Compare the Length of Objects Indirectly
Warm-up: Number Talk: Add within 100 (10 minutes)
- Display one expression.
- “Give me a signal when you have an answer and can explain how you got it.”
- 1 minute: quiet think time
- Record answers and strategies.
- Keep expressions and work displayed.
- Repeat with each expression.
Find the value of each expression mentally.
- \(35 + 20\)
- \(35 + 25\)
- \(30 + 45\)
- \(37 + 45\)
- “Did anyone have the same method but would explain it differently?”
- “Did anyone approach the problem in a different way?”
Activity 1: Which is Longer? Which is Shorter? (15 minutes)
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.
Advances: Listening, Representing
Materials to Gather
- Each group of 4 students needs access to the materials from the previous lesson and one unsharpened pencil.
- Create a two-column chart with the headings “longer” and “shorter” for the synthesis.
- Groups of 4
- Give each group an unsharpened pencil and access to the objects from the previous lesson.
- Display two objects that are not the same length (for example, a crayon and a marker).
- “How do the lengths of these objects compare?” (The crayon is shorter than the marker. The marker is longer than the crayon.)
- 30 seconds: quiet think time
- Share responses.
- “You are going to compare the length of objects to the length of the unsharpened pencil. Find two objects that are longer than the pencil and two that are shorter than the pencil. Write a sentence for each comparison.”
- 8 minutes: independent work time
- Monitor for two objects that are close in length but one is found to be longer than the unsharpened pencil and one is found to be shorter.
Find 2 objects that are longer and 2 objects that are shorter than the unsharpened pencil.
Write a sentence that compares each object to the pencil.
Example: The bulletin board is longer than the pencil.
- 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 length of objects to the pencil, we know that some objects are longer or shorter than others without lining them up.”
Activity 2: Measure Your Desk (20 minutes)
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 can not 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 a table, identify one side of the table that is near the same length as one of the table legs for students to measure.
Supports accessibility for: Attention; Visual-Spatial Processing
- Each group of 2 needs a piece of string longer than the length of the side of the students’ desks shown in the activity.
- Groups of 2
- Give each group a piece of string and scissors.
- “We saw that sometimes we can compare length without lining up the objects. Now, you are going to compare the length of a side of your desk to the length of one of the legs of your desk.”
- Display the image.
- “This image shows which side we will be measuring. Trace the length of the side you will measure with your finger.”
- “Why is it important that everybody knows which side of the desk we should measure? Does it matter which leg of the desk you measure?” (One side is longer than the other, so we need to make sure we are measuring the same thing. All the legs are the same length, so it shouldn’t matter which one we measure.)
- “Compare the length of the side and the length of one of the legs of your desk using the string. Then, show how you know which is longer using words or drawings.”
- 10 minutes: partner work time
- Monitor for students who compare indirectly by marking or cutting the string to match one length and then comparing the string to the other length.
Compare the length of the side of your desk and the length of one of the legs of your desk using the string.
Use a drawing or words to explain how you know which is longer.
Advancing Student Thinking
- “How did you use the string to compare the length of the side of the desk and the length of the leg?”
- “How could you use the string to tell whether the side or the leg is longer?”
- Invite previously identified students to share.
- “How was the string useful in comparing the lengths?” (You could put the string next to each part of the desk to see which one is longer.)
Display three objects and the statements:
“The pencil is longer than the crayon.”
“The pencil is shorter than the tower.”
“Jada says that the crayon is shorter than the tower. Do you agree? Why or why not?” (Yes, if the crayon is shorter than the pencil and the pencil is shorter than the tower, then the crayon is shorter than both.)
“What other statements could we say about the objects?” (The crayon is shorter than the pencil. The tower is longer than the crayon and pencil.)