Science/Math and Technology Applications and Research

(STAR)

an Illinois Math/Science Partnership Grant

Originally developed as part of the (COIILS)

Edited by: Mike Schneider, Bob Williams and Marylin Lisowski

Soon to be Field Tested by: STAR teachers

Description: This activity allows students to apply different mathematics concepts when measuring and counting a variety of different things found in a typical schoolyard. They are challenged to submit the results of several different measurements as a contest.

Grade Levels: 4-8 (Note: This experiment can be simplified or made more challenging depending on the developmental levels of your students. See Teacher Information.)

Approximate Time Involved: This activity is very adjustable to the amount of time you have available. There are a wide range of tasks that can easily be split up into one or several assignments during a class period.

National Mathematics Standards Addressed:

Standard 1: Mathematics as Problem Solving - The study of mathematics should emphasize problem solving so that all students can:

• (K-8) - use problem-solving approaches to investigate and understand mathematical content;
• formulate problems: (K-4) - from everyday and mathematical situations (5-8 - from within and outside mathematics);
• (K-4) - develop and apply strategies to solve a wide variety of problems (5-8 - with emphasis on multi step and nonroutine problems);
• (K-8) - verify and interpret results with respect to the original problem;
• (K-8) - acquire confidence in using mathematics meaningfully;
• (5-8) - generalize solutions and strategies to new problem situations.

Standard 10: Measurement - In K-4, the mathematics curriculum should include measurement so that students can:

• understand the attributes of length, capacity, weight, mass, area, volume, time, temperature, and angle;
• develop the process of measuring and concepts related to units of measurement;
• make and use estimates of measurement;
• make and use measurements in problem and everyday situations.

Standard 13: Measurement - In 5-8, the mathematics curriculum should include extensive concrete experiences using measurement so that students can:

• extend their understanding of the process of measurement;
• estimate, make, and use measurement to describe and compare phenomena;
• select appropriate units and tolls to measure to the degree of accuracy required in a particular situation;
• understand the structure and use of systems of measurement;
• extend their understanding of the concepts of perimeter. area, volume, angle measure, capacity, and weight and mass;
• develop the concepts of rates and other derived and indirect measurements;
• develop formulas and procedures for determining measures to solve problems.

Illinois Applications for Learning: Through applications of learning, students demonstrate and deepen their understanding of basic knowledge and skills.

• Recognize and investigate problems; formulate and propose solutions supported by reason and evidence.
• Express and interpret information and ideas.
• Use appropriate instruments, electronic equipment, computers and networks to access information, process ideas and communicate results.
• Learn and contribute productively as individuals and as members of a group.
• Recognize and apply connections of important information and ideas within and among learning areas

Illinois Math Goal 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

• Standard A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings
• Standard B. Investigate, represent and solve problems using number facts, operations ( addition, subtraction, multiplication, division) and their properties, algorithms, and relationships.
• Standard D. Solve problems using comparison of quantities, ratios, proportions, and percent.

Illinois Mathematics Goal 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

• Standard A. Measure and compare quantities using appropriate units, instruments, and methods.
• Standard B. Estimate measurements and determine acceptable levels of accuracy.
• Standard C. Select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.

Illinois Mathematics Goal 10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

• Standard A. Organize, describe and make predictions from existing data.
• Standard B. Formulate questions, design data collection methods, gather and analyze data and communicate findings.

Illinois Language Arts Goal 1: Read with understanding and fluency.

• Standard C. Comprehend a broad range of reading materials.

Illinois Language Arts Goal 3: Write to communicate for a variety of purposes.

• Standard A. Use correct grammar, spelling, punctuation, capitalization, and structure.
• Standard B. Compose well-organized and coherent writing for specific purposes and audiences.
• Standard C. Communicate ideas in writing to accomplish a variety of purposes.

Illinois Language Arts Goal 5: Read with understanding and fluency.

• Standard A. Locate, organize and use information from various sources to answer questions, solve problems and communicate ideas.
• Standard B. Analyze and evaluate information acquired from various sources.
• Standard C. Apply acquired information, concepts and ideas to communicate in a variety of formats.

Teacher Information:

Challenging Your Students to Be Problem Solvers:

To make this activity more challenging to your students, you may want to pose some open-ended questions such as: Determine the number of bricks that were used in the construction of the school building using the simplest method possible. Determine the height of the tallest tree in the schoolyard and describe the method(s) you used to accomplish this task. Do an inventory of all of the trees in the schoolyard and then use a computer spreadsheet program such as Microsoft Excel to create a table and chart (graph) of your data. Determine the percentage of the school property that is covered with concrete, asphalt, and or gravel. Determine the percentage of the school grounds that is used for team sports. Determine the highest and the lowest point on your school property in feet above sea level. Convert this standard measure to a metric measure. If the area of the schoolyard was equally divided among all of the students in your school, how much space would each student occupy? Using only a meter stick, determine the approximate length and width of the schoolyard within a twenty minute period of time.

This is also a great time to add a bit more technology to your students’ measurement activities.  One instrument that is becoming a common piece of technology is the Global Positioning System or GPS.  Your students can use the GPS to measure certain things in the schoolyard and then compare its accuracy to a less technical instrument the students may be using.  By collecting and naming the waypoints, your students can later download the information into the computer to be plotted on a map using a Geographical Information System or GIS.  This computer software is also becoming an important on-the-job technology component in many career fields.     

This should become a team exercise where your student groups might each develop an inventory form of their own design, determine the most efficient way for the group to collect and record the data, design a schedule for collecting the data, gather their materials and equipment, and conduct a self-evaluation of their work. An excellent way to assess this activity is to have the teams repeat each other's steps for solving some of the open-ended problems they have been assigned. This will replicate some of the same challenges faced by engineers, carpenters, landscapers, and others as they gather data to complete a real world project.

Student Instructions Available to download as a PDF file.

Needed Materials:

The materials for this activity will vary according to the methods the students choose to solve their open-ended problems. It is best to challenge the students to determine what materials and equipment they may need. Part of the open-ended problem may indicate what materials or equipment the students are permitted to use.

Safety Rule:

Students should be made aware that this is an instructional activity and appropriate behavior is expected when they are conducting these activities in the schoolyard. All equipment is expected to be used for the appropriate purpose.

Procedure :

Student Information: In this activity, you may be challenged to conduct and determine a variety of measurements and quantities. Part of your assignment may be to describe the method(s) you used to take your counts or determine your measurements. It is important to recognize that mathematical problems can be solved in a number of different ways. Your challenge may be to come up with a method that is both fast and accurate. Sometimes, it can also be beneficial to do a little research ahead of time. You might look in your math textbook for a method, or you may want to search the Internet. These are just a couple possible ways to help you solve your measurement problems. Many times your accuracy can be greatly enhanced by taking an average of several measurements or counts. When you have completed your schoolyard inventory, be sure to submit your findings using the online schoolyard inventory form. After you have submitted your data it will be displayed with other existing data and can be edited. It will also be a downloadable Excel file. You will be able to download the spreadsheet and then bring it up on your computer and do comparison tables of your school inventory to the inventories of others.

List of Schoolyard Inventory Possibilities

• 1. Click on the “View Data” link at the Schoolyard Inventory Activity web page. Click on “View” in the blank sample listed on the chart.  What comes up is the data collection sheet that will be used in this activity.
• 2. The following information provides you with a variety of measurement activities that you can conduct on your school grounds as part of a collaborative student group.
• 3. It is up to you, with some help from your teacher, to choose the appropriate measuring devices for each measurement activity you have been assigned.
• a. Total amount of: school property area, schoolyard area, parking area, driveway area, schoolyard used for team sports, schoolyard occupied by playground equipment, blacktop space, schoolyard instructional space, school property space occupied by school buildings, unspecified schoolyard space, catch basin area, other.
• b. What percentage of the whole school property does each of the areas in #1 represent?
• c. Tallest: oak tree, pine tree, cedar tree, maple tree, elm tree, ash tree, sycamore tree, fruit tree, gum tree, other.
• d. Tree with the largest circumference and widest girth at one meter above the ground.
• e. Tree with the largest number of board feet of lumber.
• f. Total number of trees, bushes, wildflowers, flowers, other
• g. Tallest bush
• h. A contour map of the schoolyard showing the lowest and highest elevations above sea level
• i. Total length and square meters of fencing around the schoolyard
• j. Total cubic meters of snow occupying the schoolyard at any one time in 2004-05
• k. Total number of natural rocks exceeding 15 centimeters in diameter found on school property
• l. Deepest point to which the soil froze at any one time in the winter
• m. Total cubic meters of topsoil in the schoolyard
• n. Length of the schoolyard
• o. Number of telephone or power line poles on school property
• p. Amount of aquatic space on school property (including wetlands)
• q. Total number of different species of plants found in one square meter anywhere in the schoolyard
• r. Total number of different species of animals found in one square meter anywhere in the schoolyard
• s. Total number of birds to visit a bird feeder in a ten minute period of time.
• 4. After group and classroom discussions have occurred, login to enter your data.

The reporting form for this experiment is set up so that you can submit your determined measurements and total amounts for several different tasks listed above. NOTE: In some cases, your measurements and total amounts will be much more accurate if you compare your results and or take averages.  In some cases, you will not be able to collect data for a certain task.

Below is a list of questions that can be used to stimulate student discussions. If your students are at a developmental level where you are able to challenge their higher level thinking skills, then only present them with the first set of questions from each group below. Use the second list of questions as a way to stimulate thinking when you students seem unable to expand their knowledge on their own.

Examining Local Data

Discussion Questions That Will Require Critical Thinking Skills to Compare Local Data to the Online Data of Others

• What conclusions that your data present?
• What might you infer based on your conclusions?
• What might you recommend based on your conclusions and inferences?
• How would you redesign your measurement or counting technique to get more accurate and faster data the next time?

Discussion Questions that Require Less Critical Thinking Skills

• Based on your collected data, which tree was the tallest in the schoolyard?
• Which group came up with the most accurate and easiest way to determine tree heights? How many different ways did you find to determine tree height?
• What techniques did you use to increase your speed at measuring certain things? How did this impact the data you collected?
• Describe your methods for determining percentages of the school property.
• What factors may have influenced the accuracy of your counts or measurements? How could you improve the accuracy of your counts or measurements?
• What sources did you use to help you decide the best ways to measure or count some of the things in your schoolyard?
• What sources did you use to make metric or standard conversions? Why?
• What factors may cause your data to change over time?
• What real life applications would your schoolyard inventory experience have?

Examining Online Results

Discussion Questions That Will Require Critical Thinking Skills to Compare Local Data to the Online Data of Others

• How did your data compare with the data of others?
• What conclusions can you make when you compare your data with the data of others?
• What inferences can you draw from differences in your data and the online data?
• Has the additional information caused you to question the accuracy of any of your data? Why or why not?
• What changes would you now make in your data collection methods based on the information you now have?

General Discussion Questions that May Occur as a Result of Comparing Local Data to the Online Data of Others

• Where is the geographic location of the schools who have provided online data?
• How did the data you collected from your schoolyard compare with that of others?
• What environmental factors may have contributed to differences in the data collected?
• What similarities existed among those schools who provided online data? What differences existed?
• Which school had the tallest oak tree? Maple? Most schoolyard space? etc?
• Based on the collected data on an online school site, describe the appearance of the schoolyard? Figure out a way to contact the school to get a photo as a comparison.
• What is the location of the school with the tallest pine tree?

Assessment

Assessment can be conducted in several ways.

• You may want to use the above questions as a method of assessing what understanding and knowledge your students have gained from the schoolyard inventory activities. To score assessments with open-ended responses, you will need to a rubric. It is important that you review your students' responses before you establish your assessment rubric. A quick review will usually make it possible for you to create three stacks of papers: those that exceed expectations, those that meet expectations, and those that do not meet expectations. You will have some papers that are "fence sitters", making it difficult to determine where they belong. As you make a closer examination of the three groups of student work, list the things that define each group. With this information, you should now be able to determine where your "fence sitters" go and you should have a rubric for continued development.

Mathematics Rubric for Open-ended Problem Solving

Download this pdf file to receive a mathematics rubric developed by the Illinois State Board of Education for the assessment of open-ended mathematics problems. This file can be read and printed on virtually any platform -- Macintosh, Windows, or Unix. You can download the Acrobat player for free from Adobe. For Netscape users, you'll want to use the Acrobat plug-in that makes viewing Acrobat files a snap!

If you have not done so, follow your browser's directions to allow it to recognize and open Adobe Acrobat files. If you need help, you'll find that in the Adobe site as well.
Open-ended Problem Solving Math Rubric

Measurement Conversions Link

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