lost in translation of word problems,% & fractions

[missy_muffett]

I have just started a uni course, already I am struggling in this weeks work which is fractions, decimals & percentages. My main problem is I dont know the process in how to work the problems out.

Three children camping out & go to sleep with a pack of marshmallows unopened in their ten. ONe child wakes up & eats 1/4 of the marshmallows & then goes back to sleep. A short time later another child wakes up & eats 1/3 of the remaining marshmallows & then goes back to sleep. Later in the night the other child wakes up & eats half of the remaining marshmallows & then goes back to sleep. When they all awak in the morning there is only 9 marshmallows left, How many marshmallows were in the pack at the start of the night?

Do I start by converting the fractions into %, all I know is 9 is my starting point.

 

[JeffM]

I have just started a uni course, already I am struggling in this weeks work which is fractions, decimals & percentages. My main problem is I dont know the process in how to work the problems out.

Three children camping out & go to sleep with a pack of marshmallows unopened in their ten. ONe child wakes up & eats 1/4 of the marshmallows & then goes back to sleep. A short time later another child wakes up & eats 1/3 of the remaining marshmallows & then goes back to sleep. Later in the night the other child wakes up & eats half of the remaining marshmallows & then goes back to sleep. When they all awak in the morning there is only 9 marshmallows left, How many marshmallows were in the pack at the start of the night?

Do I start by converting the fractions into %, all I know is 9 is my starting point.

This is a problem in algebra, not arithmetic. Do you know any algebra? What is the name of the course you are taking?

 

[Deleted member 4993]

I have just started a uni course, already I am struggling in this weeks work which is fractions, decimals & percentages. My main problem is I dont know the process in how to work the problems out.

Three children camping out & go to sleep with a pack of marshmallows unopened in their ten. ONe child wakes up & eats 1/4 of the marshmallows & then goes back to sleep. A short time later another child wakes up & eats 1/3 of the remaining marshmallows & then goes back to sleep. Later in the night the other child wakes up & eats half of the remaining marshmallows & then goes back to sleep. When they all awak in the morning there is only 9 marshmallows left, How many marshmallows were in the pack at the start of the night?

Do I start by converting the fractions into % - NO, all I know is 9 is my starting point.

Let's call

the first child that woke up → F

the second child that woke up → S

the third child that woke up → T

You have to do this problem "walking backwards"

When T woke-up (before half was eaten up) how many marsh mellows were there?

Since T ate half the marshmellows and after T finished 9 were left - there must have been 18 marshmellows when T woke-up.

18 marshmellows were left when S finished eating.

So

When S woke-up (before 1/3 was eaten up) how many marsh mellows were there?

Continue.....

 

[missy_muffett]

Course

my course is called personal & professional numeracy, I am studying to be an early childhood teacher, children aged between babies & 8 years old, this is part of my degree, no I dont know algebra,

 

[JeffM]

my course is called personal & professional numeracy, I am studying to be an early childhood teacher, children aged between babies & 8 years old, this is part of my degree, no I dont know algebra,

Subhotosh Khan will show you how to solve this problem without algebra, but, personally, I feel bad that you have been posed a problem without having been given the tools that make it easy to solve. That is a recipe for discouraging people from learning math. And to discourage future teachers from learning math and understanding that it can be taught to virtually everyone should be considered criminal.

 

[Deleted member 4993]

Subhotosh Khan will show you how to solve this problem without algebra, but, personally, I feel bad that you have been posed a problem without having been given the tools that make it easy to solve. That is a recipe for discouraging people from learning math. And to discourage future teachers from learning math and understanding that it can be taught to virtually everyone should be considered criminal.

Surely NOT!

In my opinion, almost every word problem is an algebra problem!!!

 

[Deleted member 4993]

How many words are needed in order to make a "word problem"?!

2 + 3 = ? ; definitely not a word problem

What is answer to 2 + 3 ? ; is that enough words?

42

 

[HallsofIvy]

I have just started a uni course, already I am struggling in this weeks work which is fractions, decimals & percentages. My main problem is I dont know the process in how to work the problems out.

Three children camping out & go to sleep with a pack of marshmallows unopened in their ten. ONe child wakes up & eats 1/4 of the marshmallows & then goes back to sleep. A short time later another child wakes up & eats 1/3 of the remaining marshmallows & then goes back to sleep. Later in the night the other child wakes up & eats half of the remaining marshmallows & then goes back to sleep. When they all awak in the morning there is only 9 marshmallows left, How many marshmallows were in the pack at the start of the night?

Do I start by converting the fractions into %, all I know is 9 is my starting point.

I would not use % or algebra.

There were 9 marshmallows left and the last child had eaten 1/2 of what there were. That means there must have been 2(9)= 18 marshallows before that child. The previous child had eaten 1/3, leaving 18 marshmallows which was 2/3 of the previous amount. That previous amount must have been 3/2(18)= 27 marshmallows. The first child ate 1/4 of the marshmallows, leaving 27 marshmallows which must be 3/4 of the original amount. 4/3(27)= 36 marshmallows.

I did not use "algebra", expressing the unknown as a symbol like "x", but I did use the kind of "arithmetical reasoning" that algebra makes explicit: if we take away fraction "r" of something, that leaves "1- r" of it and the inverse of taking fraction "a/b" is multiplying by the reciprocal, "b/a".