what exactly is pre-algebra?

[kiwik]

Sorry but I have been wondering. Here you do "maths" until the last year of school when it is split in to calculus and statistics and kids choose to do one, both or none.

[kiana]

Usually pre-algebra is a review of all the arithmetic computations learned in elementary math, including addition/subtraction, multiplication/division, fractions/decimals, percent/ratio, an introduction to signed numbers if negative numbers have not previously been taught, an introduction to square roots if not previously taught, an introduction to exponents if not previously taught, and some work on beginning algebra. The beginning algebra usually includes properties such as associativity, commutativity, and distributive, as well as order of operations. It also includes manipulation of linear equations. Graphing (at least plotting points) is also usually included. Topics in geometry (such as the Pythagorean theorem) are frequently included as well. It is less common to see a chapter on probability but this still frequently appears. Pre-algebra courses designed for more talented students or which follow a more challenging elementary school curriculum frequently go further into the beginnings of algebra.

[Arcadia]

Honestly I don't know since I'm a foreigner here. I don't know what is pre-calculus either. Everyone back home just did calculus with statistics and/or mechanics for 9-12th grade. Hubby and I did everything.

We just treat pre-algebra as a filler/gap year thing.

[jennynd]

I came from Taiwan. There is no such thing as Pre algebra. 7th grade is algebra

[go_go_gadget]

Yes, it's basically just elementary math with harder problems, designed to be a comprehensive review before beginning algebra, with a few additional topics, which vary from program to program. I think it's worth doing, though I think it can easily be covered in far less time than is generally allotted. In the US, it isn't unusual for all three middle school years to cover just prealgebra, which is about two years and six months too long, IMO, with the exception of really rigorous programs like AoPS.

[SorrelZG]

This has been helpful. When I went to school it was just Maths until 11th when it split into Maths A, B, and C. :lol: (everyone was assigned to either A or B and C was an elective for Math B students).

[NittanyJen]

When I went through school, back in the stone ages (think early 80's) at least in my district, pre-algebra was reserved for students "who needed extra help" before embarking upon that fearful subject, algebra.

 

Typical students simply started algebra, and the top students started algebra a year early, skipping even the last year of general arithmetic, expected to have picked that up on their own time.  Pre-Algebra was seen as a mere reinforcement year, and not particularly necessary for anybody destined to apply for college.

 

Pre-Calculus simply never existed.  A student would move from trig straight into calculus, if there was time before graduation, and there was no desire for a different course such as consumer math or statistics instead.

 

 

[kiwik]

Okay thanks so it is basically consolidation and review and getting a bit older.

[Lori D.]

It is math that solidifies foundational math (grades 1-6), and introduces basic algebra topics. A typical pre-algebra course covers topics such as: Absolute Value, Order of Operations, Base, Decimals, Graphing Coordinates, Fraction Topics, Factoring, Geometry Topics, Integers, Percents, Polynomials, Prime Factors, Rational and Real Numbers, Sets and Series, and Square Roots.

[mom2bee]

Prealgebra is supposed to be a thorough review of Arithmetic with an emphasis on fractions, decimals and percents, basic geometry, properties of real numbers and a preview of basic Algebra-1.

 

 

I have no idea why it is a year-long course all to it self.

[Crimson Wife]

My DH didn't have a year of pre-calc in between Algebra 2 and calculus. Trig was integrated with Algebra 2 and the more advanced topics covered in the Algebra 2 class I took such as matrices and vectors were not touched upon at all. The pre-calc I took in 11th had 1 semester of trig and the 2nd semester was a gentle intro to calculus.

 

DH's sequence was Algebra 1 in 9th, Geometry in 10th, Algebra 2 with Trig in 11th, and Calculus in 12th.

 

My sequence was Algebra 1 in 8th, Geometry in 9th, Algebra 2 with advanced algebra topics in 10th, Pre-Calculus in 11th, and Calculus in 12th.

[Lori D.]

I have no idea why it is a year-long course all to it self.

 

 

JMO:

 

For the average person, the logic and abstract portions of the brain do not start physically maturing and activating until along about age 13-14. Algebra is largely about abstract (non-concrete) topics. By inserting a year of Pre-Algebra (solidifying foundational and arithmetic skills, and gentle introduction to basic algebra concepts), it allows students an extra year for brain maturity so that they much more easily and naturally connect with Algebra because their brains are ready for it.

 

While the trend has been to push to do Algebra in 8th grade as the standard, and sometimes even in 7th grade, that doesn't make it a good trend. What I see in the local public schools is that more than half of the students who took Algebra 1 in 8th grade end up taking it again in 9th grade because they really didn't quite "click" with it or get it down solidly. The combination of seeing it a second time with waiting until they have more brain development to make it easier to grasp helps them move forward much more strongly.

 

Doing a year of Pre-Algebra serves a similar purpose -- allows time for brain maturity, and gives a preview for easier understanding.

 

Obviously, there are always exceptions, and will always be students who get Algebra in 7th grade, or even 6th grade. But they are the small minority at the far right end of the bell curve. :)

 

That's the beauty of homeschooling -- being able to introduce subjects when it is appropriate for each individual student. I had one DS who did some Algebra in 7th grade (13yo), and then a full formal Algebra program in 8th grade. The other DS was polar-opposite -- needed Pre-Algebra in 8th grade, did a full Algebra 1 program in 9th, didn't really "click" for him, and re-did a second, different full Algebra 1 program for the first half of 10th grade (almost 16yo). Finally clicked.

[Penelope]

I'm sure it's true that some students aren't ready for the abstract, but probably in ps some students are also just not solid in arithmetic or aren't ready for the abstract because math was taught more procedurally than conceptually all along. There could different reasons for different students.

 

I have a theory, though, that in schools, part of the reason is that students in classrooms are difficult to manage at this age. A least that is what it felt like when I was a student, even though I did take algebra in eighth. Middle school felt like a giant holding pen before we were actually "allowed" to learn anything of substance. (Actually, come to think of it, most of school prior to college felt like that to me, but especially middle school, where a lot of things seemed to just. Stop. But I digress).

 

And I'm still not clear on what pre-calculus includes. In my school the year before calculus AB was trigonometry and analytical geometry.

[kiana]

And I'm still not clear on what pre-calculus includes. In my school the year before calculus AB was trigonometry and analytical geometry.

 

Pre-calculus usually includes a review of functions, exponential and logarithmic functions, and a large amount of trigonometry. Other frequently included topics are a brief introduction to conic sections and/or matrices. Pre-calculus courses with better prepared students will often spend less time on functions, exponential and logarithmic functions, and use the time saved to do a brief introduction to calculus (usually limits and/or sequences and series). You would find a substantial amount of overlap between a standard pre-calculus course and your trigonometry/analytical geometry class.

[Incognito]

It is math that solidifies foundational math (grades 1-6), and introduces basic algebra topics. A typical pre-algebra course covers topics such as: Absolute Value, Order of Operations, Base, Decimals, Graphing Coordinates, Fraction Topics, Factoring, Geometry Topics, Integers, Percents, Polynomials, Prime Factors, Rational and Real Numbers, Sets and Series, and Square Roots.

 

I know a specific pre-algebra course would be at a higher level, but this list made me smile because Life of Fred elementary as covered almost all of those topics (and we aren't quite halfway through).  :)

[Lori D.]

I know a specific pre-algebra course would be at a higher level, but this list made me smile because Life of Fred elementary as covered almost all of those topics (and we aren't quite halfway through).  :)

 

 

Yes, Singapore Primary does too. ;)

 

Side note: always felt sad that Life of Fred came out just a few years too late for us to try it out -- our DC were always just beyond the levels that were published... Glad you are getting to use it, though! :)

[linders]

DS13 says it is torture, but "not as much really serious torture as I was expecting." :glare:

 

We are using Dolciani Pre-A, and it seems to be a review of the first 6 years but with more depth, along with more algebraic thinking (generally just one variable).