Is there a 7th grade math teacher here? Ages & Stages

2babygirls · 08-31-11, 12:37 PM

Sheri or Beth maybe? I can't remember if either of you teach math.

How do you solve this probem...
Pens cost $0.60, Pencils cost $0.40. If Megan wants to spend exactly $8.00, what combinations of pens/pencils can she buy?

I can get the correct answer but I'm not sure if I'm doing it the way I'm supposed to and I can't find anything in the book about it.

3Princes · 08-31-11, 08:14 PM

Well, 60+40 is 1.00. So you need 8 pens and 8 pencils, no? Normally, it's a guess and check type situation, but in this case the kids should see that 6+4 is 10. I think there is more than one right answer though, so it really doesn't matter. She shoudl show her work--- label the columns, and show how she added it up.
This is the type of problem we would have on a 4th grade OAA-- we solve them all the time.

**Chickie** · 08-31-11, 08:45 PM

.6x + .4x = 8
1x = 8.00
1x/1 = 8/1
x = 8

2babygirls · 08-31-11, 10:36 PM

Chickie - that doesn't make sense. Is "x" pencils or pens?

Sorry, I didn't word the problem correctly. The answer needs to show ALL the different combinations of pens & pencils that will add up to exactly $8.00.

I emailed the teacher and she said there is no one way to do the problem, its supposed to make them think. But I'm sure Rachel had this type of problem in 5th or 6th grade and I think she was supposed to solve it by finding either greatest common factor or lowest common factor...or something else I can't remember !

rudolphia · 08-31-11, 10:38 PM

I'm not a math teacher, but I like math. This is a solution set problem, and at this age, I'm sure it's just based on trial and error - checking to see what fits in whole numbers, since you can't have a fraction of a pen or pencil.

Your solution sets would be, with # pens first, # pencils second: {0,20}{2,17}{4,14}{6,11}{8,8}{10,5}{12,2}. Doing the trial-and-error process will show the kids a pattern as well. Every interval adds 2 to the number of pens and subtracts 3 from the number of pencils.

Not sure if at this age the kids would be expected to find the formula and discover the sets using the formula. In this situation, the formula would be:

.6x + .4y = $8.00
(let x = number of pens and y = number of pencils)

In higher levels of math, students would probably need to find the formula to demonstrate the pattern between the number of pens and number of pencils. Though I can see the pattern, I can't for the life of me remember how to express it as an equation.