Active+Learning+Investigation

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**WHAT FLOATS YOUR BOAT? **
 * Grade Level: ** 4-6
 * Prep Time: **45 minutes
 * Lesson Time: ** 60 minutes


 * Overview: ** In this active learning investigation students are challenged to make a “boat” out of aluminum foil that can fit the most boxes before it sinks. The lesson serves as an active way for students to chart data and use that data to create a box-and-whisker plot chart. They will be asked to find the five key numbers needed to make this chart including the median, high and low quartile, and smallest and greatest value. After analyzing the first set of class data, they will be given a chance to build another boat to see if they can increase the number of boxes that will fit into their boat before it sinks. This allows students the opportunity to look at the data collected in a box-and-whisker plot chart to problem solve, and think about what they would change to create the most effective boat design moving forward.


 * Rationale: **The important concepts the students will be focusing on throughout this active learning investigation will be using data to problem solve and draw conclusions. The students will understand how to create a box and whisker chart and to use that information to problem solve. Using charts to plot data helps students to visualize findings and analyze data, which is especially effective based on real life experience. During this investigation, students must work on their communication skills. They must discuss how they would build their boat and how they would change it a second time after analyzing the class data. They must also think about the size of foil they have been given, the size of the “lake”, the approximate weight of the cubes, and the ideal placement of the cubes to ensure the highest capacity. These skills improve their ability to cooperate and problem solve. This investigation also connects to the students’ lives because it allows them to think of boats in the real world and the best types of structures that boat makers use to carry cargo. Analyzing and evaluating the information from the class, will allow students to draw conclusions on the mathematical data.

**Washington State Standards:** 3.5.E. Construct and analyze pictographs, frequency tables, line plots, and bar graphs. 4.4.E. Determine the median, mode, and range, of a set of data and describe what each measurement indicates about the data. 4.5.A. Determine the question(s) to be answered given a problem situation. 4.5.E. Select and use one or more appropriate strategies to solve a problem and explain why that strategy was chosen. <span style="font-family: 'Cambria','serif'; font-size: 16px;">4.5.G. Explain why a specific problem-solving strategy or procedure was used to determine a solution. <span style="font-family: 'Cambria','serif'; font-size: 16px;">4.5.H. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. <span style="font-family: 'Cambria','serif'; font-size: 16px;">4.5.I. Summarize mathematical information, draw conclusions, and explain reasoning. <span style="font-family: 'Cambria','serif'; font-size: 16px;">4.5.J. Make and test conjectures based on data (or information) collected from explorations and experiments. <span style="font-family: 'Cambria','serif'; font-size: 16px;">5.5.B. Determine and interpret the mean of a small set of whole numbers.


 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Materials Needed: **
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Plastic containers – at least 8” wide, 8” long and 4” deep - quantity depends on # of groups
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Plastic cubes – approximately 3-5 grams - 100 per group
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Aluminum foil
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Water to fill each container


 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Preparation: **
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Fill plastic containers with 3” of water – each of these containers can be referred to as lakes (label them specifically, if you wish)
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Cut 6” x 6” squares of aluminum foil – 2 for each group


 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Learning Targets: **
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Students will be able to plot data on a box-and-whisker chart.
 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Students will be able to use box-and-whisker charts to compare sets of data and problem solve.


 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Description: **
 * 1) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Introduce the learning targets to the students to set up the intention of the active learning investigation
 * 2) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Place the “lakes” around the room and assign students to the “lake” that they will be working with
 * 3) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Give each group two pieces of 6" x 6" aluminum foil (specify that only one piece will be used for the first part of the activity)
 * 4) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Next to each “lake” place approximately 100 plastic cubes
 * 5) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Explain to the students that they will be making a boat using ONE piece of their aluminum foil. They can make the boat however they would like to, but their goal is to put as many plastic cubes into their boat before it sinks. Define sinking as when any amount of water makes it into the boat.
 * 6) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Each group must record the capacity, or the total number of cubes that they were able to fit into the boat BEFORE it sank.
 * 7) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Record the capacity of each group on a table on the overhead projector then work as a class to complete the box-and-whisker chart. Begin by finding the mean of the class, then the lower quartile, the upper quartile and finally the range.
 * 8) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Based on the data in the plot chart, have the class make conclusions about effective boat designs and their capacity.
 * 9) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Break the students back into their groups and allow them to create a second boat and try the experiment again with their second piece of aluminum foil.
 * 10) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Follow the same steps, recording each group’s capacity on the overhead projector, creating a box-and-whisker plot chart, and calculating the key data points from the chart.
 * 11) <span style="font-family: 'Cambria','serif'; font-size: 16px;">Conclude the lesson asking students what they learned. Guide students to tell you their mathematical observations, but also real life observations as well.


 * <span style="font-family: 'Cambria','serif'; font-size: 16px;">Assessment: **<span style="font-family: 'Cambria','serif'; font-size: 16px;">Each student will be given a third set of data assuming that the experiment was conducted yet again. They will be asked to complete a box-and-whisker chart specifying the 5 key numbers: median, high and low quartile, and smallest and greatest value. Depending on time, each student could be asked to explain how they would construct their boat a 3rd time and why they see this as the most effective boat design. They should also be encouraged to think about what they learned and how they could apply this to real life.

<span style="font-family: 'Cambria','serif'; font-size: 16px;">**Resource:** Illuminations - Resources for Teaching Math


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