The following is an elementary-level Math Kangaroo multiple choice question:
What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?
I have the answer key, so I can work backward to sort of get how to solve this problem. However, as I was trying to write a solution for my students, I realized I could NOT help them eliminate the wrong answer choices. The following is what I have got so far:
This is a tricky problem. You might have no glue the first time reading the question, but you can still capture some keywords such as “maximum” and “three-digit number”. These keywords can give you some information to start solving the problem.
When you saw the word “maximum”, “three-digit number”, you could started trying out with the biggest three digit-number, which is 999. Now you can plug in the number into the question, then you will find out the question is asking “What is the maximum value of the sum of the digits of the sum of the digits of 999?”
Now, the question is getting clearer. First, you need to solve the sum of the three-digits number 999, which is 9 + 9 + 9 = 18 + 9 = 27. The question turns into “What is the maximum value of the sum of the digits of 27”. Then you need to solve the sum of 27, which is 2+7 = 9.
Take a look at the answer choices; there is a 9. This is a signal that you are on the right track, but before you circle the answer, don’t forget the power of double check! You need to ask yourself, is nine the maximum value you can get from combining two single digits?
Now I am stuck with how to help the student eliminate other answer choices.