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Ways to make 60 cents

What’s the quickest way to help this student?

Thanks to Triangleman for another excellent submission.

(Also, did I get the categorization right on this one?)

4 replies on “Ways to make 60 cents”

I like the Coffey/Wells approach here (they’re not wrong, they answered a different question). They have a good connection that factorial can be used for how many questions, and seized on how to get numbers from the words. Help the student figure out what question they did answer. To get back to the problem at hand, I might ask for a list of all the ways (after assuring them it is very much fewer than 1250).

I’d also recommend giving the student some actual nickels, dimes, and quarters, and trying to figure it out with some concrete objects in their hands, and then help them translate that into a more abstract method.

I might give them dimes, but not quarters. They can draw circles! And show me the ways.
But are they assuming that putting in different coins counts as a “different” way?So (easiest) 2 quarters with dates 2001 and 2002, then a dime with date 1995, is different from 2 quarters with dates 2005 and 2006 and a dime from 2010.
Now I’ve made an unanswerable mess out of this question, I can see how factorial looks like something manageable!

What about another question?
Ex. Find 3 ways you make 60 cents with nickels, dimes and quarters.
How many nickels did you use for each?
Can you make 60 with only 1 nickel (adding dimes and quarters)? How about just 2 nickels?
The student might feel capable of solving more ways if 2 or 3 attempts have already been made.
Then, ‘How many different ways can YOU use these coins to make 60?’