Borrowing a problem from the comments in the excellent blog CorkboardConnections. Hope that's ok...
Mdm Shanti bought 1/3 as many chocolates as sweets. She gave each of her neighbours' children 4 chocolates and 3 sweets, after which she had 6 chocolates and 180 sweets left.
(a) How many children received the chocolates and sweets?
(b) how many sweets did she buy?
ans: 18 children; 234 sweets.
FROM THE COMMENTER ON THE BLOG ABOVE
This is the questions our 12 year old do for their National exams.. is this type of questions easier or tougher than your core maths ?
Dave MarainOctober 21, 2014 at 7:02 AM
1. Unless Singapore Math materials are being used, US students could only solve this with algebra. For example, let y=# of children,etc. Students trained in Singapore Math might consider a "bar model" approach.
2. Problems of this level of complexity are unusual in US texts. Most 7th graders here are in prealgebra. This type of question would fit into 1st year algebra but I haven't yet seen many problems requiring this level of reasoning.
3. My instinct is that many of our **secondary** students would struggle with this! That's easy enough for teachers to verify.
4. Yes, Common Core has raised the bar but the proof will be in the difficulty of the problems students are expected to solve. If 12 year olds in your country are expected to solve this question on a National Exam then they must have been exposed to similar questions in their classes. In my opinion, we are not there yet...
1. I hope you'll take exception to my comments above and prove me wrong by copying a page from a current COMMON CORE 7th-10th grade text. A page of problems similar to this one. Similar not only in content but in **difficulty**. An algebra problem tied to ratio concepts. In yesteryear, Dolciani would have problems like:
Determine a fraction in lowest terms with the property that that when the numerator and denominator are each increased by 2 the result is 4/5 (this one is easy; Mary P. Dolciani had harder ones!)
2. Some of my faithful readers are far more proficient with Singapore bar model methods). I tried it, it worked but I personally felt it wasn't worth the effort for me. Algebra seemed more natural. If you see a straightforward model solution, pls share!
3. What do you see as the complications in the problem above. The stumbling blocks for some of your students? Remember the commenter is talking about a 12 year old, a 7th grader...
I asked myself if my 11 yr old grandson will be ready to tackle this next year? I think so if he's exposed to similar problems.
And that's the whole point of this post. Higher expectations are necessary but are they sufficient?