Mass and Volume
Description:To familiarize students with basic lab skills, as well as integrate math into science, we begin this unit with two hands on laboratory activities. Students will learn the techniques of massing objects, measuring volume and displacement, and identifying the meniscus of a liquid. The difference between mass and weight is addressed, and demonstrated through the use of differences in gravity on other planets. Finally, students will design an experiment to determine the volume of a paperclip.
Last Updated:Oct-27-2009
Subject(s):- Mathematics
- Mathematics > Arithmetic
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Experiment/Lab
- Curriculum: Unit
-
- Contributed By: Micki Halsey Randall
Mass and Volume - Teacher Introduction
Description:Timeline and instructions for implementing this unit in your classroom
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Measurement
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Curriculum: Scope & Sequence
National Standards:
UCP.2: Evidence, models and explanationRationale:
UCP.3: Change, constancy and measurement A.1: Abilities necessary to do scientific inquiry A.2: Understanding about scientific inquiry B.2: Structure and properties of matter
The meniscus and displacement lab introduces the students to several terms common to labs. Additionally, students learn an alternative method for determining the volume of an object. The Oreo lab creates interest by using a brand students are familiar with and the excitement of getting to eat the lab samples at the end of class. After spending the beginning of this unit with hands on activities, students settle down for note taking and worksheets. The worksheets include hands on application and illustrations by students. The cube activity has student construct a figure and then construct a similar figure with 100 times the volume. This reinforces the concept of volume and allows students to kinesthetically experience a dramatic increase in volume. Finally, students design their own experiments to determine the volume of a paper clip.Integration: Include the math teachers in this unit. Coordinate with them to reinforce volume, measurement and averages during their classes.
Day 1:
Meniscus and Displacement Lab with clay (see document in this unit)Day 2:
Oreo Lab (see document in this unit). Have students complete the first section of the lab the first day and save the cream fillings (with labels) for the next day's activities.Day 3:
Finish Oreo lab. After all lab equipment is cleaned, have students discuss their results as a class. Make a list of all of the averages from each group on the board.Day 4:Find the average of each column. Discuss this as a class. What is the advantage of looking at all of the data together? (More samples correlated to more accuracy). Did the Double Stuf cookie have double the stuffing? Which measurement best supports this conclusion? How many groups' final conclusion matched the class' conclusion? What were sources of error? Was anyone surprised by the results? You may want to briefly discuss advertising and ask students what they think of the name "Double Stuf."
Groups Mass
(regular)Mass
(Double Stuf)Volume
(reg)Volume
(DS)Displacement
(reg)Displacement
(DS)1 2 3 4 Class average
Discuss Mass vs Weight using the brief notes provided in this unit. Follow up with the worksheet comparing mass and weight on different planets in our solar system. Students may need help with the calculations to begin, so I suggest completing the first planet as a class. The mass should be written down the entire column so students become familiar with the idea that mass does not change. After the tables are completed, students will use hand held masses to experience the difference in weight of a textbook on different planets. You will need to have a scale available to them to measure the textbook's initial mass.Day 5:
Volume of different shapes worksheet. Provide visual examples of each shape listed in the table and talk through the formulas with them using the physical examples. To complete the worksheet, students illustrate an example for each shape and label the dimensions (length, width, radius, etc.). Follow up with the using formulas practice worksheet.Day 6:
Cube activity (see handout in this unit)Day 7:
Demo: What happens to the mass and volume of water and sugar when mixed?Day 8:Use a 250mL beaker and about 8 cubes of sugar. Add 150 mL of water to the beaker. Mass out the beaker with water in it. Record on the board. Mass the sugar and record. Measure the sides of the sugar cubes and calculate the total volume and record. Add the sugar to the water. Ask students to make observations. Stir the sugar. Ask for observations again. Determine the new volume and mass of the sugar water mixture. Record. Does the new mass equal the mass of the water/beaker plus the mass of the sugar? Discuss. Did the total volume change? Discuss. You may want to introduce the idea of conservation of mass.Introduce the document: lab report basics
Culminating Activity: What is the volume of a paper clip? Introduce this activity along with the lab report basics document. Students develop their own experiments to answer the question. Encourage students to think about all of the activities they have done before deciding on a procedure. Also, require multiple trials in their experiment. After reading the lab handout together, have students sit and think of ideas for accomplishing their task. Then, ask for ideas and list them on the board. Students may need to hear the ideas of others before they are able to come up with their own experiments. If students choose to do a displacement lab (the method I would suggest), they will notice the water does not overflow when it reaches the top of the container. (This could start a discussion on water cohesion and hydrogen bonding.) However, if they continue to add paper clips, when the water overflows, the water could be collected and measured to determine the amount of volume displaced.Day 9:
Finish experiments and work on lab reports. Be sure students understand your expectations for an appropriate lab report.Day 10:
Lab report peer review. Students review the lab reports of their teammates using the provided worksheet. Students may rewrite their reports using the critiques of classmates. Be sure students understand they are not scoring the work of their classmates. Instead, they are offering suggestions for improvement. By reading the reports of others, they are also reflecting on their own work in comparison. Reflection, use the reflections document for students to reflect on their learning and to communicate with you.
Meniscus and Displacement
Description:When using a ruler is not the most efficient way of determining volume, we need to offer other suggestions. In this lab, students determine the volume of an object by finding the displacement of the liquid when the object is added to a beaker.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Measurement
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Experiment/Lab
Problem: What is a meniscus? How much water is displaced when an object is dropped in a container of water?
Background information:
Define and illustrate meniscus.
Define and illustrate displacement.
Define Mass.
Define Volume.Hypothesis:
Materials: Beaker, graduated cylinder, clay, water
Procedure:
1. Measure 50 mL of water in a graduated cylinder.
2. Draw the meniscus.
3. Measure the mass of an empty 250 mL beaker. Record.
4. Pour the water into a 250 mL beaker.
5. Repeat steps 1 and 2, then pour the water into the beaker.
6. Record volume and mass.
7. Draw the meniscus.
8. Obtain a piece of clay and measure the mass. Record.
9. Gently place the clay in the beaker of water.
10. Record the new volume of the contents of the beaker.
11. Determine the displacement of water in the beaker. Record.
12. Remove clay from beaker and dry the clay.
13. Measure the mass of an empty 50mL graduated cylinder. Record.
14. Measure 40 mL of water in a graduated cylinder.
15. Draw the meniscus of the graduated cylinder.
16. Measure the mass of the clay. Record.
17. Gently place the clay in the graduated cylinder of water.
18. Record the new volume.
19. Record the new mass.
20. Repeat steps 13 through 19 with 20 mL of water.
21. Clean table and equipment. Keep clay at your table. Return all other clean materials to cart.
22. Mold clay into a rectangle. Measure and record length, width, and height in centimeters. Multiply these values to determine volume, record.
23. Mold the same piece of clay into a sphere. Measure the diameter of the sphere in centimeters, record. Determine the volume using the formula: v=(4/3)πr³, record.
24. Return clean clay to appropriate location on cart.Data:
| Trial Number | 1 (100mL) | 2 (40mL) | 3 (20mL) | Average |
|---|---|---|---|---|
| Initial Mass of Beaker (g) | XX | |||
| Init. Mass of Graduated Cylinder (g) | XX | |||
| Amount of Water (mL) | XX | |||
| Volume of Water and Beaker/Grad. Cyl. (mL) | XX | |||
| Mass of Water and Beaker/Grad. Cyl. (g) | XX | |||
| Mass of Clay (g) | ||||
| Mass of Clay, Water and Beaker/Grad. Cyl. (g) | XX | |||
| Volume of Clay, Water and Beaker/Grad. Cyl. (mL) | XX | |||
| Displacement (mL) |
| Rectangle | Sphere | |
|---|---|---|
| Length (cm) | XX | |
| Width (cm) | XX | |
| Height (cm) | XX | |
| Diameter (cm) | XX | |
| Volume (cm³) |
Analysis: Please answer these questions.
1. What was the displacement of water for each trial? 2. What was the mass of the clay for each trial? 3. What was the volume of the sphere? rectangle?
Conclusion:
1. What did you notice about the amount of displacement in each trial?
2. Did the mass of the clay change during the experiment? Explain.
3. Compare the volume of the clay in the sphere to the volume of the clay in the rectangle.
4. Compare the volume of the clay in the rectangle to the average displacement of the water.Reflection:
Oreo Lab
Description:Oreo lab
Last Updated:Oct-21-2011
Subject(s):- Mathematics
- Mathematics > Measurement
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Experiment/Lab
Problem: Are Double Stuf Oreos really double stuffed?
Hypothesis:
Procedure:
Day 1
1. Obtain 2 regular Oreo cookies and 2 Double Stuf Oreo cookies.Day 2
2. Weigh each cookie individually. Record data to the nearest hundredth of a gram (0.XX)
3. Measure the width and diameter of the cream filling of a regular Oreo. Record data to the nearest millimeter. Repeat for all 4 cookies.
4. Find the volume of each cookie using this formula:
volume = width x 3.14 x (½ x diameter)².
5. Carefully remove the chocolate wafers of one regular cookie and weigh the wafers and then the cream separately. Record data to the nearest hundredth of a gram (0.XX). Repeat for all four cookies.
6. Store and label your cream fillings in a sealed bag. Clean your work area and the scale thoroughly.
7. Collect your cream fillings and a 50ml graduated cylinder. 8. Pour 20 ml of water into the graduated cylinder. 9. Place one of the the cream fillings in the water. The filling may crumble, or need to be broken up to fit in. 10. Measure and record the displacement. 11. Repeat steps 8 through 10 for all four fillings. 12. Clean up and wash your hands.Data:
Day 1
| Cookie | Mass Whole Cookie (g) | Width (mm) | Diameter (mm) | Volume (mm³) | Mass Chocolate Wafers (g) | Mass of Cream (g) |
|---|---|---|---|---|---|---|
| Filling | Regular 1 | Regular 2 | Double Stuf 1 | Double stuf 2 |
|---|---|---|---|---|
| Initial volume of water (mL) | ||||
| Final Volume of water (mL) | ||||
| Displacement (mL) |
Analysis:
1. Average the masses and volume of your regular cookies from table 1.
Mass of whole cookie: _________ Mass of chocolate wafers: ____________
Mass of Cream: _______________ Volume: ______________
2. Average the masses and volume of your Double Stuf cookies from table 1.
Mass of whole cookie: _________ Mass of chocolate wafers: ____________
Mass of Cream: _______________ Volume: ______________3. Average the displacements of your cookies from table 2. Regular displacement: _____________________ Double Stuf displacement: _______________________
Conclusion:
1. Based on your data, are Double Stuf Oreos double stuffed? Support your answer.
2. How did the volume from the first day compare to the displacement the second day? Explain.
3. Which method of measuring volume (ruler or displacement) was most efficient for this experiment? Why?
4. What sources of error happened in your lab?
5. How could you improve this lab for next time?
Mass vs. Weight Notes
Description:An outline of notes to be used on an overhead or written on the board for students to copy.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Measurement
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Asset: Audio/Speech/Lecture
the amount of matter in an objectstays the same regardless of location of the objectmeasured in pounds or kilograms
the force exerted on an object by gravityvaries depending on location (you weigh less at the top of a mountain than at the sea level)measured in Newtons
Mass vs weight on different planets - worksheet
Description:A worksheet for students to compare the weight of objects on each of the planets using the gravitational pull of each planet.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Arithmetic
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Graphic Organizer/Worksheet
| Planet | Mass (lbs) | Gravity (relative to Earth) | Weight (N) |
|---|---|---|---|
| Mercury | 0.38 | ||
| Venus | 0.91 | ||
| Earth | 1.00 | ||
| Moon | 0.165 | ||
| Mars | 0.38 | ||
| Jupiter | 2.34 | ||
| Saturn | 1.06 | ||
| Uranus | 0.89 | ||
| Neptune | 1.13 | ||
| Pluto (dwarf planet) | 0.07 |
| Planet | Mass (lbs) | Gravity (relative to Earth) | Weight (N) |
|---|---|---|---|
| Mercury | 0.38 | ||
| Venus | 0.91 | ||
| Earth | 1.00 | ||
| Moon | 0.165 | ||
| Mars | 0.38 | ||
| Jupiter | 2.34 | ||
| Saturn | 1.06 | ||
| Uranus | 0.89 | ||
| Neptune | 1.13 | ||
| Pluto (dwarf planet) | 0.07 |
3. Use mass bars to feel the difference in weight between your textbook on Earth (just hold your textbook) and your textbook on Jupiter, the moon, and Pluto. Write down your observations in the table below.
| Planets | Jupiter | Earth's moon | Pluto |
|---|---|---|---|
| Weight | |||
| Observations |
Volume Formulas
Description:A listing of formulas for volumes of various shapes
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Geometry
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Asset: Audio/Speech/Lecture
| Formula | Illustration | |
|---|---|---|
| Cube | side³ | |
| Rectangle | length x width x height | |
| Cylinder | πr²h, where h is height | |
| Cone | (1/3)πr²h | |
| Sphere | (4/3)πr³ |
Volume - Formulas practice worksheet
Description:Use this worksheet for practice with volume formulas.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Arithmetic
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Graphic Organizer/Worksheet
Use this worksheet for practice with volume formulas.
Mass and Volume - Cube Activity
Description:Students build a cube using the template provided and measure its volume. Then students build another cube with sides 10 times the size of the original cube. They will determine the volume of the new cube and compare it to the original.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Arithmetic
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Exercise
Paper (2 pieces)RulerScissorsGlue
1. Use a ruler to draw your template with 1 cm sides for your first cube, be sure to remember to draw flaps like this model.2. Cut out the cube as one large piece.3. Glue your cube together by gluing the flaps to the corresponding sides.4. Use your ruler again to measure the sides of your cube.5. Determine the volume of your cube using the formula for the volume of a cube.6. Repeat steps 1 through 5 to build a cube with 10 cm sides.
Data Table
| Cube | side measurement (cm) | volume (cm³) |
|---|---|---|
1. Compare the measurements of the sides of the two cubes.
2. Compare the volumes of the two cubes.
Conclusion
1. What do you notice about the difference in side length compared to the difference in volume of the two cubes?
2. Does your answer to #1 surprise you? Why or why not?
3. How many of your first cubes would you need to make a large cube the size of your second cube?
4. What could you have done differently to improve this lab?
Lab Report Basics
Description:A generic outline for preparing an appropriate laboratory report.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Science
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Experiment/Lab
The intent of a laboratory report is to convey information to the reader about what you did, why you did it, and what your results were. As with all scientific endeavors, lab reports must be organized. As your teacher, I am asking you to write reports you turn into me in the following format. There is no one way to write an appropriate lab report, however, following this template will help me to understand your experiment and results.
Background information
Include in this section information gathered about the problem you are investigating. Prior knowledge and experience should be included as well. This section should be at least one paragraph.
Hypothesis
This is a statement about what you anticipate the outcome to be based on your background information. The information in the statement must be testable.
Procedure
1. Write a procedure in step by step form.
2. These are directions for conducting your experiment
3. Detail, detail, detail
4. These steps should be written so anyone could follow them exactly and come up with the same results
5. There is no limit on the number of steps in a procedure
Data and Analysis
| Data | Analysis |
|---|---|
| Information in tables, charts, graphs | Use words to describe data |
| Color can often help illustrate data | Be specific to data shown in report |
| Titles, labels, units must be noted |
Conclusion
Write a paragraph about your results. Be sure to state whether your hypothesis was supported or not. Remember not to use the term proven; a single experiment cannot prove or disprove anything. Refer back to your background information. This section ties the entire lab together. If I wanted to learn the results of someone’s experiment and did not want to read the whole thing, this is the section I would turn to. Therefore, it needs to be thorough and to the point. Also, state any possible sources of error in your lab.
Reflection
Tell me what you learned in this lab. This part of the lab report is for me only and can be written in first person. What could you have done differently? What could I have done differently? How well did your group work together? Include anything else you would like to share with me. Also, use this as a reflection (hence the name) on your own work and learning.
Mass and Volume - Inquiry Lab
Description:Students design and complete an experiment to determine the volume of a paper clip.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Arithmetic
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Experiment/Lab
Draw and label a paper clip:Describe previous experiments in which you learned about volumes of geometric figuresWhat do you know about the shape of a paper clip? How might that pose a challenge for finding the volume?
Suggestions to think about when developing your hypothesis:
Which method of finding volume will work best for you?
Why do you think your method will be the best?
What results are you expecting?
Provide a complete list of items you will use in this experiment.
Write a detailed, step-by-step procedure to follow in your lab experiment. You will need to have this authorized by your teacher before collecting materials. The procedure must be so well written anyone could pick it up and follow it exactly as you will follow it. Be specific.
| Trial Number | |||
|---|---|---|---|
| Initial volume of water | |||
| Number of paper clips | |||
| etc. | |||
Write in words what your data tells you. Only state facts as evident in the data.
1. Was you hypothesis supported? Why or why not?2. What challenges did you find?3. What is the volume of a paper clip? Compare this with classmates and describe your comparison.4. What errors did you experience in your lab?5. What else did you learn?
1. Overall, how did the lab go for you?2. What would you do differently next time?3. What did you learn? How did you learn it?
Lab Report Peer Review
Description:Use this form to have students evaluate each others' lab reports. After evaluations are complete, students receive one day to correct/improve their lab reports before submitting to the teacher.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Geometry
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Experiment/Lab
| Section | Yes or No | Explain |
|---|---|---|
| Problem: Is the problem clearly stated and makes sense for this project? | ||
| Background information: Does the information presented clearly relateto the project? Does it lead toward a hypothesis? Are the referencessited accurately? | ||
| Hypothesis: Is the hypothesis valid, testable, and measurable? Does it relate to the problem? | ||
| Materials: Do the listed materials match the items used in the procedure? | ||
| Procedure: Is the procedure detailed, easy to follow, step by step and able to be replicated by an outside party? | ||
| Data: Does the report contain an accurate and complete data table and graph? Are they labeled appropriately? | ||
| Analysis: Is the data explained in words? | ||
| Conclusion: Does the conclusion explain the results? Does it discuss the hypothesis? Do you think it is complete and worthwhile? |
Mass and Volume - Reflection
Description:Use this at the end of the unit for students to reflect on their learning, offer suggestions for improvement, and communicate with you.
Last Updated:May-10-2011
Subject(s):- Mathematics
- Mathematics > Arithmetic
- ...
- Grades 6-8 / Ages 11-13
- middle
- 6th
- 7th
- 8th
- tween
- Activity: Exercise

