length.

If students use one object to match the length of Clare’s path and a different object to match Mai’s path, consider asking:

• “Tell me more about how you are using tools to figure out who has the shorter path.”
• “How could you use one tool to figure out who has the shorter path?”

• Invite previously identified students to share.
• “How was using a tool helpful to compare the lengths of the paths?” (We couldn’t put the paths next to each other so it was helpful to have a tool that could be moved from one path to the other to compare.)

The purpose of this activity is for students to compare the length of two objects using a third object. When students decide if the teacher's desk will fit through the door or compare other large pieces of furniture, they will need to be precise about which lengths they are measuring as objects like the teacher's desk, a rug, and a bookcase, have a length, width, and in some cases a height (MP6). Next, they will need to select an appropriate third object to use to compare the lengths they have chosen. Teachers may choose to assign different questions for different groups to start with to facilitate student movement around the room. Teachers may also change any question that does not apply to their classroom.

• Each group needs measuring materials from the previous activity.

• Groups of 2
• Give students access to measuring materials.
• “Have you ever seen someone move a large piece of furniture, like a couch, from one room to another? Is it easy to move big pieces of furniture? Why or why not?”
• 30 seconds: quiet think time
• Share responses.
• “I have been thinking about getting a new desk. If I do, I will have to move this desk out of the room. I am not sure if this desk will fit through the door. How can we check to see if it will fit?” (We could measure with a string.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

• “You are all going to check to see if my desk will fit through the door. You are also going to compare the length of some other objects in the room.”

• 15 minutes: partner work time
• Monitor for a group that measures the width of the teacher's desk and one that measures the length.

• Invite previously identified students to share.
• For each student, ask: “How did they compare the length of the objects? What tool did they use? What part of each object did they measure?”