"Reasonable" Math Problems

Here is the post that showed up on I Want to Teach Forever on April Fool's Day, reposted in its entirety here:

As I mentioned the other day, we have dived in headfirst to the "tough stuff" of the 3rd grade curriculum. Word problems, 2-step problems, and now, "Reasonable" problems. It's pretty ironic, but even with 4 years of high school math under my belt, 3 ½ years of college math and engineering, and 2 years of graduate school math and engineering, I had NEVER come across this type of math problem in my life until I started teaching 3rd grade.

Here's a typical problem:

Mr. Sutton buys 4 tools at the hardware store. The least expensive tool is $10, and the most expensive tool is $20. What is a reasonable total for all 4 tools?

In my opinion, Mr. Sutton should look at his receipt and find the exact prices of each tool and add them, or at least round them and add. This lowest and highest deal is silly. Yet teach it we must.

Oh, and there's also a second kind of reasonable question.

Suzy the Squirrel can bury 3 to 5 nuts every day. How many days will it take her to bury 40 nuts?

Nevermind the fact that I always have to stop and deal with giggle fits every year when we do this problem in class (the kids giggle, too. NUTS!), but I think this kind is more difficult than the first because it requires something beyond just adding to find a total.

Speaking of unreasonableness, I have been working on getting my honeymoon booked. My fiancé and I have decided upon Turks and Caicos (mostly just because it is incredibly fun to say), and a 5 night stay at an all-inclusive resort there. However, the airfare is redonkulous!! Almost 700 bucks per person! Of course, if it was some of my kids charging me airfare, it wouldn't be so bad, because 2 people at 700 dollars each would only be 702 dollars. Possibly even 698 dollars. However, in the real world, it's so much more than that.

Ideally, my book would win the Amazon Breakthrough Novel Contest and the $15,000 prize that goes along with it. Realistically, though, that's probably not going to happen. Any chance everyone could encourage their friends and neighbors to buy a couple of copies of Learn Me Good? On the Kindle even?

Coach K has already come through and delivered on my request. Somehow I doubt he's going to come to the wedding, but at least he gave me my early present.

Is it still "reasonable" to think that Duke can win it all?

Unreasonableness

The lesson/task/tip of Day # 7 in the Problogger 31 Day Challenge (yes, we're on Day #9, but I'm a little behind) was to give a little "link love" to another blogger. In other words, to link to and comment on a post from another site.

Last night, as I was looking through the sites that I frequently read, I came upon Mrs. H's post about her countdown to the TAKS test. Mrs. H is a Texas high school teacher, so she is counting down to a slightly more advanced version of the TAKS than the one my 3rd graders will be taking, but our goal is the same -- to kick the CRAP out of the TAKS. Er, I mean, to get all of our kids to score high.

Mrs. H says that one of her goals is getting her kids to recognize the difference between reasonable and unreasonable answers. I can so totally relate. What SHOULD be a simple thought process -- Hmmm, if I have 4 friends, and I want to share a bag of 20 peppermints with them, each friend is NOT going to get 80 peppermints!! -- is often anything but simple.

I tend to use the words "Does your answer make sense" more than "is it reasonable," mainly because there is a classification of 3rd grade math questions called "reasonableness." We started our lessons on Reasonableness questions today, with varying results.

If I might brag about my own education just a bit, I was an excellent math student in high school, I took graduate level math classes as a senior in college, I then took graduate level math classes as a graduate student, and then I used some pretty advanced math in my job as a thermoelectric design engineer for almost four years. However, I NEVER came across this type of "reasonableness" questions until I started teaching 3rd grade.

Here is an example of a Reasonableness question:

Mrs. Nestor bought 6 games for her son. The least expensive game cost $10, and the most expensive game cost $30. What is a reasonable total amount that she spent on the games?

My question is, who on earth doesn't track the exact total that they spent at the store?? Why do you need a "REASONABLE" total, when you can just add up the exact amounts, or round them to the nearest dollar and add??

The strategy of solving a problem like this involves finding a number in the middle of the range (10-30 dollars) and using that for each game. Furthing confounding things is the fact that the answer choices are always either ranges themselves ("between $100 and $150") or single numbers that are usually close to, but not exactly what the kids compute. So after all these months of telling the kids that, when taking a math test, if their answer doesn't match any of the answer choices, NOT to just pick the closest one, but rather to go back and find their mistake -- now we get to tell them, Oh yeah! If you see this word "Reasonable," THEN it's ok to pick the closest answer...

(For those of you wondering if the kids can just multiply 6 times $10 and 6 times $30 to find the range of answers, I just want to say. . . THAT WOULD BE FAR TOO EASY!!! Often times, using the extreme ends of the range yield an answer considered incorrect.)

I will say though, that after the first day of doing a brand new type of problem like this, the kids did pretty well with it. They certainly have the skill of finding a central number down, and hopefully this skill won't go out of their brains in two weeks. Like telling time seems to have done.

We also looked at a type of problem today we call "Missing info."

Try this example. Answer to follow tomorrow.

Mister Teacher has 15 sweaters and 22 shirts in his closet. What other information is needed to find the number of sweaters that are blue?

A) The total number of shirts and sweaters
B ) How many sweaters are white
C) How many sweaters are not blue
D) How many shirts are blue