How would I help my 7th grader with this?

OK I was afraid it wouldn’t line up right and it didn’t.

OK, I will use periods where there should be white space to try to get this to line up right.

… _ _ _
….x _ _
__________
.._ _ _ _
2 _ _ _
__________
2 _ 5 _ _

fingers crossed that that worked!

What there was my thought process—Because the first digit of the answer is 2, you need two numbers multiplied together that will give an initial digit of 2. In 2,3,5,7 that would give only 7 x3 =21. So, the initial digit of one number must 3 and the other 7. The last digits of the two numbers when multiplied together must result in a number that ends in a 2,3,5, or 7. The only pair that meets this is 3 and 5 so the final digit of one number must be 3 and the other 5. You then have four possibilities into which you can test numbers: 3_3 x 75, 3_5 x 73, 7_3 x 35, and 7_5 x 33. I plugged each of 2,3,5,and 7 into these until I hit the right answer on my sixteenth and last try. There must be a more direct way to get at the answer without all the plugging using the clue of the 5 in the middle of the answer, but I had just a limited time I could allow myself to get sucked in. What exactly are seventh graders supposed to be learning from this?

I have no idea. They still haven’t gone over this in class and apoint I’m not sure that they ever will. I am pretty angry with this assignment because I wasted so much time on it.

By the way how did you limit the last digits to 3x5?
7x5, 5x5 and 3x5 all produce answers ending in 5.

And to come up with a first digit of 2 there are 2 choices
3x7=21 and 5x5=25

I allowed myself a limited time to this problem as I was at work and must have short-circuited my thought process. The additional choices would make the number of plugins you’d have to do really multiply. I guess I was lucky to get an answer after 16 tries. This makes the clue of the 5 in the middle of the answer even more crucial to figure out. In any case, I can’t see assigning this to a seventh grader, except possibly for voluntary extra credit. Makes it look as though the teacher is more interested in saying “Aha! You’re not as smart as you think” to the kids than in getting them to learn.

Thanks for trying anyway :-)

Marie gave us the clue re the 2x,xxx solution requiring a

(5xx X 5x) or

(7xx X 3x) or

(3xx X 7x) problem.

That yields 16 x 4 possible variations for each example; a total of 192 possible variations.

(5xx X 5xx)

577,575,573,572,557,555,553,552,537,535,533,532,527,525,523,522
X
57, 55, 53, 52

(3xx X 7x)

377,375,373,372,357,355,353,352,337,335,333,332,327,325,323,322
X
77, 75, 73, 72

(7xx X 3x)

777,775,773,772,757,755,753,752,737,735,733,732,727,725,723,722
X
37, 35, 33, 32

There are 7 solutions that are constructed using only the four numbers:

27335 or 77x355
25275 or 75x337
27375 or 73x375
23725 or 73x325

25725 or 35x735
25375 or 35x725
25575 or 33x775

Only one correct answer (given to us a long time ago by Marie):

25575

Enter the above variations into an Excel spreadsheet to check.

Sorry, the homework is past due. I only saw the post tonight.

This kind of thing is asigned as a “puzzle problem” — the idea is to encourage the kids to try to figure things out logically, and also to give them lots and lots of practice in multiplication.
If this were assigned as an optional extra-credt problem, or as the very last “see if you can do this one” problem on the homework, I would say OK to it. Not a kind of puzzle that ever appealed to my mathematical taste since it it just plug and chug, but many people like this kind of thing, the same as many people like word searches which bore me to death.
Sometimes a unit on problem-solving methods is taught, and this kind of problem would also be suitable as an example of solving a problem by logical elimination.
It should not be assigned as a part of regular homework in general.

Teachers in elementary and junior high school are usually very very badly prepared in math themselves, and often assign text problems blindly, not realizing what kind of work is required and what the focus should be. There’s no easy cure for ignorance, unfortunately.

With two days to work at it, then it’s “how to solve this problem” that is the issue — do *lots* of trial and error (and get lots of skills practice) and hopefully see some patterns in the numbers (like - okay, if the first digit on that line is a 2, then the answer to that times tables might start with two, so try 7 x 3 first…)
With an anxious kiddo, I’d tell him that it doesn’t matter whether or not he figures it out at all, as long as he can show that he worked on it and, say, tried 10 different combinations.

Have you ever heard of magic squares-they take a little time to teach, but double digit multiplication is a cinch after they learn them . let me know if you would like the directions.