Students will learn how to solve a particular type of word problem, called age problems. Next, give your students this challenge. I would add that the teacher's age is less than 100. Finally, give your students this challenge, which is a combination of an age problem and a logic puzzle.
Watch these Khan Academy videos:
Age word problems by Khan Academy
Next, give your students this challenge:
Which Numbers? (2) by NRICH
Conclude by leading this investigation:
Fractured Fractions – equivalent