My daughter had the same type of assignment in 4th grade a few years back. She called me for help. I took her out for ice cream and took her step by step through basic algebra stuff. The next day the teacher scolded her for using algebra. She was supposed to “guess and check”. 
well, at that age, I would have used my calculator and algebra (although I didn’t know at the time it was algebra) and written down the correct answer, erased it, written it again (to look like i really guess-n-checked the wrong answer first), and told the teacher I guessed and checked, which I did with my calculator. But nobody ever bought me ice cream for it.
On a related note, I got in trouble in first grade for spelling kite k-i-t-e because I was supposed to know that the e was silent and therefore, spell kite k-i-t and learn about silent e in a few weeks. In the mean time, I guess I wasn’t supposed to know what a kit was. Good thing I didn’t need any first aid.
Just a wild ass guess, but I think such simple problems that are solveable by a 4th grader albeit by a somewhat crude method such as trail and error instill a better concept of the relationship of numbers, and the fact that such problems with solutions exist. When the student gets older they may better appreciate the value of algebra. I know I did.
I cannot tell you how much that infuriates me.
If my child were ever subjected to that, and it was a valid, school-approved lesson plan (as opposed to a whacky teacher), my kid would be out of that school so fast he’d leave a kid-shaped pocket in the air. That’s nonsense.
He-he. I got in trouble when I moved down to Georgia in fourth grade. We had a spelling test, and the teacher said “peninsula”, but she had a thick accent and pronounced it “peninsular”. So I wrote p-e-n-i-n-s-u-l-a-r. The test came back graded and the only word I missed was “peninsular”. I complained, “That’s how you said it” and proceeded to imitate her accent. That got me a whooping down at the Principal’s office for my trouble. Probably didn’t help that the principal pronounced “envelope” as “en-vel-up”.
I corrected my 7th grade English teacher when she said “EP-<schwa>-tome” for epitome.
(Anybody know how to make a schwa on this board?)
I always got in trouble for not showing my work. 
Oh I agree that learning to solve problems by trial and error is definitely worthwhile. The idea is to do the solution search in a methodical, but ideally not completely brute-force, way. In time, as one matures in math, the value of intelligent guessing will be invaluable. In fact, it will be called mathematical intuition. Great math is not always the result of a linear path.
I would be curious to see an example of a hard fourth-grade math question, if this is supposed to be a middling item.
I’ll post one of the 5-star ones when I get home tonight, if I remember.
In SAMPA, it’s spelled /@/. If you want the actual Unicode symbol, you will need to do something OS-specific to type it into a text box.
I went over multiple solutions with The Girl this evening, including the original algebraic solution, but not done on the fly and with a little better explanation. In the end she prefers the algebra, so we’re going to solve some more simple equations with this tomorrow so that she’s comfortable with it. She just thought that solution “made the most sense”. It will be interesting to see how her teacher responds. I told The Girl that she needs to be able to truly understand this solution and explain her work to her teacher.
Here’s a couple of the other problems*:
**** 1. The students in Mr. Renick’s 4th grade class started a mathematics club and a science club. They drew a Venn diagram to show which students were in each club. Use the Venn diagram below to answer the questions about the clubs.
{Diagram shows two overlapping circles titled “Mathematics Club” and “Science Club”, with four names solely in MC, five names solely in SC and three names in the intersection}
(a) How many students were in the mathematics club?
(b) How many students were in the science club?
© How many students were in both clubs?
(d) If one-half of Mr. Renick’s class is in either the math club or the science club or both clubs, what is the total number of students in Mr. Renick’s class?
Number 2 is a bit difficult to describe, but an interesting picture and asks how many right angles including the background.
-
- If the 7th day of a month is on a Friday, on what day is the 24th day of the month?
**** 4. Think about the following list of number pairs. Three is the first number of a pair, and 8 is the second.
=======
3 --> 8
4 --> 11
5 --> 14
6 --> 17
…
…
…
10 --> 29
…
…
…
a. If 50 is the first number, what is the second number?
b. If 200 is the first number, what is the second number?
c. If 89 is the second number, what is the first number?
d. If a number n is the first number, what is the second number?
** 7. In your class, 9 students received an “excellent” on a recent project. Your teacher would like to buy pencils for those 9 students. The school store sells them for 10 cents each or 3 for 25 cents. What is the least amount of money your teacher will have to spend in order to buy one pencil for each of the 9 students?
*My early supposition that the stars correspond to difficulty may have been incorrect. It might rather correspond to the number of answers. At least that’s what the girl said, although the seventh question in the example shown has 2 stars but only one required response.
Just for CookingWithGas – Sorry, also meant to post the schwa: ə
This sort of constructive learning of mathematics is gaining favor in the education community. If done correctly, the student develops a process rather than relying exclusively on trial and error. For example, a (fairly well-known) problem would be
Solve:
1
1+3
1+3+5
1+3+5+7
What is the sum of the first 10 odd numbers
What is the sum of the first 20 odd numbers
What is the sum of the first 100 odd numbers
Starting out, trial and error makes since, but T&E is not efficient for the last problem so (hopefully) the student has discovered the realtionship that the sum of the first n odd digits is n^2.
Question 4 is another excellent example of this. HOWEVER, this method of learning takes time and benefits from group work. Giving these problems as homework is probably (ok - definately) not the best way to do this. Also the problems seem disjointed. For example, if the unit is linear equations, #7 could be rewritten giving a variety of budget constraints for the teacher, #3 could give dates troughout the year (what is the 119th day of the year, what day is Veteran’s Day, etc.) Again, the goal is for the student to not have to count dates in a calender and “discover” modulo 7 arithmetic.
For what it’s worth, I’m actually writing my dissertation on the effectiveness of this style of learning for my Ed.D. in Math Education as we speak (type).
To be fair, these are homework assignments given out on Friday and due in the next Friday. So they have some time to work through this stuff. They also have “regular” sorts of homework. And I have no idea what they do in class, but I imagine that there is group or class work that supports this. Also, these are kids who are mostly 9 years old, so the last couple of examples you’ve given might be a bit of a stretch for them just yet. That said, using problems like these is a good way to build up to that.
Sounds like an interesting thesis.
Did you hear anything back from The Girl on how the teacher solved it?
I asked my homeschooling sister about the math problem, and she explained how to solve it! Damn, so much for me feeling smart.
She uses what’s called Singapore math and here’s how Singapore Math teaches it:
"The problem fits a “part, part, whole” model of arithmetic. You identify the number 72 as the whole, then determine how the parts add up to make that whole. A graphical method to aid in solving the problem :
//______________________ 72
?/?__/48 72
"The fact that the difference is 48 allows you to show that there are 2 equal
parts of unknown length and a part with length 48 that add to 72.
"So subtracting 48 from 72 leaves 24, which divided by 2 equals 12.
“So the numbers are 12 and 60 (12+48).”
If didn’t follow this exactly, until you think about the meaning of subtraction. By definition you are taking one part "A"and then subtracting the same amount from the whole gives you two equal parts and the difference(48 in the case). Knowing the difference allows you to find the amount which is twice “A.” 72 - 48 = 24. Dividing by two gives you “A” (12) then adding the difference 48 gives 60.
My sister likes this because it allows a method of solving these problems without
algrebra.
Which is of course, precisely what Dooku did…beating me to the punch 