In this season, the Sabers baseball team has a loss:win record of 21:33. What is the total number of games that the Sabers played to earn this record? A full season has 162 games. If they keep this ratio for the remainder of the season, what will their loss:win record be at the end of the season?

I teach that kind of problem using ration tables. So we would set up a three row table with loss/win/total for each row. So the kids would fill in the total for the 21:33 ratio (54 games total) then reduce that ration in the next column (7:11:18). Then the next column they'd enter the total 162 andfigure out a multiplier--18 times what equals 162? 9. Then multiply 7 and 11 each by 9 to get the final ratio, 63:99.

We do a lot of similar problems with these part: part: whole ratios. So there are really 3 parts to the ratio you are tracking.

KatieViolet, thanks for your truthful response. However, what would you award a kid whose response is 42:66:108? And say that this is out of 3 points? Where did the kid make an error in his thinking? I wonder if this kid understood what he needs to look for. Clearly, the kid's figured out that 54 games had been played and the remainder (and I emphasize that word) is 108.

It sounds to me like the kid did not know what he was supposed to look for. The question asked for how many games had already been played, and he gave you how many still needed to be played. It asked for the total record at the end, and he gave you the record for the remaining games. Is language an issue at all?

I'd probably give a point if some work was shown, but more importantly, I would meet with the kid and ask him to explain his answer to me. I would praise what he did well, then go over the question with him and show him how to "disect" it and figure out what they were really asking for.

Yep, it could be. I mean the kid knows what he's doing and so I'm suspecting that when he picked up on the word "remainder", he subtracted and did the part (the remainder) to whole comparing. And so I wonder if the kid would get it if the question were worded this way, "If they keep this ratio, what will their loss:win record be at the end of the season?" You know the part without "for the remainder of the season"

I grade all math problems this way: 3 points per problem. 1 PT for trying/showing work, but maybe the work is wrong or far off. (I also give 1 point for a correct answer that has no work shown!) 2 pts for mostly correct work, but perhaps an incorrect final answer. Maybe a calculation error, or not completely answering the question, answering the wrong question but the math is on track. 3 pts for good work and correct answer.

So I would give 2 pts credit for that answer. He understood a lot about The problem but answered the wrong question.