Pearl writes down seven consecutive integers and adds them up. The sum of the integers is equal to 7 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Guest Sep 21, 2022

#1**+2 **

Pearl writes down seven consecutive integers and adds them up.

The sum of the integers is equal to 7 times the largest of the seven integers.

What is the smallest integer that Pearl wrote down?

7x+1+2+3+4+5+6 = 7(x+6)

This question makes no sense.

Melody Sep 22, 2022

#2**+1 **

Your are supposed to read their minds!! I think "7 times" should read "6 times"! I believe it was posted recently as 6 times:

[n + (n+ 1) +(n + 2) + (n + 3) +(n + 4) + (n + 5) + (n + 6)]==6(n + 6), solve for n

7n + 21 ==6n + 36

7n - 6n ==36 - 21

**n ==15 - the smallest integer**

Guest Sep 22, 2022

#4**+1 **

*ok, I'm not a mind reader*.

Actually, you are ...in a metaphorical sense. You’ve demonstrated such skills on more than one occasion. I think most teachers need above average skills in *mind reading* to be a good teacher. Beyond basic mind-reading is the quintessential skill of *filling in the thoughts* for thought processes that are **missing** essential information in the student’s mind.

For teaching younger students, this is a common and relatively easy requirement because younger students are usually just missing information. The difficulty is in persuading the student to use his/her mind to its full capacity.

For the older student, however, the requirements are more arduous because wrong and errant information may be firmly entrenched. The student needs to be willing to excise errant thought process to make room for the correct processes.

There is a valid argument that to read a mind, there needs to be a mind to read. *Mindlessness* is a real phenomenon. It’s exceptionally difficult to comprehend and hence exceptionally difficult to treat.

GA

--. .-

GingerAle
Sep 23, 2022

#5**+1 **

Thanks Ginger,

When i was teaching in a classroom:

I think the biggest problem with teaching mathematics to older children, especially older children who have had very limited success in the past, is that they have too many holes in their knowledge and understanding.

An analogy: You cannot be taught to spell if you do not know the names of the letters.

On top of their lack of knowledge they lack confidence and interest in trying to learn.

Put 30 of these children in a classroom and a syllabus that is unsuitable, and chaos reults.

Now days:

I suspect the new problem to teaching maths, perhaps more relevant to the more mathematically capable students, is the climate of instant gratification.

Sometimes, when I was a kid, I would chew on a problem for days. These days people, almost immediately consult the internet. This is not always bad but it has to cut down on an individuals ability to nut a problem out by themselves.

For the benefit of others:

This is why sites like AoPS (Art of problem solving) dislike sites like this one so much.

How can their students master problem solving if they just get instant internet answers?

Melody
Sep 23, 2022