My gifted students work on Problems of the Month from our district, but they come with no solutions... help!
Level C
Courtney visited her grandmother. Her grandmother used to collect stamps. She had a shoebox full of 5 cent, 6 cent, and 7 cent stamps. Courtney thought, "I could make a lot of different-sized letters and postcards with these stamps." She tried to figure out the different amount of postage she could make with a combination of those stamps. What totals could she make what totals are impossible? Explain how you found your solution. How do you know your solution is correct?
Level D
Courtney's grandmother said, "Your grandpa has different shoeboxes with other stamps. His shoebox has just 4 cent, 6 cent, and 8 cent stamps. Which totals can you make with these stamps?"
Courtney said, "I wonder why there is a different between Grandma's and Grandpa's shoeboxes. I like finding the largest total I can't make, but Grandpa's box has an unlimited amount of totals I can't make. I wonder why it works for some and not for others." She continues, "I am going to investigate which three stamp amounts are like Grandma's shoebox and which three stamp amounts are like Grandpa's shoebox. I am going to compare three different sets. I will try 6 cents, 7 cents, and 8 cents. Then I will try 6 cents, 9 cents, and 12 cents. Finally I will try 6 cents, 8 cents, and 9 cents." Explain how the three different sets are like either Grandma's shoebox or Grandpa's shoebox.
Level E
Determine a method for predicting whether a given set of any three stamps would have a largest impossible total, or infinite impossible totals. Justify your method using mathematical reasoning.
For those sets of three stamps that have a largest impossible total, make a conjecture about how to find that total.
Help.
Level C
Courtney visited her grandmother. Her grandmother used to collect stamps. She had a shoebox full of 5 cent, 6 cent, and 7 cent stamps. Courtney thought, "I could make a lot of different-sized letters and postcards with these stamps." She tried to figure out the different amount of postage she could make with a combination of those stamps. What totals could she make what totals are impossible? Explain how you found your solution. How do you know your solution is correct?
Level D
Courtney's grandmother said, "Your grandpa has different shoeboxes with other stamps. His shoebox has just 4 cent, 6 cent, and 8 cent stamps. Which totals can you make with these stamps?"
Courtney said, "I wonder why there is a different between Grandma's and Grandpa's shoeboxes. I like finding the largest total I can't make, but Grandpa's box has an unlimited amount of totals I can't make. I wonder why it works for some and not for others." She continues, "I am going to investigate which three stamp amounts are like Grandma's shoebox and which three stamp amounts are like Grandpa's shoebox. I am going to compare three different sets. I will try 6 cents, 7 cents, and 8 cents. Then I will try 6 cents, 9 cents, and 12 cents. Finally I will try 6 cents, 8 cents, and 9 cents." Explain how the three different sets are like either Grandma's shoebox or Grandpa's shoebox.
Level E
Determine a method for predicting whether a given set of any three stamps would have a largest impossible total, or infinite impossible totals. Justify your method using mathematical reasoning.
For those sets of three stamps that have a largest impossible total, make a conjecture about how to find that total.
Help.