Forwards Add Backwards

What happens when you add a three digit number to its reverse?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Forwards Add Backwards printable worksheet

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Forwards Add Backwards



The number $747$ can be formed by adding a $3$-digit number 
with its reversal: $621 + 126 = 747$, for example.



Can you find the other two ways of making $747$ in this way? 

 

 

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Forwards Add Backwards



Which other numbers between $700$ and $800$ can be formed from a number plus its reversal? 

There are more than five...

Can you explain how you know you have found all the possible numbers?

How many numbers between $300$ and $400$ can be formed from a number plus its reversal? And between $800$ and $900?$...

The number $1251$ can be formed by adding a $3$-digit number with its reversal.

Which other numbers between $1200$ and $1300$ can be formed from a number plus its reversal? And between $1900$ and $2000?$...

With thanks to Don Steward, whose ideas formed the basis of this problem.