Three coin problem

Pedagogical suggestions

Three coin problems allow learners an opportunity to enter and explore a problem at multiple levels to make discoveries and enjoy their learning.

The goal is to explore and find several possible combinations. To extend from there they can review coin values, add and compare total amounts, and make conjectures about what amounts are possible and not possible.

 

Materials

Coins - quarters, dimes, nickels, and pennies (?); sack or bag.

Vocabulary

Combination is a selection of a given number of elements from a larger number without regard to their arrangement.

 

Procedure

Exploration

1. Decide on an initial problem.
   Shake your pocket, purse, or sack and say: I have some coins. I wonder what I will get if I take three coins out?
2. Accept all answers and write them for all to see.
3. Explain. That today they are going to explore combinations of American coins: quarters, dimes, nickels, and pennies and make a list of different combinations.
4. Decide if they will use the picture on the worksheet or if they will have a bag with coins in to select one coin at a time (record it), replace it, select a second (record it), replace, it and finally a third.
5. Provide time to explore in pairs and record their findings.

Invention

1. Bring learners together and have them display their findings.s
2. Record them and discuss if each is possible and label them as possible combinations of three coins.
3. For lower grades a list of possible combinations is a good place agree upon and moveon to the values of different combinations of three coins. For more advanced learners you might explore what might be all of the possible combinations of three different coins.