Do the same game as above but ask your child to tell you 3 different ways how they know which number is hiding and then prove it. For example in the picture with the goat on number 6 your child could say any of the following things...
1) I know it is 6 because it is one more than 5
2)I know it is 6 because it is one less than 7
3)I know that it is 6 because number 6 is between 5 and 7
They could then prove it by showing you that 6 is one more than 5 by collecting 5 objects and then getting one more object and explaining " one more than 5 is 6 because I had 5 and then I got one more and so now I have 6"
Being able to explain their answer in a variety of ways is a sign of a great mathematician and by proving it to you in their own way shows that they fully understand the concept at a deeper level. In class we are always asking the children to "prove it"