( inspired by Leaffan’s daughter’s homework question , whch I think is too advanced for a 5th grader, or that we in India are far behind in teaching the right topics ).
From my son’s 5th grade maths text ( he is 10 years 4 months)
Large numbers ,roman numbers.rounding of numbers…
Addition,subtraction,multiplication etc ( advanced than 4th grade),factors,multiples…
fractions , multiplication,division etc. decimals and their addition,multiplication etc…
Lines. angles their measurement…
shapes, their perimeter ,area, measurement of volume
temparature,money,measures of time, data collection and pictorial representation.
How about you ??
I remember my fifth grade teacher introducing us to long division and telling us it was the hardest thing we would learn in primary (elementary) school.
I think we did pretty much everything short of algebra. We did that in the first year of high school, and then went on to trigonometry and other stuff. I am a mathematics ignoramus though, so my brain refused to accept any information from about 4th grade onwards. I could grok adding stuff up, but the rest of it just became swimming numbers on a page. I remain like that to this day.
I know we learned long division in 4th grade. I don’t think I got most of that stuff until at least a few grades later.
OT for a sec, has anyone seen that show Are you smarter than a 5th grader? Are the questions really things beginning elementary schoolers are supposed to know? When I was in 5th grade I didn’t know most of this stuff!
We learned long division starting in 3rd grade (I still remember chanting estimate, multiply, compare, subtract, bring down, repeat), but I didn’t learn about pi until 6th grade.
I was trying to figure out how to get on that show because the questions were easy, but I am not very telegenic and I have a horrible, nasally voice. However, I was looking at a companion book in the bookstore one day, and the million dollar questions were pretty obscure and not part of a general 5th grade curriculum. For example, IIRC, they wanted to know if acne was an infection of a sebaceous gland or some other gland which I can’t remember. I happen to know that the correct answer is sebaceous, but it sure wasn’t anything I learned in school.
I also learned long division in fourth grade, and we started very basic algebraic concepts in fifth. (For example, we’d see 5 + = 9 and have to fill in the box.) We had to do these by intuition – we didn’t start learning how to actually solve equations until seventh grade. As I recall, most of fifth and sixth grade was spent on sort of abstract problem-solving skills, including lots of word problems and logic exercises, which were meant to prepare us for the rigors of algebra and geometry which we started in middle school. (That’s 7th-8th or 7th-9th in most places in the US; these things vary a lot.)
I’ve been editing a few supplementary curriculum guides, largely starting with sixth and seventh grade math and science and then up through high school. One of the purposes of the materials is to help individual school districts meet state standards, so while there are differences between states, it’s more a matter of semantics and not a sizable difference content-wise.
All lessons describe what they consider prerequisites and are explicit when new material is introduced. As for Indian’s list, it is safe to say that all my sixth grade materials have taken it for granted that students already know how to work with things on the list. This doesn’t mean that the students learn it in fifth grade, just that it is firmly established by sixth.
If it sheds any further light on the subject (heh), one text just introduced Cartesian quadrants. Students had graphed before, but I was surprised they had only been exposed to graphing positive numbers. I’m fairly certain it wasn’t just applying the name, as part of the lesson plan involved overlaying two transparencies over each other to form the quadrants. I may have this out of context (I included a note in the file to double check this assumption), as later on students were also given their first exposure to **y = *mx * + b, so it seemed a fast pace to go from graphing in other quadrants to working with slopes in the same unit (i.e., two week period).
If you’re interested, many states have their curriculum requirements and standards on line. Florida Michigan California
… Google “state curriculum guide” and you should find others.
Rhythm
Looks about right. He’s also got some algebra, and some stuff I never heard of before, for example stem and leaf plots.
I don’t mind telling you that the boy’s homework kicks my ass. We frequently have to use the internet or get my husband involved (he’s good at math, but can’t teach us). I’m glad to hear that he’s going to have to repeat this class next year because he certainly didn’t learn much this time around.
The Fibonacci sequence in grade 5? I think CC’s Post #35 is an excellent assumptive insight into what’s going on. That is, while it’s not necessarily the case that the fifth grade students are learning all the higher level math that is alluded and used in the thread as a whole, the lessons are chock full of exploratory bits and pieces that show not only the practical side of math, but also the beautiful insights and wiz-bang fun things inherent to number theory (and biology and Earth sciences).
Of course it’s up to the individual teacher to do something with the lessons and decide how stringently assignments are graded, but most areas have journal prompts and critical thinking exercises to point kids in the right direction. I have to say that before taking these projects on (a little over a year ago) I took the NCLB Act and the associated fall out somewhat with a curmudgeonly grain of salt. While what I see could be described by an agenda-pushing pundit as teaching to the test, I must say that all lessons are filled with a lot of substance and a lot of opportunity for developing critical thinking skills.
Oh, for the non-USA: the No Child Left Behind Act included, among other things, certain grade-level standards. Some criticisms included the notion that rather than teaching math, the teachers would just teach how to solve a particular problem. The above paragraph is my view (admittedly very limited), that these ills are not happening. Note, though, that I’m not any more familiar with NCLB than the average Doper, nor am I involved in education other than teaching SAT prep courses and editing curriculum guides.
So, should a fifth grader be able to have generated or followed many of the posts in Leaffan’s thread? Probably not. But I don’t see it anywhere out of the ordinary for them to have been at least exposed to it – again, see CC’s post for a great insight.
Also, I don’t see anything in the problem in the other thread that’s not on the list you just gave. It’s all addition, subtraction and multiplication. It’s also “noticing patterns” but of course you won’t find that as a specific chapter heading in your or any math textbook. I’d be suprised if the textbook you’re talking about doesn’t ask its students to think about patterns like this.
National Curriculum online, for the English perspective. In particular, the ‘expected level’ at the end of Year 6 (= 5th Grade) is Level 4. (It can’t be the ‘average’ level, of course, because that wouldn’t make mathematical sense!)