The Winter Olympics are coming! Here at Central School we are going to hold a mini-olympics. The countries participating are Germany, France, Switzerland, Japan, Canada and the U.S.A.. There will be a total of 24 medals given out. 3 medals will be given for each event: 1 gold, 1 silver, 1 bronze. There are 8 sporting events. These include slalom skiing, downhill racing, ski jumping, figure skating, speed skating, bobsledding, luge and freestyle snowboarding. Your assignment is to mathematically determine which countries should get medals in which events so that all of the medals are given out, resulting in 3 winners for each event. Each country must win at least 2 medals. Remember to show how you organize your work and the steps you follow to solve this problem. Good luck! 1 of 11
Suggested Grade Span 3 5 Task The Winter Olympics are coming! Here at Central School we are going to hold a mini-olympics. The countries participating are Germany, France, Switzerland, Japan, Canada and the U.S.A.. There will be a total of 24 medals given out. 3 medals will be given for each event: 1 gold, 1 silver, 1 bronze. There are 8 sporting events. These include slalom skiing, downhill racing, ski jumping, figure skating, speed skating, bobsledding, luge and freestyle snowboarding. Your assignment is to mathematically determine which countries should get medals in which events so that all of the medals are given out, resulting in 3 winners for each event. Each country must win at least 2 medals. Remember to show how you organize your work and the steps you follow to solve this problem. Good luck! Alternative Versions of Task More Accessible Version The Winter Olympics are coming! Here at Central School we are going to hold a mini-olympics. The countries participating are Germany, Canada and the U.S.A.. There will be a total of 9 medals given out. 3 medals will be given for each event: 1 gold, 1 silver, 1 bronze. There are 3 sporting events. These include slalom skiing, downhill racing and ski jumping. Your assignment is to mathematically determine which countries should get medals in which events so that all of the medals are given out, resulting in 3 winners for each event. Each country must win the same number and value of medals. Remember to show how you organize your work and the steps you follow to solve this problem. Good luck! More Challenging Version The Winter Olympics are coming! Here at Central School we are going to hold a mini-olympics. The countries participating are Germany, France, Switzerland, Japan, Canada and the U,S.A.. There will be a total of 24 medals given out. 3 medals will be given for each event: 1 gold, 1 silver, 1 bronze. There are 8 sporting events. These include slalom skiing, downhill racing, ski jumping, figure skating, speed skating, bobsledding, luge and freestyle snowboarding. Your assignment is to mathematically assign medals to each of the 6 countries, resulting in 3 winners for each event and all countries receiving the same total value of medals. Remember to show how your organize your work and the steps you follow to solve this problem. Good luck! 2 of 11
Context We have been working on mathematical representations in problem solving that include graphs, plots, charts, tables, models and diagrams. This problem gives the students an opportunity to utilize a mathematical representation to solve a task and to communicate the steps they followed. It is a task that also requires the use of multiplication and division, which we are studying in class. What This Task Accomplishes This task enables the teacher to see how well and how effectively students can represent their solution. It also gives insight into students understanding and use of multiplication and division. Time Required for Task 60 minutes (approximately). Interdisciplinary Links Our physical education teacher is currently teaching each Olympic event to the students, and classes are holding mini-academic Olympics. These are just some ways to integrate the Olympics into the classroom. Another way is to have students follow the Olympics, making predictions and then recording actual winners for each event. Students can collect news and magazine articles to share, as well as draw maps and research the different countries participating in the real Olympics. Teaching Tips Students will first need to decide how to represent all the information given to them in the problem. Some may use charts or tables, while others will create their own form of representation. Student will then need to decide who wins what medals and for what events, following the guidelines given in the problem. How they decide will be up to them, as long as the criteria are met. Students may think about the numbers themselves, their factors and how they can be grouped. Much of this process will involve managing information, checking and comparing to make sure all of the medals are given out for each event. Some students may need a head start or some ideas to help them get started in solving the problem. Other students can be challenged to come up with more than one solution. It is important for students to have previous exposure to various types of representations so that they have some knowledge to draw upon. The newspaper USA Today is an excellent source of examples of a variety of mathematical representations. You can focus a bulletin board in your classroom on Math Representations of the Week. Students could discuss the pros and cons of the different types of representation and critique, as well as model, those that appear in the paper. 3 of 11
Suggested Materials Pencil Paper Manipulatives if needed Possible Solutions There are many possible solutions. There are also a number of patterns evident in some solutions that students may discover. The important thing to consider is how well students represented their solutions and the degree to which their solutions meet the guidelines given. More Accessible Version Solution See the solution to the original version. More Challenging Version Solution See the solution to the original version. Task-Specific Assessment Notes Novice While the Novice may attempt to solve the problem by creating a chart, the strategies and reasoning will be difficult to understand or are not indicated by the representation. It will also be difficult to see the steps or process the student followed. The Novice s chart may be inappropriate in that it makes it hard to ascertain whether or not the solution is correct. The Novice s work demonstrates the need to continue to work on the skill of mathematical representations. Apprentice The Apprentice will have a partially correct solution or a solution that has some flaws. The Apprentice will use an appropriate representation. There will be some evidence of the student s strategy and reasoning. The Apprentice may neglect to discuss the steps followed for finding a solution, and math language will be limited. Practitioner The Practitioner s solution will show a good understanding of mathematical representation and will demonstrate a good application of the concepts in solving this problem. The Practitioner will describe the steps and process followed and will use an effective strategy for solving the task. The explanation will be clear and the solution will be accurate. Math language will be used to communicate. 4 of 11
Expert The Expert s strategies and reasoning will be even clearer than the Practitioner s. The Expert may be able to further describe the concepts of multiplication that are used, along with other mathematics applied to the solution. The Expert s representation will be clear and the solution will be correct. An accurate use of math notation and language will be applied throughout. The Expert will make mathematically relevant observations about the solution. 5 of 11
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