Students need to be encouraged to investigate problems for patterns, rather than just have exercises which have single answers.
Too often maths Teaching is about asking Closed Questions, that is a question that has just one answer. We need to change this to Open Questions, where students investigate and come up with various answers which they have to Justify.
A simple way to start with Open Questions is to start with the "answer" and ask what is the question/start? e.g. The answer is 36 what is the question?
The beauty of this is that it caters for all abilities in a mixed ability class or group. (One child might suggest "what is one more than 35?" while another, "what two numbers produce a product of 36?" and another, "What is The Square Root of 36?"
What a rich discussion could eventuate as all responses are shared and discussed
Try this with your class, allow calculators if necessary, as the process is the important issue here
• Choose three single digits all different
• Using the three digits make all the two-digit numbers.
• Add the 6 two digit numbers together
• Add the original 3 single digits
• Divide the sum of the 6 pairs by the sum of the 3 digits
• What did you get? Why do you think this happens?
• Try with another set of 3 digits. Does the same thing happen?
• Does it work with 2 digits? 5 digits? 6 digits?