I'm seriously frustrated with algebra...need help with a question and those like it

[4kids4me]

I cannot stand algebra. I hate math. DD (gr.8) is doing LoF algebra this year and will be repeating algebra in TT next year (she's not a math person either). The next few years will be hell in math.

 

This is the type of question that we just CANNOT "get"...there's only an answer to this in the book, not how they got it...so if you can tell me the process of getting it, I'd appreciate it.

 

Alex and Betty walk at 4mph to their car. It takes them almost an hour. In their car they travel at 16mph the same distance they walked. All together, their walking and traveling by car takes exactly an hour. How long did they walk?

 

That's it. I realize it's pretty basic but you give us any question like that and there's no way we'll figure out how to make the equation. Give us the equation and it's easy peasy to figure it out from there. How in the world are we going to get better at this if we can NEVER EVER figure out how to do it?????????????? :crying::crying::crying:

[elegantlion]

d=rt. We're working on similar problems right now in LOF. They confuse me and I've been having to look at the answer to figure out who get the "t" and where we add or where they are equal.

 

What lesson is that in?

 

I'm taking cold medicine right now and can't think straight, but I'll see if I can help.

Edited February 24, 2011 by elegantlion

[kiana]

This is in the distance = rate*time chapter, right?

 

General word problems: Write down everything you DO know.

 

They walk at 4 mph (this is a rate).

They drive at 16mph (this is also a rate).

They drove the same distance each time (we aren't given the distance, but the fact that it is the SAME is important).

The total times took an hour.

 

What do we want to know? We want to know how long (this means we're looking for time) they walked. Since that's what we're looking for, let's call it x.

 

We know that walking time + driving time = 1 hour. Since our rates are also hours, let's leave it in hours for now. So x + driving time = 1 hour. So driving time = 1 - x (hours).

 

Using d = rt with the walking time, we get d = 4(mph)*x (hours).

Using d = rt with the driving time, we get d = 16(mph)*(1-x)(hours).

We were given that d was the same each time.

 

So d = 4x, and also d = 16(1-x).

 

So 4x = 16(1-x).

 

So x = 16/20 = 4/5.

 

This isn't enough for an answer, so look back at the original work. What was x? It was the time that they walked. So they walked for 4/5 of an hour.

 

An hour is 60 minutes, so 4/5 of 60 is 48 minutes. If you'd rather have the time in minutes, they walked for 48 minutes.

 

 

 

Here's another explanation of how to work with word problems using this formula, if what I said made no sense perhaps this will help. http://www.purplemath.com/modules/distance.htm

[elegantlion]

This is in the distance = rate*time chapter, right?

 

General word problems: Write down everything you DO know.

 

They walk at 4 mph (this is a rate).

They drive at 16mph (this is also a rate).

They drove the same distance each time (we aren't given the distance, but the fact that it is the SAME is important).

The total times took an hour.

 

What do we want to know? We want to know how long (this means we're looking for time) they walked. Since that's what we're looking for, let's call it x.

 

We know that walking time + driving time = 1 hour. Since our rates are also hours, let's leave it in hours for now. So x + driving time = 1 hour. So driving time = 1 - x (hours).

 

Using d = rt with the walking time, we get d = 4(mph)*x (hours).

Using d = rt with the driving time, we get d = 16(mph)*(1-x)(hours).

We were given that d was the same each time.

 

So d = 4x, and also d = 16(1-x).

 

So 4x = 16(1-x).

 

So x = 16/20 = 4/5.

 

This isn't enough for an answer, so look back at the original work. What was x? It was the time that they walked. So they walked for 4/5 of an hour.

 

An hour is 60 minutes, so 4/5 of 60 is 48 minutes. If you'd rather have the time in minutes, they walked for 48 minutes.

 

 

 

Here's another explanation of how to work with word problems using this formula, if what I said made no sense perhaps this will help. http://www.purplemath.com/modules/distance.htm

 

Thank you, I was trying to work it out for myself. I was on the right track anyway. Algebra and Mucinex do not mix well. :lol:

[4kids4me]

Elegant Lion and Kiara....are those type of word questions ALWAYS d=rt? There's nothing else I'm ever looking for???

 

This question comes after chapter four in the cities section: El Campo. These types of questions are also found in the pre-algebra texts and they ALL make me want to stab myself in the eye with a dull pencil. If *I* can't get them, then how can dd get them???? Sigh. Hopefully after doing one year of this in LoF, when we move on to TT it'll be easier.

 

Thanks for the help. Both dd and I will be sitting down and reviewing how Kiara got the answer.

[regentrude]

Elegant Lion and Kiara....are those type of word questions ALWAYS d=rt? There's nothing else I'm ever looking for???

 

Of course there can be *other* word problems where they look for different stuff. But whenever you have somebody cover a distance in a certain time with a certain speed, the relationship you need it the definition of speed:

speed is distance traveled/ time it takes. Basically, all the student needs is an understanding of what "4mph" means.

 

The key to solving these types of problems is not to memorize a formula, but to analyze the problem and to understand what exactly is going on . In order to do so, the student should make it a habit to begin each word problem with a sketch, labeling all given and looked for information.

[4kids4me]

Regentrude, what you're saying makes sense because this is the other question she couldn't figure out (can anyone help with this one???...and maybe help us figure out WHY we're not able to "get" these???):

 

Betty and Alex are the same age. Betty has announced that if she were to get younger at the same rate that Alex were getting older, in 11 years, he would be three times her age. How old are they now?

 

 

Thank you, thank you, thank you!!!!!

[regentrude]

Betty and Alex are the same age. Betty has announced that if she were to get younger at the same rate that Alex were getting older, in 11 years, he would be three times her age. How old are they now?

 

 

Right now, their ages are x.

 

in 11 years: Betty's age is x-11, Alex's age is x+11

At that point: x+11= 3*(x-11)

x+11=3x-33

44=2x

x=22

 

 

The key to doing these problems is to write out what you know and assign variables to suitable quantities, then "translate" all the word statements into equations.

[4kids4me]

Right now, their ages are x.

 

in 11 years: Betty's age is x-11, Alex's age is x+11

At that point: x+11= 3*(x-11)

x+11=3x-33

44=2x

x=22

 

 

The key to doing these problems is to write out what you know and assign variables to suitable quantities, then "translate" all the word statements into equations.

 

Sigh -- can one of you math whizzes just come and live with me? I'm going to have a nervous breakdown with this. Thanks for helping! (My dd thanks you all, too!!!)

[regentrude]

This is how I taught my son:

1. give each quantity that occurs a symbol name (variable).

2. write down everything form the problem as equations using these symbols.

3. find relationships between the different variables you defined

 

A beginner would most likely introduce more than just one variable. She might first write:

current age of Betty and Alex: "x" (the unknown you are looking for)

Betty's age in 11 years: "b" (symbols for variables should have some relation to the quantity - "B" is for Betty)

Alex's age in 11 years: "a"

 

Next, she needs to read the problem and see what it tells her about these quantities. She might write:

b=x-11 (Betty gets 11 years younger)

a=x+11 (Alex gets 11 years older)

a=3b (Alex will be three times as old as Betty)

 

This is all correct. Now the student just needs to put these relationships together to get the simpler answer.

At the beginning, my son would come up with different variables for every single quantity. To see that you can do it all in terms of the current age right away takes practice and some experience; so if the learner's solution does not look as concise as mine, that's OK - she needs to understand the process of translating quantities into variables and relationships into equations.

Try teaching your DD doing it with many variables and gradually reducing the number through the relations given in the problem

[Brindee]

 

Sigh -- can one of you math whizzes just come and live with me? I'm going to have a nervous breakdown with this. Thanks for helping! (My dd thanks you all, too!!!)

If one of them comes and lives with you, I'm coming too! I need the help! :tongue_smilie:

[Guest Dulcimeramy]

I don't know if this would be helpful to anyone to hear, but I'll say it anyway:

 

As my oldest son was finishing grammar stage math, I looked ahead to Algebra and began to be afraid that I wouldn't be able to rely on my understanding of Algebra that I acquired more than 20 years ago.

 

I put myself through Saxon Algebra I and Mr. Khan's Academy, and then I was ready to help my son begin Algebra.

 

You can't teach what you don't know.

[Jann in TX]

many kids just can't read the problem and 'simply' pick out the necessary equations. The chart method really helps make those equations pop out! It is a fast and easy way to organize these pesky problems.

 

I teach with Lial-- and she also used the chart method in her texts.

 

Here is your problem worked out using the chart method:

 

To figure out what to put for Distance in the chart I just used the formula: Distance = rate x time to get the 4x and the 16y

I also noted on the chart that the distances were the same and that the time = 1 hour total. This allowed me to EASILY see the 2 equations. I used substitution to solve.

Edited February 24, 2011 by Jann in TX
graphic

[4kids4me]

Everyone...I am overwhelmed with gratitude toward all the responses, both in encouragement and actually helping me with the problem! I now have a few more tools and will be printing this all up and pouring over it so I can learn it!!!!

 

Hugs to you all!!!!!! :grouphug: :)

[Dana]

I strongly encourage using words as a transition between the word problem and the math. Regentrude gave a good example. I also encourage writing what you know on a sheet of paper and then getting away from the original problem. I find it too easy to stare at the problem and hope something will pop out at me. It never does. But staring at what I wrote will sometimes give the leap to the next step.

 

I don't like charts & tables for many problems, but they are the BEST way I have seen to do d=rt problems. The chart is really worth it. Jann's example is also a very good one.

[4kids4me]

I strongly encourage using words as a transition between the word problem and the math. Regentrude gave a good example. I also encourage writing what you know on a sheet of paper and then getting away from the original problem. I find it too easy to stare at the problem and hope something will pop out at me. It never does. But staring at what I wrote will sometimes give the leap to the next step.

 

I don't like charts & tables for many problems, but they are the BEST way I have seen to do d=rt problems. The chart is really worth it. Jann's example is also a very good one.

 

Thanks, Dana. Are you willing to move in anytime soon? :D

[Teachin'Mine]

It sounds to me like you need a different text - one which teaches you how to translate word problems into equations. Some say that's just memorizing algorithms, but it works. Saxon does this. It also has step by step instructions in the solutions manual. I don't know if this would be a fit for you, but I'd suggest finding something which does teach the system of converting word problems to equations, and which does have a good solutions manual. I think it would help tremendously.

[4kids4me]

It sounds to me like you need a different text - one which teaches you how to translate word problems into equations. Some say that's just memorizing algorithms' date=' but it works. Saxon does this. It also has step by step instructions in the solutions manual. I don't know if this would be a fit for you, but I'd suggest finding something which does teach the system of converting word problems to equations, and which does have a good solutions manual. I think it would help tremendously.[/quote']

 

Thanks -- I'll look into this. :)

[homeschoolally]

many kids just can't read the problem and 'simply' pick out the necessary equations. The chart method really helps make those equations pop out! It is a fast and easy way to organize these pesky problems.

 

I teach with Lial-- and she also used the chart method in her texts.

 

Here is your problem worked out using the chart method:

 

To figure out what to put for Distance in the chart I just used the formula: Distance = rate x time to get the 4x and the 16y

I also noted on the chart that the distances were the same and that the time = 1 hour total. This allowed me to EASILY see the 2 equations. I used substitution to solve.

 

This is how he teaches it in LOF Pre Alg with Economics--I agree with the others that I never understood this type of problem until shown in the 'box' method.

[NicksMama-Zack's Mama Too]

I bought a used copy for less than $10.

 

This looks good like a very similar book and very inexpensive:

http://www.amazon.com/Problems-Algebra-Proven-Techniques-Expert/dp/0071343075/ref=pd_cp_b_1

 

We are using Larson's for Algebra I along with this type of supplement.

 

I have a huge math library in my home. I barely passed Algebra I in high school, so I've had to reteach myself. After six years of Singapore Math and now Dr. Mosely's lectures, I feel like I'm actually good and math!

 

hth

K

[Dana]

Thanks, Dana. Are you willing to move in anytime soon? :D

 

We could talk... but since I go to long underwear when it drops to the 60s, I doubt it'd be a good fit :D

[MicheleinMN]

:lurk5:

[4kids4me]

We could talk... but since I go to long underwear when it drops to the 60s, I doubt it'd be a good fit :D

 

Yes, I believe you're right. Living in Canada may prove much too cold for you. Well, we'll just have to move my family in with yours! :)