Summary
Small group activities help students understand and estimate the measurement of volume.
Materials
Marshmallow Mouth
- Mini-marshmallows
- 5 Bottles of different sizes
- 5 cups of rice
- Pigs in the Pantry; Fun with Math and Cooking
- Math Journals
Crazy Cups
- Quart milk cartons
- Containers
- Rice
- Measurement containers
- Measurement "cups"
- Crazy Cups
Additional Resources
Books
Pigs in the Pantry; Fun with Math and Cooking, by Amy Axelrod; ISBN 0-689-80665-5
Background for Teachers
Volume and capacity are the measurements used to describe the
inside of a container. The definition of volume is the measurement of
space occupied by anything. The definition of capacity is the amount
a container holds. An object such as a rock or a brick has volume but
no capacity. People began measuring volume, as they did with mass
and weight, using natural objects like eggshells. The problem was
that eggshells could differ in size. It became necessary for people to
develop a standard unit of measurement.
The Babylonians were the first to develop a standard unit for
measuring capacity. They used a hollow cube with specific linear
measurements filled with water. This gave them the first unit of
capacity. Today, a cube filled with water is still used as a standard unit
of capacity.
Intended Learning Outcomes
1. Demonstrate a positive learning attitude.
2. Develop social skills and ethical responsibility.
Instructional Procedures
Invitation to Learn
Have the students correct silly sentences. They can record their
corrections in their Math Journals.
For example:
- John is very thin. He weighs 60 inches.
- Sarah poured juice for each student. She gave each child a quart.
- Susan walked a long way. She walked 10 centimeters.
- The bug crawled across the desk. It went about 6 miles.
Instructional Procedures
Marshmallow Mouth
- Read Pigs in the Pantry to the class. Discuss what happened
that made it so difficult for the pigs' recipe to turn out correctly.
Discuss how important it is to use accurate measurement when
asked to do so.
- Have several containers at the front of the room that vary in
capacity. Try to use bottles that are short and fat, long and
slender, as well as bottles that are familiar to the students.
- Work as a class to order the bottles by capacity. Be sure that
the labels are removed so that the students cannot see the
capacity listed on the label.
- Once the bottles have been put in order, fill the bottle that is
predicted to hold the largest amount to the top with rice. Use a
black marker line to show the full capacity
- Use the rice from the largest bottle to fill the next largest bottle.
Talk with the students to determine if this container is filled to
capacity. Repeat with the remaining bottles. Be sure to always
use rice from the first/largest bottle. The main point for the
students is that if the rice from one container overflows when
poured into a new container, the first container has a larger
capacity. If the rice does not come to the rim or top of the
container then the first container has a smaller capacity.
- Rearrange the bottles, if necessary, in the correct order from
largest to smallest. It is important that the order does change
from the original order so that the students understand that
looks can be deceiving.
- Relate to the students that they have just determined the
capacity of the bottles. Use the correct terms throughout the
lesson so that the students become familiar with their meanings.
- Group the students into pairs. Have each student estimate how
many mini-marshmallows it will take to fill their own mouth to
capacity. Students will keep their teeth clenched and fill their
mouths between their teeth and cheeks to avoid any possible
choking hazards. Students will record this observation in their
Math Journals. Partners should also estimate each other's
mouth capacity by looking into their partners open mouth.
Record this observation as well.
- When all estimates are done, pass out a generous handful of
mini-marshmallows to each team. Tell them that their mouths
are filled when their lips can still close over the marshmallows.
There is no eating until all of the work is done. Have students
begin filling their mouths with the marshmallows. One student
fills his/her mouth while their partner counts and records the
data.
- Make a large chart that shows each child's name and the
capacity of marshmallows his/her mouth can contain. Compare
largest to smallest, equal to, not equal to, etc.
Instructional Procedures
Crazy Cups
- Place the following containers at the front of the room. Have
the containers labeled:
1 gallon, 1 quart, 1 pint, 1 cup.
- Discuss where they have seen these objects before.
- Review the need for a standard from of measurement.
- Using the rice, show several examples of the relationships
between the different containers.
- Have the students break into small groups. Each group should
have 5 containers that can be filled with rice using a 1 cup
measure.
- Have them estimate how many cups they would find in each
container. Record it on the Crazy Cups blackline.
- Using rice, have students measure the correct amount into each
container. Record their findings on their Crazy Cups blackline.
Extensions
Curriculum Extensions/Adaptations/
Integration
- Have students bring in containers that they think hold 1 cup.
Break into teams and explore.
- By pairing up, students who do not understand or have other
special needs can still participate and have a successful learning
experience.
Family Connections
- Have students choose 4 bottles or containers at home and have
them determine the capacity of these bottles from greatest to
least. Have them record data and return it to school.
- Have students help cook something for dinner with their
parents. Request that the recipe calls for measurement
using cups. Have the student report to the class about their
experience.
- Compare written estimates in children's Math Journals for
reasonable estimates and measurements.
Assessment Plan
- Use the class graph as a discussion/assessment tool. Review
what capacity means.
- Discuss how various containers may have capacities larger or
smaller than expected.
- Show students a 1 cup container. Have students list 5 other
containers that would have less than 1 cup capacity. Record
estimates in their Math Journal.
Bibliography
Research Basis
Rommel-Esham, K., (October, 2007). How Much Popcorn Will Our Classroom Hold?
Science and Children 45(2) 22-26.
How much popcorn will our classroom hold? This intriguing
question sparked a terrific integrated science and math exploration
conducted with fifth and sixth-grade students. In the process of
finding the classroom's volume, students developed science-process
skills (e.g., developing a plan, measurement, collecting and interpreting
data, prediction, inference, communication, and using number
relationships) and applied mathematical processes (determining an
estimate, using benchmarks, measuring, mapping, etc.) in a meaningful
way-getting an authentic glimpse of how these two subjects are
inextricably linked.
Downey, J.A., Cobbs, G.A., (January 2007). "I Actually Learned A Lot from This": A
Field Assignment to Prepare Future Preservice Math Teachers for Culturally Diverse
Classrooms. School Science and Mathematics 107(1) 391-403.
Teacher education programs are cognizant of the need to prepare
preservice teachers (PTs) to work effectively with children from diverse
cultural backgrounds. Well-constructed field experiences can help
PTs develop awareness and gain understanding of important cultural
considerations related to effective teaching and learning (Sleeter,
2001). This paper describes a unique field assignment created for an
Elementary Math Methods course in which 61 PTs were trained to
conduct a semi-structured interview with a student whose cultural
background was different than their own. PTs transcribed their own
interviews and completed a guided reflection on their experiences.
Reflections were submitted and analyzed for emerging themes.
Analyses suggest that the structured interview component of this field
assignment provided PTs with increased insight into mathematics
instruction and the learning needs of diverse students. It also discusses
the value and limitations of this instructional innovation and propose
avenues by which to continue to help PTs grow toward becoming
culturally relevant pedagogies (Irvine, 2003).