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Always, Sometimes or Never? Number statement cards
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 print off and cut out the statement cards from the top of this page and arrange them in this grid.
Alternatively, you may like to try out your ideas using the interactivities below:
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Let's say you can only use two different lengths  2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?