In a few short weeks, I will be making a presentation at Twitter Math Camp on my favorite Nrich Tasks.  I know a lot of teachers have reservations about integrating rich mathematical tasks into their regular routines so I want to focus on problems that have that “traditional” feel while still allowing students to explore mathematical relationships more deeply.

Pair Products is an amazing offering by Nrich and its low barrier to entry makes it accessible for all students.  After working through the problem myself, Nrich offers additional questions to raise the ceiling.

Additional Questions to Ask:

1. What happens when you use 4 consecutive even or odd numbers? 5? 6? n?
2. What happens when you use 4, 5, 6, n consecutive multiples of 3? Multiples of 4? 5? 6?
3.  (My Favorite) What happens when you use n consecutive multiples of w?
4. Does your generalization from #4 hold for numbers that increase by .5?  (For example: 3, 3.5, 4, 4.5)

My favorite Nrich pair, Charlie and Alison, offer two different approaches.  Charlie explains a clear algebraic manipulation to arrive at two expressions with a numerical difference.  Alison, on the other hand, represents the product of numbers with an area model.

An interesting challenge might be to ask students to show the area model that Alison employs for some of the additional questions.