72-27=9x5; What about 7A2-2A7?

CONCRETE --> ABSTRACT (ALGEBRA)

Answers to previous post:

9 appears for the 1st time in the 73rd position; 90th number in the sequence is 9.

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CLASSROOM TIME ALLOTTED: 10 MIN

POSSIBLE INTRO TO LESSON

After they do 72 -27 to get 45, introduce the terminology pairs of ‘2-digit reversals'. Then ask them in their groups to find other pairs of 2-digit reversals whose difference is also 45.

What do they notice? How might you proceed?

I'll stop here except to suggest an algebraic extension:

If a,b are tens’ and units' digits, a ≥ b, then (10a+b) - (10b+a) = 9a - 9b = 9(a-b) etc

The 2nd part of the question in the title regarding 3 digit numbers is an extra challenge which can be briefly discussed at the beginning of the next lesson.

Note that ‘A’ represents the tens' digit they share.