Math Challenge Problem

We took our Unit 3 math test yesterday.  This was the challenge problem at the end of the test:

Carlos wants to buy chocolate milk from the vending machine. (Students had a picture of a vending machine with items to look at.)  The milk costs 75 cents.  Carlos has 2 quarters, 5 dimes, and 5 nickels.

Show all the possible coin combinations Carlos could use to pay for the milk.  Use N, D, and Q to record your answers.

*The trick for the students was to use on 2 quarters, 5 dimes and 5 nickels.  Today I will talk with them about the different strategies that different students used to solve the problem.  One way of finding the different combinations is by starting with the "biggest" coins first: Q Q D D N.  Next "break down" the coins that you can to create different combinations.  For example one of the quarters can become 2 dimes and 1 nickel.  So the new combination would be: 
Q D D N D D N.

These problems are great for expanding and challenging their higher level math problem solving skills!  If you have time, look over this problem with your child.  Ask him/her to explain how he/she worked through the problem.