Your friend has just lost a tooth. The tooth fairy always gives your buddy 25 cents each time she loses a tooth. The tooth fairy s piggy bank is full of coins. Determine the ways the tooth fairy can pay your friend. 1 of 11
Suggested Grade Span 3 5 Task Your friend has just lost a tooth. The tooth fairy always gives your buddy 25 cents each time she loses a tooth. The tooth fairy s piggy bank is full of coins. Determine the ways the tooth fairy can pay your friend. Alternative Versions of Task More Accessible Version Your friend has just lost a tooth. The tooth fairy always gives your buddy 10 cents each time she loses a tooth. The tooth fairy s piggy bank is full of coins. Determine the ways the tooth fairy can pay your friend. More Challenging Version Your friend has just lost a tooth. The tooth fairy always gives your buddy 50 cents each time she loses a tooth. The tooth fairy s piggy bank is full of coins. Determine all the ways the tooth fairy can pay your friend. Context These students have been working with money and finding different combinations that equal different sums. What This Task Accomplishes This task allows the teacher to determine how well students can group coins to equal a sum of money and how well they can organize their approach to find all combinations. 2 of 11
Time Required for Task One class period was required (about 45 to 60 minutes). Interdisciplinary Links This task could link to a unit on currency. Recently, the U.S. mint published some interesting facts about coins: The U.S. Mint has produced over 312 billion pennies over the last 30 years, but 198 billion have dropped from circulation. They are probably stashed away in penny jars or hidden in car ashtrays, etc. This leaves 114 billion pennies in circulation, or more than 426 pennies for every man, woman and child in the nation. It would be fun to have students investigate the number of pennies they have stashed at home. The number of coins produced in 1998 includes 10,257,508,500 pennies, 11,323,623,000 nickels, 2,335,250,000 dimes, and 1,867,380,000 quarters. As a study of number sense, students could determine how much cash those coins equal. The U.S. has also started making quarters designed in honor of each state. This would be an interesting study as students could link an investigation to U.S. geography. Teaching Tips Give students play coins to work with, allowing them numerous opportunities to play." They should also practice making change before attempting this task. Suggested Materials Provide students with play money. 3 of 11
Possible Solutions The correct solution is that there are 13 ways. Pennies Nickles Dimes Quarters 25 0 0 0 20 1 0 0 15 0 1 0 15 2 0 0 10 1 1 0 10 3 0 0 5 0 2 0 5 2 1 0 5 4 0 0 0 5 0 0 0 3 1 0 0 1 2 0 0 0 0 1 More Accessible Version Solution 10 pennies, one nickel and five pennies, one dime, or two nickels More Challenging Version Solution Quarters Dimes Nickels Pennies 2 0 0 0 1 2 1 0 1 2 0 5 1 1 3 0 1 1 2 5 1 1 1 10 1 1 0 15 1 0 1 20 1 0 0 25 1 0 2 15 0 5 0 0 0 4 2 0 4 of 11
0 4 1 5 0 4 0 10 0 3 4 0 0 3 3 5 0 3 2 10 0 3 1 15 0 3 0 20 0 2 6 0 0 2 5 5 0 2 4 10 0 2 3 15 0 2 2 20 0 2 1 25 0 2 0 30 0 1 8 0 0 1 7 5 0 1 6 10 0 1 5 15 0 1 4 20 0 1 3 25 0 1 2 30 0 1 1 35 0 1 0 40 0 0 10 0 0 0 9 5 0 0 8 10 0 0 7 15 0 0 6 20 0 0 5 25 0 0 4 30 0 0 3 35 0 0 2 40 0 0 1 45 0 0 0 50 5 of 11
Task-Specific Assessment Notes Novice The Novice may make an attempt to solve the problem but may not have a complete understanding of what the task requires The solution documented will be vague and difficult to understand. Little math reasoning will be present, and little math language used. Apprentice The Apprentice will have an approach that will work for solving the task but will not reach a correct answer due to a reasoning error, a computation error or a lack of organization. Some parts will be clear, but math language will be limited. Practitioner The Practitioner will reach a correct solution that includes all combinations of 25 cents. Work will be organized, and the solution will be complete. Math language will be used, and representations will be labeled and accurate. Expert The Expert will show a unique understanding of the task, resulting in a correct solution. Work will be clear and labeled, showing the relationships between monetary values. The Expert will use math language throughout and will make mathematically correct representations. The Expert will also make mathematically relevant comments about the solution. 6 of 11
Novice 7 of 11
Apprentice 8 of 11
Practitioner 9 of 11
Practitioner 10 of 11
Expert 11 of 11