Time Frame
Allow 5 minutes for the preliminary (introductory) measurement activity. (This may be done the day before.) The initial inquiry-based math ice investigation will take approximately one hour. The optional extended inquiry-based "Further Investigations" may take one to two weeks.

Engagement and Exploration (Student Inquiry Activity)
A. Each group will set up for the ice activity by placing an absorbent pad or towel on the table. The plastic shoebox-size container will go on top of the towel along with a two-liter bottle of water. The students will pour the water into the container when instructed. It is helpful to have a roll of paper towels for each group. Each pair of students will have a centimeter ruler, a black Sharpie, and 2 strings or laminated paper strips (~21 cm long). Since ice melts quickly, it is helpful to keep the cups of ice in the cooler or freezer until students are ready to work with the ice.

B. Pass out worksheets, "A" and "B", to each group of four students. One pair will record answers for "A", while the other pair records answers on worksheet "B".

Give each pair of students frozen ice: one pair will get "A" (half-filled), and the other pair will get a "B" (full) 3-oz Dixie cup with frozen ice. The students will remove the paper cup after warming in their hands for five seconds. The students will record the measurements of their ice in the top section of the worksheet. The students will measure and record the height. Review and demonstrate if needed. Then have the students measure the diameter by measuring the flat surface across the top. The students will use a strip of paper or piece of string (mark with a Sharpie or pencil) to note the measurements of their ice, then correlate measurements to the centimeter ruler. The students will need to record each measurement on their worksheet before moving to the next step. The students will measure the circumference around the bottom, middle, and top. (Demonstrate if needed, and remind students to record the measurements each time.)

C. Procedure for the bottom of the first worksheet: The students will be involved with an inquiry-based "hands-on" ice investigation: "Will the dimensions of the ice (size or amount) make a difference in how ice will float in the water?"

1. Each group of four students will have a two-liter bottle filled with water and a plastic shoebox-size container. The students will fill each container two-thirds with water. 2. The students will make a prediction of how the ice will float when gently placed in water. 3. The students will draw a water line in the perimeter box at the top of the page before drawing their prediction of how they think the ice will float in the water. 4. Each pair of students will place their ice in the container of water and record their observations on their worksheets. Encourage the students to "talk" about what they are seeing. 5. The students will draw a water line and their "results" in the box at the bottom of their worksheet. 6. The students will write down their conclusion (Why do the students believe it happened? What caused it to happen?).

D. On the third worksheet, the "Ice Activity Summary Page", the students will work in groups of four. Each group will have a recorder to write down notes for this page. A representative from each group will disclose the results of their investigations.

The students will write a final conclusion based upon the comparison of the two investigations. Did the ice in the cup filled "halfway"(A) and the cup filled "to the top" (B) do the same thing when placed in the water? In this case, the one variable changed for the investigation was the amount of water (size of ice) in each cup.

Explanation (Discussing)
The observations and conclusions should be different for the ice on worksheet "A" and "B". The students should discover that the "half-filled" ice would float upright, while the ice from the "filled" cup will in most cases float on its side. The way it floats depends on the height and width of the cup. (Students later tried ice experiments with various water levels and containers to see if their predictions held true. For this comparison study, the students used milk cartons. They discovered that if the ice dimensions were almost the same, then the cube-shaped ice floated on any side, while ice from a "filled" quart-sized milk carton floated sideways.) NOTE: The biggest surface area of the ice will float on the top if the ice dimensions are significantly different. QUESTION: If one variable were changed, would the results be different? The students will answer this question in their own inquiry-based, hands-on investigations.

Elaboration (Polar Applications)
Future Experiments: This section on worksheet 3 is optional. These inquiry-based investigations may be extended class investigations, or homework. It is worth the time and effort and proved to be the best part of the activity.

1. The students will collaborate together in groups of four to think of other ice investigations. The goal is to encourage students to ask investigative-type questions. (Questions that may be answered through a hands-on investigation). On a separate sheet of paper, the students will begin by listing several "I wonder if…"questions. On day 2, they will choose one of their questions to "investigate". The investigation will lead to discovery if the students only change one variable at a time.

2. The teacher facilitates and guides the students to stay focused on their investigation. It is important not to tell ideas to the students because the "inquiry" part of the lesson is based on what they come up with on their own. Let the students discover through their own investigations. Failures or mistakes may lead to new discoveries or new questions. Learning is like a gift….Don’t open the package for the student. The joy of learning is in the discovery, and the process of learning is based on this discovery.

3. The teacher will approve and monitor the students’ investigations. The teacher’s main goal is to guide the students in keeping focused on their investigation. The students must be reminded several times that only one variable can be changed. Writing down a list of supplies and verbally discussing their plans with the teacher help keep the students focused. Remind students that they must consult teacher before making changes or adding to the approved investigation. Otherwise they tend to add extra variables or bring in other supplies, which changes their project, or keeps it from being a valid investigation.

4. The students will gather supplies, and pre-test (at home) whatever is needed. One group decided to pre-test certain liquids to see which would freeze before making a final decision on the liquids for their investigation (syrup-no, oil-yes). The students were encouraged to use different means of measurement, such as scales, thermometers, pH strips, and tape measures.

5. Presentation: If time is limited, students may do further inquiry investigations jump-started from this ice investigation as an extended learning project at home. This project could be used as an end of term project to be presented in class. Each group of fourth grade students who pre-tested this investigation needed a class period to share their investigations. They chose to involve their classmates in each investigation as they made their presentations by having students help record data, observe results, and discuss observations. If this is not possible, the students may present data on a tri-fold display board, present a power point, or give a brief demonstration of their project along with charts, data, and results.

Exchange (Students Draw Conclusions)
To check out some amazing investigations developed by fourth grade students, go to the "I wonder if…" investigations and summaries from the fourth grade students on the TEA Activity Page titled: "Cold Hard Facts….What Inquiring Minds Will Know". Their ice investigations far surpassed the initial inquiry-based investigation. These activities may be additional ice investigations modified for middle school and high school.

Evaluation (Assessing Student Performance)
In today’s classrooms, limited time and the emphasis on testing keep many teachers and students from doing in-depth investigations. While "further investigations" is listed as optional, pre-testing this ice investigation with students reinforced the importance for including this part of the activity in the final lesson. It was observed that the greatest learning took place when students investigated their own questions and presented it to the class. As classroom teachers, we noted that learning evolved as the students went from the beginning phase of writing the "I wonder if…" questions, to collecting, discussing, measuring, observing, and recording their data. They gained tremendously as they presented their investigations to the class. The questions and observations improved during each presentation. They began to learn terminology, such as transparent, translucent, opaque, spicules, grams, circumference, density, and pH as part of their vocabulary rather than vocabulary needed to pass a test. The students grew the most when they presented the investigations to the class, then reflected on the outcome of their investigation in a group conference with the teacher. As the students summarized their investigation (In the case of fourth graders, the teacher typed their responses), the students discussed what did and didn't work, and whether they would have made any changes in their project. Taking time to discuss the project proved to be beneficial in the evaluation of their project for both the students and the teacher. The students gained a greater understanding of the scientific process by reflecting and talking over the results of their investigation. When the students gathered their notes and verbalized their investigation, they began to analyze and discuss what they had learned and what they would have done differently. This led to the realization that the summarization process, which is often bypassed due to time constraints, is critical in moving students to a higher level of learning.

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