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The Prime for solving problems at school - one example close to me

Math classes in my children school are split by levels, so that children can advance at their own pace. In a 66-strong year, there have been established 4 levels. The top level holds just 4 children. I had access to the admission test for that level, and the problems were easy but interesting. We’re talking about 11-year old kids, in a British system school. 
I sat with my eldest child and reviewed some of the problems. The first one I came across was about squares drawn with small lightning sticks. 
The order 1 has just 4 sticks.
The order 2 (2 sticks per side) has 12 sticks in total.
The order 3 (3 sticks per side) has 24 sticks.
You are asked to tell the 4 side and the 5 side. Then, you are asked to find a rule, and calculate how many sticks are in the 100 per side figure.
The point here is counting in the right way, so that you can draw the rule from it. My son found it quite fast - at least faster than me.
You first count the vertical sticks: there are 5 columns of 4 sticks each = 20; the horizontals are the same: 5 rows of 4 sticks each. Total 40.
For the order 5: there are 6 columns of 5 sticks, and 6 rows of 5 sticks too - therefore 60 sticks.
In general, for a side with n sticks: (n+1)*n*2.
(This my son called “the template”, which I liked as a definition. They have not learned yet to use functions or variables, so that was his first encounter with them. He then proceeded to apply the template to the case n=100)
Then I said, “it would be good to have the template applied automatically to any number you want - without having to calculate it all the time”. “Yes!”, he replied.
So we opened up the Prime, and entered the formula in the Function app. I changed the integer variable “n” for the standard “X” used there. Then I showed to him how to enter a formula in the system. As it is easy, he was able to do it quite fast. 
“And now?” he asked.
We clicked on the table buttons. Very fast we came to the right “zooming” and he was able to see the value of the template for any integer. He then proceeded to check the values he hard found, and found them right. But now he had learn to enter “templates” and how “templates” could help him to solve real problems. 
The second question was to imagine the tridimensional case. We will discuss it the next day. Again, the key to it was to count it properly.
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