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Pre Alegebra Boot Camp

mgardner

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As a side job, I am a professional tutor. I have a student that struggled through his last year in Pre-Algebra, and ultimately failed the final, despite all the work I did to prepare him. So, next year, they are going to put him in Pre-Algebra again. His mother and I have agreed to spend this summer getting him proficient in the very basic of basics of algebra. So, I am preparing a very small "boot-camp" style set of problems that we are going to go over this summer until he is proficient in at least the most basic concepts.

What would you all suggest as a minimum level of competency to succeed in a pre-algebra course?
 
mgardner said:
As a side job, I am a professional tutor. I have a student that struggled through his last year in Pre-Algebra, and ultimately failed the final, despite all the work I did to prepare him. So, next year, they are going to put him in Pre-Algebra again. His mother and I have agreed to spend this summer getting him proficient in the very basic of basics of algebra. So, I am preparing a very small "boot-camp" style set of problems that we are going to go over this summer until he is proficient in at least the most basic concepts.

What would you all suggest as a minimum level of competency to succeed in a pre-algebra course?
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I'm not sure what set of skills constitutes pre-algebra the don't also constitute regular math.

If he's having trouble with PEMDAS and similar stuff, I'd start to worry about dyslexia. Rather than tutoring, he may benefit from a full-on education assessment. The school district is probably required to do it if requested.
 
Ensure that the student knows and understands the properties of equality, what equality means and implies, and the difference between an expression and an equation, i.e. why the word "equation" starts with the letters "equa."

Then algebraic manipulation can be understood as the results of the properties of equality.

For slope, note that a slope of one ALWAYS goes exactly diagonally corner to corner through at least one pair of the boxes on graph paper (in basic Algebra problems, anyway.) Then it's easy to tell whether a slope is greater or less than one.

Once that's understood, you can go on to negative slopes, and calculating slopes by counting the boxes and with the slope formula.

With an understanding of these few basic things, most of the rest of a pre-Algebra class easily follows.
 
I have always tried to introduce algebra as the written language of maths. An English statement like "Jack has 2 balls" can be translated into algebra as "j = 2". Until students see algebra as a way of communicating ideas, they will always see it as meaningless mental torture.

One introductory strategy that seemed to work when I was a kid was asking students "which number goes into the square"? or "which number goes into the circle"? If they can handle that then they may transition easily from squares and circles to x's and y's.
 
There is an app called DragonBox which is a fun way to learn how to solve for a variable. I recommend the 12+ version, not 5+.

One of the all-around most useful skills is factoring.
 
Did some training with folks that were doing mentoring for middle school students that were having some difficulties in math. They said they found correlation of future math success on their ability to be comfortable with two core areas: negative numbers and fractions.

I haven't done any tutoring since then, but I'd start with making sure they're really well set in those areas before going on.
 
BowlOfRed said:
Did some training with folks that were doing mentoring for middle school students that were having some difficulties in math. They said they found correlation of future math success on their ability to be comfortable with two core areas: negative numbers and fractions.

I haven't done any tutoring since then, but I'd start with making sure they're really well set in those areas before going on.
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I've seen a lot of students grasp negative numbers pretty quickly but fractions bring many of them to a screeching halt. Some adults, too.

If they have a problem with calculating percentages, I have them calculate their shooting percentage with ping pong balls. If he is interested in sports, that can help connect the subject matter to something in his life. It's a good way to learn statistics and also football has negative numbers.

Properties of exponents would probably help. Sooner or later scientific notation crops up. Mean, median and mode as well.

Since the OP mentions failing the final, I wonder if test anxiety contributes to his struggles. It's a good idea to look at that test to figure out what he needs and also if there are any strengths to build on.

IXL Math is expensive but the company used to offer free trials.

Kahn Academy is good too, although it moves pretty fast.
 
I've always felt that if you can find real world stuff to relate it to, it's more interesting. As it happens, I tutor college students in finance, so that part isn't an issue for me; usually the problems are real world.

It does sadden me sometimes to see some finance students struggling with basic algebra, because I can tell they have little or no chance of passing the course.

If you think that finance-type problems might interest him, I would be happy to supply some, but I would need to know the general concepts that you are trying to get across. Some finance problems of course are very complex, but others are actually quite simple--things like figuring the total cost of a video game including the sales tax, or reversing that--knowing the sales tax rate and the total price, what is the store keeping?
 
Brainster said:
I've always felt that if you can find real world stuff to relate it to, it's more interesting. As it happens, I tutor college students in finance, so that part isn't an issue for me; usually the problems are real world.
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Teaching about compound interest is one of our state's standards, but rates are now so low that the benefits don't look very convincing.
 
Brainster said:
I've always felt that if you can find real world stuff to relate it to, it's more interesting. As it happens, I tutor college students in finance, so that part isn't an issue for me; usually the problems are real world.
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I filled in for a lawyer years ago for a class on junior college class on business law. I spent the entire hour talking about widgets and contractual performance - you order a million widgets and get 968.000, or you order blue widgets and you get white. What does substantial performance mean? At the end of the class, I asked if there were any questions. One student raised his hand and asked, "What's a widget?"
 
One way to stimulate an interest is learning something like casting out nines as a way to check arithmetic and catch about 90% of the errors people make. It's first presented as a "trick" and is most useful if the kid feels here's learning something special that others don't know.

Then going into why it works. This makes kids think. Key is to develop an interest in numbers and how they work beyond necessary memorization.
 
Minoosh said:
Teaching about compound interest is one of our state's standards, but rates are now so low that the benefits don't look very convincing.
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Maybe try credit card interest that one pays. It's high enough to matter.
 
I mentioned in my thread in FC (coincidentally on PEMDAS homework for my kid a couple of nights ago) that my son's class is working on the P-MDAS in the fourth grade. No unknowns, just series of functions that have to be performed in the correct order.

I see everywhere that Pre Algebra is considered a 7th grade topic. I think the system they're working with my son is more sensible. Teach them "order" and have it ingrained. Introduce variables and unknowns, one at a time, later. When I went to school the toughest things we were doing through the sixth grade were fractions, particularly multiplication and division of...

It's not the Thai school system. It's the international schools in the Thai system that have taken on Cambridge Math (the Cambridge English, otoh, is pretty cruddy and their science a little weak). I think teaching them basic processes and such from an earlier age is probably very helpful. Takes some of the fear factor out when they start seeing it three years later.
 
marting said:
Maybe try credit card interest that one pays. It's high enough to matter.
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That's a great idea.

My state has 2 years of algebra now and both levels at least touch on exponential functions. There's also "financial algebra," a class usually populated by seniors. Four years of HS math are required. I subbed recently in one of those classes and the assignment was basically applied arithmetic.

I'm conflicted on this; I don't want to perpetuate math phobia but the truth is most people do not need to know how to factor quadratic expressions. They can hold their phones over it and get the answer. There are a few who hunger for more complexity but they are definitely not the majority.
 
psionl0 said:
One introductory strategy that seemed to work when I was a kid was asking students "which number goes into the square"? or "which number goes into the circle"? If they can handle that then they may transition easily from squares and circles to x's and y's.
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Here it's called the "missing addend" and yes, it's the exact same thing as using a variable and they can do it in 3rd grade. For some reason introducing letter variables throws some students.

Frequently heard, "I was good at math until they put the alphabet in it."
 
Khan Academy is free, online and works from K-12 plus a bit in most subjects. I strongly suggest it: https://www.khanacademy.org/

and, no, it really is free and I have seen no info that it sneaks your data for advertising or related.........
 
I'm old and struggling with the concept of "pre-algebra". We had arithmetic through grade six then straight into algebra. Around 60 years ago.
So what is "pre-algebra"? Is it like "pre-pregnancy"? Or "pre-death"?

Then again, I recall we had something called "pre-calculus". I was sufficiently defficient in regular algebra that I wasn't qualified for it.
 
Trebuchet said:
I'm old and struggling with the concept of "pre-algebra". We had arithmetic through grade six then straight into algebra. Around 60 years ago.
So what is "pre-algebra"? Is it like "pre-pregnancy"? Or "pre-death"?

Then again, I recall we had something called "pre-calculus". I was sufficiently defficient in regular algebra that I wasn't qualified for it.
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Because a non-small number of students have trouble with some of the new ways of doing math (which for me complicate it rather than make it easier) the big whigs have come up with way "interesting" ways to "simplify" and "help students" be "better" prepared. They do not. Also why I note Khan Academy as they do what works not what is currently en vogue.
 
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