Start a class discussion about oil spills in the news and their
effects on the environment. If your students remember the 2010 Gulf of
Mexico Oil Spill, the discussion could begin there. Early, accurate
area measurements for that spill were difficult to locate; as more oil
spread, it broke up, and sunk. Weeks after the leak began in April,
2010, descriptions of surface area were no longer used. The following
rough numbers were based on information broadcast by National Public
|Date||Approximate Area (sq mi)|
No matter what oil spills have occurred within your students'
memories, you can have them research information. Have students search
resources such as Scholastic News Online for "Oil Spills." Students
should take notes on what they learn.
Prior to the lesson, form your students into groups of 3 or 4 and
gather a cake pan for each small group. Prepare a transparency of the
10×10 unit grid for each pan using the Oil Oil Everywhere Grid Activity Sheet.
Oil Oil Everywhere Grid Activity Sheet
Demonstrate the process of creating an oil spill for the students by using a document camera. Fill the pan with about 1 to 1 1/2 inches
of water. Measure 3 to 5 tablespoons of oil and pour gently into the
pan in one place. Less than 3 tablespoons may result in a small area
(less than 10 square units) which may be too easily counted by the
students. The oil should touch the water directly and not come into
contact with the side of the pan; otherwise the oil may stick to the
If the oil forms more than one rounded area, use the spoon and
gently move the spills together. Show students that slow movements work
best; if the oil moves too quickly it divides into smaller and smaller
droplets. This is a cross-curricular connection to science, as constant
wave actions breaks up oil in the ocean. However, for this activity the
oil spill needs to stay intact.
Show and discuss the Oil Oil Everywhere Grid Activity Sheet
transparency with the students. Ask them to observe the grid; explain
that each square on the grid is called a square unit. Pour 3 to
5 tablespoons of oil into each group's pan and have students observe
their spill. Using the square units, ask students to estimate the size
of their oil spill and write their prediction on the Oil Oil Everywhere Activity Sheet.
Oil Oil Everywhere Activity Sheet
Have students carefully hold the transparency across the top of the
pan. With a non-permanent marker, one student can trace the outside
edge of the oil spill, disregarding the grid lines on the transparency.
Remove each transparencies from its pan, place on a piece of white
paper so it is easily seen, and set it aside.
Use the Fractional Amount
Overhead and demonstrate how to find an estimated unit total. Students
work in half or whole square units to estimate their oil spill. Take
one color pen and color a variety of units that would estimate to a
whole unit. Then, take a second color pen and color a variety of units
that students would estimate to be about 1/2.
The whole and half units are added together to arrive at the total
estimate. With the students, use the same process and estimate the oil
spill at the bottom of the Overhead for group practice.
Students then take their own transparency, estimate the area of
their oil spill, and write their estimation on their individual
activity sheet. Have students compare their prediction to the estimate
and determine how close they were. Direct each student to write a
comparison statement on the activity sheet. For example: "My prediction
was 3 square units more than my estimation." Have students share
predicted and estimated whole number units for each group's spills.
Clean off each transparency.
Students next use spoons and gently pull the oil spills into
different shapes. If the spill divides, it can stay in two pieces or
gently be formed into one spill again. The goal is to have a shape
distinct from the previous more rounded one. Instruct students to keep
the oil away from the sides as much as they can; a tendril-like shape
is optimal. The oil tends to eventually move back into a rounded form.
Move the oil slowly, and then let it stabilize.
Have students make a new prediction of area and record it on the
activity sheet. Then hold the transparency onto the pan in a quick and
smooth manner and trace the area of the new shape of spill. Students
remove the transparency and estimate the area as they did before. They
record the estimate and write a comparison statement for the second,
differently shaped oil spill.
Wrap up the hands-on part of the lesson by using these questions to spur student thinking:
- What surprised you about the interactions between the oil and water?
[Answers will vary. Students may not have understood that
oil and water really do not mix, that the oil floats on top of the
- Did you expect that the area of the oil spill would remain the same no matter its shape? Why did you think that?
[Answers will vary. It makes sense that the area would remain constant since no other oil was introduced.]
- If your oil spill changed its area measurement, what do you think is happening to account for that?
[Though we know the oil amount has not increased, some oil
may sink, stick to the sides or bottom of the pan, spread more thinly
on the surface, etc.]
Pose one question at a time and have students talk in their groups.
Have students share their answer using popcorn sharing. Set a timer for
2 (or more) minutes and have students randomly "pop" (stand) up around
the room one at a time to share their ideas. Do this for each question.
Having heard many comments from other students, they can then complete
Question 8 on the activity sheet. Student answers should reflect ideas
discussed during the popcorn sharing.
Strengthen the connection between the activity and real life.
Revisit and discuss the information students researched about oil
spills and the effects on the environment. Since students have created
oil spills, they can compare and contrast real-life knowledge to the
activity and complete Question 9 on the activity sheet. Students can
also reflect on the accuracy of measuring real oil spills. In real life
it is sometimes unknown how much oil has been released into the water.
The oil can stick to objects, be mixed into the water, break up into
many parts on the surface, and sink to the bottom, etc. It is therefore
very difficult to measure oil spills; once a lot of oil is released and
days or weeks go by, oil spills are not usually described in terms of
Have each group of students draw one of their oil spills on graph
paper (1-inch grid). They can draw it to scale and label the estimated
area. Next, have each group reflect on real-life and classroom oil
spills and write four different statements, each detailing a likeness
or a contrast between the two. Lastly, have students glue the drawing
onto a poster board, adding the compare/contrast statements, a title,
- Gordemer, B. (Producer/Director), & Goodwyn, W. (Interviewer). (2010, April 28). [Interview with JOHN HOUSTON, MARY LANDRY, CHARLIE HENRY, DOUG SUTTLES]. Morning edition. [Radio broadcast]. Washington, DC: National Public Radio, WAMU.
- Winkler, A. (Producer), & Block, M. (Interviewer). (2010, April 27). [Interview with Doug Helton]. All things considered. [Radio broadcast]. Washington, DC: National Public Radio, WAMU.
- Winkler, A. (Producer), & Raz, G. (Interviewer). (2010, May 1). [Interview with Greg Allen]. All things considered. [Radio broadcast]. Washington, DC: National Public Radio, WAMU.
Questions for Students
1. How easy was it to decide if a partial square was closer to 1/2 or 1 whole square unit?
[Answers will vary, students may even arrive at different conclusions, and need to discuss.]
2. Did rounding your fractional amounts to the whole number make your estimate more or less accurate?
[Students should have some concept that if more amounts
were rounded up or down then the estimate would be higher or lower than
the actual units.]
3. Read your comparison statements. Was your predicted or
estimated area larger? Was this the same for both the rounded and
shaped oil spills? How does this compare with another group?
[Answers will vary. Students may see patterns in others'
predictions and estimations, such as, "Most groups predicted higher
than the actual estimations."]
- How successful was the estimation using fractional units? Did students have good strategies to deal with the half squares?
- How motivating was it for students to work with the oil and water? Was it motivating to the point of being problematic?
- What management techniques were most successful and were your
behavior expectations followed? If not, what would improve the lesson
management next time?
- Did students make connections between the action of their oil
spills and real life spills? What important concepts did they take away
- What might you change about the lesson the next time you use it?
- Predict, estimate, and record the area of a surface covered by oil.
- Predict, estimate, and record how area changes when oil spills are split, moved, and/or recombined.
- Use whole and fractional amounts to estimate.
NCTM Standards and Expectations
- Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results.
- Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes.
Common Core State Standards – Mathematics
Grade 3, Num & Ops Fractions
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3, Measurement & Data
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
Grade 3, Measurement & Data
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-- whole numbers, halves, or quarters.
Grade 3, Measurement & Data
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Grade 3, Geometry
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Grade 4, Measurement & Data
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Grade 5, Num & Ops Fractions
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Common Core State Standards – Practice
Make sense of problems and persevere in solving them.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.