*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*

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* 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.

• Using the three digits make all the two-digit numbers.

• Add the 6 two digit numbers together

• Add the 6 two digit numbers together

• Add the original 3 single digits

• Add the original 3 single digits

• Divide the sum of the 6 pairs by the sum of the 3 digits

• Divide the sum of the 6 pairs by the sum of the 3 digits

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*• What did you get? Why do you think this happens?*

• Try with another set of 3 digits. Does the

• Try with another set of 3 digits. Does the

**same thing happen?**

• Does it work with 2 digits? 5 digits? 6 digits?

• Does it work with 2 digits? 5 digits? 6 digits?

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