Oh, duh. Yes, that one should be 4.
Wait. Are there 25 or 26 squares? There are 25 little squares but they are all inside a large square too.
There are 55 squares. There are 25 “one-unit” (1x1) squares. I suppose you can argue that the whole big square is a “one-unit” square, if you wanted to.
I find this very hard to take seriously as a ‘test’. As has been discussed, the questions are ill-phrased, and the marking seems erratic.
Certainly the ‘outside square’ in each diagram should be included. The ‘outside boundary’ is used as a border in many of the squares and triangles allowed, so I see no reason why a square made up entirely of outside boundary borders would be excluded.
The question ‘What do you notice about all these numbers’ does not make it clear that we are only talking about answers 6,7, and 8. I spent some time struggling with that answer, because the correct answers to #4 and #5 are not squares.
Methinks a teacher has gotten a bit lazy and cribbed from ‘1000 Amazing Math Puzzles to Waste Hours On!’.
What the hell is this crazy idea of ticking wrong answers? No wonder nobody can learn anything.
What bizarro world do some people live in where checking the wrong answers is considered unusual? That’s how it’s always been done.
Our firewall black listed your kid’s homework site! Down with homework! LOL
Seriously though what is the deal with that? Before this thread (and the previous one) it would never have crossed my mind that check mark* would mean anything else but “correct” (it even signifies that in computer user interfaces).
Is there a particular tradition or nationality where a check mark indicated something is wrong or incorrect?
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- I would call it a tick but I guess that is a Britishism? (I’ve been in the US for 15 year and still discovering words the American say wrong
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- I would call it a tick but I guess that is a Britishism? (I’ve been in the US for 15 year and still discovering words the American say wrong
American here. American teacher here, actually. X for me is always wrong. Check means “OK”. I don’t really do checks next to right answers, though.
Right answers don’t get marked. Wrong answers are usually marked with a checkmark, but could also be an ‘X’ or a slash through the question number. I’ve never seen a teacher put check marks next to correct answers. A perfect paper should be “clean” except for the score at the top.
American former student, current teacher’s spouse and current para.
This is an “extend your thinking” exercise. It should be the extra credit to challenge the few kids who breeze through the rest of the class math work. I’d gather the point is that the kids have learned all about squares and generally had them illustrated with grids of x by x. The extension of thinking is to realize that square patterns can emerge from things other than square grids.
A 5x5 grid has 5[sup]2[/sup] unit squares, (5-1)[sup]2[/sup] of (unit+1)[sup]2[/sup] squares, (5-2)[sup]2[/sup] of (unit+2)[sup]2[/sup], and (5-3)[sup]2[/sup] of (unit+3)[sup]2[/sup].
Would any student at this level pick up on the pattern that would let them answer how many squares of 110 there are in a 125 by 125 grid? Not too many. But it is still there to observe and recognizing that they are squares of numbers decreasing by one as the side of the square increases by one is the first step. Pick up on that and you don’t need to tediously count. That is a lesson to learn. Recognizing patterns can save work.
Tick means correct. Cross means incorrect.
But, of course, some people have to do it bass-ackwards:
I would never have imagined that American schools, or those anywhere in the English-speaking world, would use ticks to mean “wrong”, though. It just seems totally unintuitive. 
I don’t think there’s anything intuitive or unintuitive about a check mark. All it means to me is pay special attention to this item (or attention has been paid to this item.) It’s just a mark. It may mean “this item on my list has been finished” or it may mean “pay special attention to this item on the list.” X can be used in a similar manner. For example, on a ballot, you often mark your candidate by placing an “X” in the box next to their name. So it’s all context dependent.
I grew up with it meaning “these are the items you got wrong; pay attention to them.”
In college, I had at least one teacher who did use check marks on every correct answer. I assume it was to help them keep track of what questions they’ve gone over and which they haven’t. But it’s not usual, no.
We think how happy we are with online resources, there are a lot of hw helpers available. But you know, there’s something wrong with that. When I was in college more efforts were required to deal with my essays and homework assignments
I wonder if it’s regional like soda and pop.
Check was correct for me and x was wrong. But I’d have also gone by color. Red meant wrong more than what mark and I’d have understood a red check as wrong.
I wonder myself, as well. I couldn’t ascertain one way or another what regions it might be limited to based on that teachers message board I found.
Another thing occurred to me: Up through second grade, we didn’t have letter grades at my grammar school. We had three symbols: a plus sign meaning “Excellent,” a circle meaning “satisfactory” and a check mark meaning “needs improvement.” (Also, we didn’t have "F"s for some reason in elementary school. Our lowest mark was a “U” for unsatisfactory, so it went A, B, C, D, U. Also, while high school had an “F,” both grammar school and high school the percentages for each grade were a little different than what I’ve heard from other parts of the US. A was 93-100; B was 85-92; C was 75-84; D was 70-74; F/U was anything below 70.)
I’ve been following the discussion of check-marks with interest (not the math stuff, that’s all gibberish :)). We also, prior to third grade, had symbols rather than letter grades. Except our symbols were a plus sign for “excellent,” a check mark for “satisfactory,” and a minus sign for “needs improvement.” You could also get a check-plus or a check-minus, for finer gradations.
So even here, a check mark meant, at the very least, that your work was okay. A check mark means that something has been successfully accomplished. Using it to mark incorrect answers, or indicating a need for improvement? Sheer madness.
Here’s an example I found online. This is different than my report card, but you see on the right where “+” means commendable, blank means satisfactory, and a check mark means “needs improvement.” Our report card was something like this, except for all the subjects, not just the “personal and social traits” part of the report card, and a “O” indicated “satisfactory.”
So, for me, check marks were associated with things that needed improvement from a very early age. It all depends on what you grew up with. I don’t find it unintuitive or intuitive or anything. Like I said, to me, a check mark is simply a mark to bring attention to something. It can be positive or negative or neither.
Here’s another example. Scroll down for the “the dreaded ‘area of weakness’ check mark” caption. My association with check marks is firmly entrenched with this sort of connotation, as in “LOOK HERE, WE GOTTA WORK ON THIS!” whether it’s a wrong answer or a report card.