Math people: what types of problems are these?

[distancia]

These are what my DD is getting wrong on placement tests. Can you tell me what this concept is called and if it goes back to Algebra 1 or 2? Thanks!

 

Solve for b: A = 1/2 bh

 

What process are you using to solve this and what is it called?

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Factor completely: 8x^4 y^4 - 18x^2 y^6

[Read as" 8 x to the fourth y to the fourth minus 18x squared y to the sixth"

 

What is this process called and where does it go back to?

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Write in lowest terms b^2 + 6b - 16 / b^2 + 5b - 24

[Read as " b squared plus 6b minus 16 divided by b squared plus 5b minus 24"]

 

Again, what is this and where do I look for it, Alg 1 or 2?

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Which of these is the quotient of y^3 - 4y^2 - 6y + 5 AND y - 5?

 

Is this Alg 1 or 2 and what is it called?

 

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Find the distance between the points (-2,3) and (4,-5)

 

I am assuming this is a complicated process in Alg 2 because it was at the tail end of the Compass Placement section for Alg 2, but I was able to solve it just by graphing the darn things...what is the complicated concept called?

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Thank you--not sure if we should go back to Alg 1 or just review all of Alg 2

Edited February 11, 2011 by distancia

[NicksMama-Zack's Mama Too]

We are using Larson's Algebra I text this year (chalkdust) and I'm pretty sure all those types of problems are covered.

[kiana]

We teach these in intermediate algebra. They might also be covered in algebra 1.

 

1) Solving literal equations. Here's a tutorial.

http://www.purplemath.com/modules/solvelit.htm

 

2) Factoring

 

3) Reducing rational expressions

 

4) Division of polynomials

 

5) This is more application of geometry -- draw it out as a triangle. Or you could have the distance formula memorized.

[distancia]

Thanks--that's what I need to know. If we need to go way back and review all of Algebra 1, or if a thorough course of Intermediate Algebra would cover those bases. And boy, it's going to be a THOROUGH review.

Edited February 11, 2011 by distancia

[Julie in MN]

Solve for b: A = 1/2 bh

 

What process are you using to solve this and what is it called?

 

That looks like geometry -- area equals one-half base times height?

[distancia]

Hi, Julie. Yes, it is geometry, but it is the process that is being questioned. In other words: how would a person know where to start with this?

 

Let's say the problem changed to: Q = 1/2 wz [Read as "Q equals one-half (of) w times z"]. How would you know what to do? What is that process called?

 

I am very rusty with math. If someone gave me that problem, I wouldn't know what to do. I could substitute some numbers and figure it out after a couple attempts, but really, that's not the way to do it quickly.

 

The way to do it quickly would be knowing the process. This problem was taken was from a placement test for Intermediate Algebra (in college). Since the test was adaptive, and this problem was in the middle, I am assuming it was somewhere in the end of Alg 1 or start of Alg 2. Somewhere in there is an explanation of how to actually solve this problem. That is what I am looking for.

[Dana]

Most of these are from Algebra 1. Look for these topics in the table of contents of a text or index. You can check out a bunch of algebra books from a library and focus on just the topics you need. You could also see if you can use the books at a university library or community college - not check out but just use while you're there. You can look for texts titled Elementary or Elementary and Intermediate Algebra

 

These are what my DD is getting wrong on placement tests. Can you tell me what this concept is called and if it goes back to Algebra 1 or 2? Thanks!

 

Solve for b: A = 1/2 bh

 

What process are you using to solve this and what is it called?

 

Literal equations, formulas

 

---------------

Factor completely: 8x^4 y^4 - 18x^2 y^6

[Read as" 8 x to the fourth y to the fourth minus 18x squared y to the sixth"

 

What is this process called and where does it go back to?

 

Factoring. Specifically here: factor out GCF first, then difference of squares. There'll be a whole chapter on factoring generally. You need to be good at polynomial multiplication first to be able to factor well. Check out special products rules too.

 

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Write in lowest terms (b^2 + 6b - 16) /( b^2 + 5b - 24 )

[Read as " b squared plus 6b minus 16 divided by b squared plus 5b minus 24]

 

Again, what is this and where do I look for it, Alg 1 or 2?

 

Rational expressions. Reducing rationals, write in lowest terms, simplify.

Requires a SOLID understanding of how fractions work (without calculator!) and then factoring is needed.

----------------

 

Which of these is the quotient of y^3 - 4y^2 - 6y + 5 AND y - 5?

 

Is this Alg 1 or 2 and what is it called?

 

Polynomial division. (Division of Polynomials) Often found in a chapter with exponential rules and polynomial arithmetic. Synthetic division is a neat shortcut, but full long division IS needed.

 

-----------------

 

Find the distance between the points (-2,3) and (4,-5)

 

I am assuming this is a complicated process in Alg 2 because it was at the tail end of the Compass Placement section for Alg 2, but I was able to solve it just by graphing the darn things...what is the complicated concept called?

 

The Pythagorean Theorem :)

The distance formula (often found with distance and midpoint formula towards the end of an intermediate algebra text). It's really not complicated at all - just the formula looks scary. Draw a right triangle where the hypotenuse is the distance between the two points in the coordinate plane. It's a way to remember the distance formula.

 

Really, all this is Algebra I - but you can find all of it in just about any text at the cc for beginning/intermediate algebra. And you may find more problems and better explanations than you would in an algebra I or II text.

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[8filltheheart]

The first 3 are all pretty basic alg 1. The last one is finding the distance between 2 pts which is simply a formula. W/o looking I am not sure if it is typically alg 1 or alg 2.

 

 

This example: Q = 1/2 wz, solving for w, simply requires basic understanding of what occurs when you perform operations on both sides of the = sign. All you have to do is multiply both sides by 2 and divide both sices by z and w will be isolated and therefore you have solved for w. (as long as an operation is done to both sides, you do NOT change the value)

2* 1/z * Q = 1/2 * w * z * 2 * 1/z

 

2Q/z= w b/c 2* 1/2= 1 and z * 1/z (or simply / z) =1

[kiana]

Thanks--that's what I need to know. If we need to go way back and review all of Algebra 1, or if a thorough course of Intermediate Algebra would cover those bases. And boy, it's going to be a THOROUGH review.

 

I would really consider hiring a tutor to work with her, if it is at all affordable. I think the best thing to do would be to go as far back as algebra 1 and go through it quickly, taking chapter tests, looking for weak points and remediating those. But having someone who has worked with it recently to figure out exactly where her misconceptions are makes a huge difference.

[regentrude]

Which of these is the quotient of y^3 - 4y^2 - 6y + 5 AND y - 5?

 

 

 

Since the test is multiple choice, the student does not even need to be able to do polynomial division. He just needs to be able to multiply the possible answers by (y-5) and see which one works. Chances are, some of the answers can be excluded right away because they are not of the right order - you need a quadratic. (It could even be that there is only one quadratic offered which means it has to be the answer)

[Julie in MN]

Hi, Julie. Yes, it is geometry, but it is the process that is being questioned. In other words: how would a person know where to start with this?

 

Let's say the problem changed to: Q = 1/2 wz [Read as "Q equals one-half (of) w times z"]. How would you know what to do? What is that process called?

 

I am very rusty with math. If someone gave me that problem, I wouldn't know what to do. I could substitute some numbers and figure it out after a couple attempts, but really, that's not the way to do it quickly.

 

The way to do it quickly would be knowing the process. This problem was taken was from a placement test for Intermediate Algebra (in college). Since the test was adaptive, and this problem was in the middle, I am assuming it was somewhere in the end of Alg 1 or start of Alg 2. Somewhere in there is an explanation of how to actually solve this problem. That is what I am looking for.

 

Okay, I think I get it. At first, I thought you meant that on the test, he had to name the type of equation. Instead, you just mean that you want to find resources and need to know "what to look up"?

 

A problem like "solve for b" requires the student to understand (1) the fact that when you do something to one side of an equation, you must do the same thing to the other side, as well as (2) the basic ways that you can move terms around in an equation.

 

So for (1), your child needs to be able to look at an "equation" as a balanced group of numbers, and he should at least be aware that it always must stay balanced. If you have a physical balance (like a teeter-totter), and you add a sack of potatoes to one side, then you must add the same thing to the other side or it will become lopsided.

 

You might look up "balancing algebra equations."

 

For (2), your child needs to be solid in how addition/subtraction is different from multiplication/division. They behave differently in an equation. This particular equation is all mult/div, so you have a lot of freedom.

 

When my ds starts making errors on this, I have him use tiny numbers and see what works and what doesn't work. This isn't a foolproof method, but it does help my ds to "believe" that principles really work.

 

e.g. 1/2 x b x h can become (1 x b x h) all divided by 2.

so try it: plug in 2 & 3 as small, easy numbers

1/2 x 2 x 3 = 3

(1 x 2 x 3) /2 = 3

 

But you can't do that with 1/2 + b + h

which would be 1/2 + 2 + 3 = 5.5

and if you try to group them, (1 + 2 + 3) / 2 = 3

Those are not the same thing

 

That becomes important because if you group them together, then you can reduce the whole equation and get rid of the 1/2:

(1 x b x h) / 2 = a

Then multiply both sides by 2 and you get

1 x b x h = 2a, so you've gotten rid of the fraction

 

and you can check with the tiny numbers:

before, we said (1 x b x h) / 2 = a

which is (1 x 2 x 3) / 2 = 3

and now we have changed the equation to 1 x b x h = 2a

which is 1 x 2 x 3 = 6 (because above, we found out a=3, so 2a=6)

and both of these still balance

 

 

Well, I don't know if that makes any sense at all!!!

Julie

[distancia]

When my ds starts making errors on this, I have him use tiny numbers and see what works and what doesn't work. This isn't a foolproof method, but it does help my ds to "believe" that principles really work.

 

Well, I don't know if that makes any sense at all!!!

Julie

 

Okay, you all have helped greatly. Let me follow on Julie's comment: "it helps my son to "believe" that principals really work".

 

Julie, what is going on in your son's brain that makes him doubt (I don't know if doubt is the right word; maybe more like be uncertain? or remain unconvinced until seeing the proof again and again and again, that principles really work?

 

Is this a certain way of thinking? A type of learning (dis)ability? From where does it originate?

 

I think this is what is happening with my daughter (I know it did with me, when I was in high school).

 

In my case, I would be shown a formula, how to do a problem. Well, the first problem always came out okay, but by #7 or #8 it was always wrong. I think it made me doubt the formula. I could never trust anything except substituting real numbers. That is how I scored high in my SAT, I was really quick at substituting actual teeny numbers for variables and therefore I could eliminate the "wrong answers" and choose the right one. My score did NOT reflect my ability at algebraic reasoning, it reflected my ability to substitute and compute very rapidly.

 

Based upon the responses from you all, it seems I have to take DD back to the gaps in Alg 1. She is starting a commcoll Intermediate Alg course next week. It will be self-paced. This brings up another question for another post--

[Julie in MN]

Julie, what is going on in your son's brain that makes him doubt (I don't know if doubt is the right word; maybe more like be uncertain? or remain unconvinced until seeing the proof again and again and again, that principles really work?

 

Is this a certain way of thinking? A type of learning (dis)ability? From where does it originate?

 

I think this is what is happening with my daughter (I know it did with me, when I was in high school).

Interesting question, I've never thought it out :D

 

I think with my son, it's that "rules" don't stick in his brain. He's a good memorizer, but it's memorize-and-forget for things he doesn't use often.

 

And why doesn't he use math rules often? Maybe that's a bit of the distrust you mention? He has had a hard time learning new things in math until he sort of "absorbs" them by osmosis and they become a part of how he thinks. And "rules" never seem to do that. Therefore, he can easily do some very hard math, yet struggles with some basics like distribution (another thing we "proved" a lot by plugging in teensy numbers).

 

This year in Jacobs' Geometry has been a mental challenge for him, with proofs and rules and such, and a teacher who tries to bring the student into his thinking process -- but I think a challenge he needs to conquer :tongue_smilie:

 

My oldest is a big rule follower. He was a dream for a traditional math teacher. :drool: He's an engineer now, of course.

Julie

Edited February 12, 2011 by Julie in MN

[Teachin'Mine]

Basic geometry.

 

A = 1/2 bh

 

Area of a triangle = 1/2 base x height

 

It's included in Saxon before Algebra I, but is repeated there again.

[distancia]

Basic geometry.

 

A = 1/2 bh

 

Area of a triangle = 1/2 base x height

 

It's included in Saxon before Algebra I' date=' but is repeated there again.[/quote']

 

Yes, I do understand it is basic Geometry. My question is: how does one know what to DO in order to get the "b" in the A = 1/2 bh

 

It's not something you're born knowing how to do and it shouldn't be something you have to memorize. So, how do you learn what to do to isolate the "b"?

 

Julie, I think our children are alike. Early on DD learned to do math by following the rules but it became too confusing for her to discern when to use a rule and when not to use a rule--she was relying on memory and not reasoning--that she was overwhelmed. Instead of being like me (and your son) and plugging in teeny numbers over and over again to prove a rule true--an extremely slow but eventually productive way of doing things--she has become anxious, because the rules aren't working!

[regentrude]

Yes, I do understand it is basic Geometry. My question is: how does one know what to DO in order to get the "b" in the A = 1/2 bh

It's not something you're born knowing how to do and it shouldn't be something you have to memorize. So, how do you learn what to do to isolate the "b"?

 

You need to go back to the very basic understanding of a balanced equation, the fundamental concept of beginning algebra 1. (If I say "you", I mean of course, the student.)

You need to understand that the equal sign means that both sides of the "balance" are exactly the same - like the two pans on a balance. If that is the case, anything you do exactly the same way to BOTH sides of the equation still preserves the "balance" and hence produces another equation. That is the fundamental underlying concept.

 

Next, you need to practice doing this to equations. First, you will start by adding things to, and subtracting things from, both sides. the first problems will be of a type x+5=8. If on both sides you subtract 5, you get x=3.

Then, you extend that to multiplication and division. Example problem: 5x=20. If you divide BOTH sides by 5, you get x=4.

Then, you go to more complicated things. Always asking: what kind of operation would I have to do in order to isolate the thing i am looking for?

So if A=1/2 bh and I want b:

how do I get rid of the 1/2? By multiplying both sides by 2.

How do I get rid of the h? By dividing both sides by h.

 

This, in essence, is the beginning month of an algebra 1 course. Any student who can not do these manipulations is lacking basic algebra 1 knowledge and absolutely needs to get back there in order to conceptually understand what is going on.

[angela in ohio]

There is a difference between:

 

Use A = 1/2 bh to find the area of this triangle.

 

and

 

Solve for b: A = 1/2 bh

 

The first may be basic geometry and taught prior to algebra I, but the second is an algebraic problem.

 

I agree with pp who have said that these are Algebra I concepts.

[distancia]

You need to go back to the very basic understanding of a balanced equation, the fundamental concept of beginning algebra 1.

 

You need to understand that the equal sign means that both sides of the "balance" are exactly the same - like the two pans on a balance. If that is the case, anything you do exactly the same way to BOTH sides of the equation still preserves the "balance" and hence produces another equation. That is the fundamental underlying concept.

 

Next, you need to practice doing this to equations.

 

Then, you go to more complicated things. Always asking: what kind of operation would I have to do in order to isolate the thing I am looking for?

 

 

VERY WELL STATED :hurray: You said exactly what I (the student) needed to hear.

 

And the word PRACTICE...that's the answer, isn't it? Drill and drill and drill. I wish our DD had better math instruction back in middle school (when this all began). Had I known then what I know now....

 

Well, the good news is that there's room for improvement now! Thank you so much!

[mooooom]

some kids just have trouble with the instructions. My kids used to read "solve for b" and not get it when there is a formula already in front of them. "make it b=" and they have no trouble with the work. Frustrating language COULD be the confusion, it might be worth making sure it isn't a vocabulary issue.

[Teachin'Mine]

Yes, I do understand it is basic Geometry. My question is: how does one know what to DO in order to get the "b" in the A = 1/2 bh

 

It's not something you're born knowing how to do and it shouldn't be something you have to memorize. So, how do you learn what to do to isolate the "b"?

 

Julie, I think our children are alike. Early on DD learned to do math by following the rules but it became too confusing for her to discern when to use a rule and when not to use a rule--she was relying on memory and not reasoning--that she was overwhelmed. Instead of being like me (and your son) and plugging in teeny numbers over and over again to prove a rule true--an extremely slow but eventually productive way of doing things--she has become anxious, because the rules aren't working!

 

 

Kimanjo I'm so sorry. When I answered, I didn't even see the full post. I'm totally daft. :tongue_smilie: Dana gave some good information on how to reference these types of problems, and they are generally algebra I problems. And Angela is right about there being a difference between what I answered and what you had written. I have no idea what I was thinking when I posted.

 

If she's having trouble answering these, I'd suggest doing algebra I with a different program than before so she can really grasp the algebraic concepts. She'll really struggle in algebra 2 if this isn't done first.

Edited February 12, 2011 by Teachin'Mine

[Caroline]

some kids just have trouble with the instructions. My kids used to read "solve for b" and not get it when there is a formula already in front of them. "make it b=" and they have no trouble with the work. Frustrating language COULD be the confusion, it might be worth making sure it isn't a vocabulary issue.

 

Understanding the vocabulary in math is very important, and often overlooked. Certainly when it comes to applying math to physics, chemistry, etc, knowing the math vocabulary is important.