Math question

Its a bit poorly worded, but it looks like theyre looking for the number of squares in a rectangle 3*4. So

Can only assume theyve given you more 4*4 working area than necessary and they say you dont have to use them all.

How do you decide 6 of the 2*2 squares?

Just draw one 2*2 in the bottom left. Then you can move up one square and draw another and you could move right (twice) by one and draw (two) others. So 2*3 in total. Obv there is overlap between neighbouring squares.

Edit - looking at the 2*2 example at the start of the question, theyve hidden how to go about it by drawing diagonal, non-overlapping squares in two seperate grids.

Doing that I would say there are a total of 4, 2by2 squares
https://ibb.co/V27pkFC

Youve missed the two in the middle, so covering squares 2&3 along the bottom.

How about now? This should give 6 2by2 squares.

(The question still remains in terms of why do we actually draw 6 2by2 squares. How does the example given make us believe this is the right thing?)

https://ibb.co/Gxygr9W

Thats right. I guess they want you to just draw something which is clearly labelled. Theyd not be too worried about which scheme you used. Probably the simplest/smallest for me would be in the first grid to draw two non overlapping along the bottom and the middle one along the top (so 3 in that grid), then in the next grid draw the other 3 so two nonoverlapping along the top and the middle one along the bottom.

But feel free to disagree and do something different.

Note these are basically pyramidal numbers, so just google/wiki if you want to find out a bit more.

I've finally understood what the question wants - the question is asking for the max number of squares that can be formed. So the width 3 and length 4 doesn't actually mean anything to us other than the fact that this is the limit in terms of size of the rectangular boxes we are given to draw as many squares as we can. Now, that the main ideas has been understood, the next step is to start making as many squares as possible starting with as many 1by1 squares we can fit which would take up the entire 12 boxes. Following, onwards we would have to do the same procedure for 2by2 squares and then 3by3 squares. After this we would have to stop as we can't make squares of dimensions greater than 3by3 in a 3by4 rectangle. Therefore, it leads me to believe that the number of rectangular boxes we consume doesn't really matter it is more about what is most convenient for the person to work out the maximum number of different sized squares that can be formed within the of size 3by4 (or 4by3).

Pretty much. I suspect the reason for the given grids is to get you to show working/think about the problem rather than just writing down (unjustified) numbers.