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Are the following statements always true, sometimes true or never true?
How do you know?
Can you find examples or counterexamples for each one?
For the 'sometimes' cards can you explain when they are true? Or rewrite them so that they are always true or never true?
The sum of three numbers is odd 
If you add 1 to an odd number you get an even number 
Multiples of 5 end in a 5 
If you add two odd numbers you get an odd number 
If you add a multiple of 10 to a multiple of 5 the answer is a multiple of 5 

What about these more complex statements?
When you multiply two numbers you will always get a bigger number 
If you add a number to 5 your answer will be bigger than 5 
A square number has an even number of factors 
The sum of three consecutive numbers is divisible by 3 
Dividing a whole number by a half makes it twice as big 

You could cut out the statement cards and arrange them in this grid.
Alternatively, you may like to try out your ideas using the interactivities below:
These tasks are a great opportunity for learners to use reasoning to decipher mathematical statements. We often make mathematical claims that are only true in certain contexts and it is important for learners to be able to look critically at statements and understand in what situations they apply.
The examples here only refer to one key topic but similar statements could be created for any area of maths  we have made some similar problems about shape.
You may want to start with one statement and have a class discussion about whether it is true. Ask learners to think of some examples to illustrate the statement and decide whether it is always, sometimes or never true. If they decide it is sometimes true, they could think about what conditions make it true.
Groups of learners could be given the set of statement cards to sort into the grid sheet, or they could use the interactivities on a tablet/computer. Taking each card in turn they could decide if it is always, sometimes
or never true. Then they could justify their reasoning. If they think it is always true or never true, they could explain why they think this is. If they think it is sometimes true they could start by coming up with cases for each and trying to generalise.
For learners who have had more experience of reasoning it might be good to ask them to try and write their ideas down in a clear way, perhaps for just one or two of the statements to start with.
It would be worth sharing ideas as a class at the end. You could pick up on a statement that has been problematic or where there does not seem to be a consensus and support a whole class discussion.
Can you think of an example when it isn't true?
How do you know that it is always true?
Is it possible to check all examples? Are there other ways of knowing?
When discussing as a class, suggest types of numbers to consider. Learners often need to start with concrete examples to develop their understanding of a particular concept before they can develop their reasoning within that area. Concrete resources can be useful for developing an understanding of the structure of numbers, and can be used by all learners to support their arguments.
The similar problems Always, Sometimes or Never? KS1 and Always, Sometimes or Never? might be a good starting point for pupils who need more support.
Learners could be asked to come up with their own statements that are always, sometimes and never true within a topic area. Again they should try to justify their reasons and specify the conditions necessary.