Measuring Volume of Irregular Objects
Lesson 10 of 13
Objective: SWBAT measure the volume of objects not able to be measured with a ruler, using the water displacement method and a graduated cylinder.
Upon entering the classroom, each student table should have the following items: 1 graduated cylinder, 1 cup of water, a plastic cup including 5 irregular shaped objects (marble, nail, nickel, small rock, anything that is substantial in weight to move the water but small enough to fit inside the graduated cylinder).
For the first few minutes of the lesson, students respond to the following prompt on their student notes sheet within their small groups (3-4 students):
Looking at the marble on the table, discuss with your table mates how you think you will measure the volume (how much space the marble takes up). Jot your notes below.
To measure the volume of the marble, we can…
During this time, I am moving from table to table asking them questions like:
- Can we use the ruler to measure the length, width and height of the marble? Why or why not? How?
(Asking why is a good starting place, but may not uncover the thinking needed to help a student visualize and realize the mechanics of the action, and whether these are suitable to the task. Asking how (or even encouraging the student to actually attempt the task) helps the student to realize on their own why it doesn't work.)
- Can we use the graduated cylinder? Why or Why not? How?
After 4 minutes, I ask the groups to share out their responses to the whole class. I write the on the SMART or white board.
For the next 5 minutes of the lesson, I want to provide the students with an opportunity to explore how the graduated cylinder might help them in calculating volume of the marble. To do this, I have them respond to the following prompt in their notes while working with the members of their small groups:
Using the graduated cylinder and what you know about finding the volume of liquid, discuss how you might find the volume of the marble using the graduated cylinder. Jot your notes below.
To measure the volume of the marble using the graduated cylinder, we can…
- What do we measure with a graduated cylinder? (Measures the volume of the liquid). If students give you, "It measures liquids" stretch their response, as it is not complete without the information regarding the type of measurement we use for liquid. Some ways to stretch student responses include, "Tell me more", allowing a classmate to "add on", or by responding to this "almost right" answer by accepting it as having come "part of the way" - "I like where you're headed. What's the last piece?"
- What happens to the water level when you get into a full bathtub?*
- What do you think will happen if we put the marble in the graduated cylinder? Why do you think that? What will that new measurement tell us?
- Did we add more water? Is that the reason the water level went up?
- So what made the water level go up? Why do you think that happened? (It took up space.)
- What happens when you add ice to a full glass of soda?
If a group or two was able to identify how to use the graduated cylinder for measuring volume of irregular objects, I ask them to explain the steps they use to do so and write them on the SMARTBoard for others to copy into the EXPLAIN section of their notes sheet.
If no group is successful, I ask the same questions from the EXPLORE section to see if I can spark their thinking. I will visually demonstrate the steps using a graduated cylinder and the marble, writing each step on the SMARTBoard as I go. The students then write them in their notes sheet for a reference when using the water displacement method.
1. Pour the water into the graduated cylinder.
2. Record the volume of the water.
3. Put the object into the water.
4. Record the new volume.
5. Find the difference in the initial water level compared to the new water level.
6. The difference is the volume of the object.
For the next 10-15 minutes, have the students practice using the water displacement method following the steps in their notes. They need to find the volume for a minimum of 5 objects, which they should already have in the cups on their tables. It helps to give the students an extra cup to pour out the liquid and the object once finished finding the volume, as it's tough to fish out the object from the graduated cylinder. There is a data sheet they can complete to record their data in their notes sheet.
I walk around and monitor the progress of the groups, making sure each person gets a try and that if someone is struggling, the others are helping in an appropriate way.
Something the students need reminders of is recording the initial volume. Be sure to do that and explain the importance.
Should a group finish before the time is complete, have an extra cup with other objects they can measure.
The last section asks the students to really think about WHY the water displacement method works in measuring the volume of objects. In order to do this, have them respond to the following prompt in their notes:
In your own words, explain how the water displacement method is effective in calculating the volume of the object. How does using the graduated cylinder help to calculate the volume of the object?
Using the graduated cylinder to measure the volume of the marble works because…
This addresses CCSS 6.1 as the students are making a claim about how it works and supporting it with evidence from their experiences.
Acceptable responses might sound like:
The graduated cylinder works to measure the volume of the marble because the liquid takes up a certain amount of space which we can measure in the g.c. When we put in the object, the water goes up even though we didn't add any more water. This means the object in the g.c. is taking up space.