Category: Pre-Algebra


Introduction to Living Math


What does calculating the cost of a grocery item per pound, measuring the dimensions of a garden, anticipating the number of days left before a family celebration, and following a recipe have in common? They are all examples of using math in daily life.  In the home education world, we call this “living math. Read More…

Importance of pre algebra

pre-algebraimportancePre Algebra is the name of a course that is generally taken in middle school math, although sometimes it is taught as early as third grade for gifted students.  For homeschoolers, pre-algebra can be taught anywhere from 8 years old to 17 years, depending on the child's foundation in math and ability to process the information.

The purpose of pre-algebra is obviously to prepare a student to take algebra and then go on to upper level math.  Without a good foundation in pre-algebra, a student may suffer academically for the remaining years they take upper level math courses.  Pre-algebra is everything about numbers that falls between the basic four (addition, subtraction, multiplication, and division) and algebra.  It even includes some geometry, although most middle schools break geometry into a separate course.  Here is a partial list of the concepts that are generally covered in pre-algebra:

Whole numbers, prime numbers, mode, median, mean, word problems, points, lines, rays, angles, area, volume and perimeter, fractions, mixed numbers, equations, exponential expressions, roots, decimals compared with fractions, proportions, ratios, negative numbers, opposites, and algebraic phrases, order of operations, variables, parentheses, ratio problems, and powers, computing interest, triangles, congruence, bisectors, advanced equations, permutations, equations of the line, conversions as well as graphing.

"Many parents believe that pre-algebra is a short bridge that can be bypassed somehow," says Dianne McLean, HECOA Director.  She feels that this is not true in most cases, "I'm all for eliminating redundancy, but I've tutored remedial algebra students for several years who simply were pushed straight into algebra without understanding pre-algebra basics. We had to stop and go back and review simple fractions and decimals, which they should have learned in pre-algebra."  As well, McLean says students should not take pre-algebra if they don't know how to do multiplication problems and long division without assistance.  "Age and grade level are irrelevant with math," she says, "Math is a process, each concept builds on something that was previously mastered.  Some can get each concept and move quickly, but others need more time.  If they are not ready, they should not move forward."  

She comments that a student must know division to learn fractions and decimals, which are a huge part of all upper level math. Fractions and decimals are mastered in pre-algebra.  Students also must know multiplication in order to factor numbers for fractions.  Both multiplication and division must be mastered before a child can learn exponents and roots.  "Algebra is about more than replacing unknown numbers with a letter," McLean says.  

The other thing that Dianne emphasizes is that math should be taught with a live instructor, or at the very least a live tutor.  While she agrees there are some exceptional people who are naturally great at computations of all kinds, she comments, "Buying expensive math curriculum is a guessing game because all students process information differently.  You can't just buy a program and expect every child to learn it by reading and watching pre-recorded videos.  Math, especially pre-algebra and higher, is the only subject that I feel most individuals can't master without some interaction from a person who has been there and can explain it in a variety of ways. "

To get a complete list of everything that is taught in pre-algebra, in the order that it should be taught (according to math experts), become a member of HECOA today and then look under the member Toolbox.

Math Relief

Are you struggling to teach an older child who is behind in math?  Did you recently transition from institutional school to home education and realize your child doesn't know the basics to be in an Algebra class?

You are not alone.  Many parents are discovering that schools have pushed children thru without really teaching the concepts – or, they spent so much time "teaching to the test" that students don't learn anything other than how to keep guessing until they get the right answer. 

Parents of children with special needs are especially frustrated.  Teachers are packed with more and more students in their class, and are not trained to teach to varying levels.  They teach one grade or proficiency level, yet studies consistently prove that most people learn math at a different pace.  Students who can't keep up are either ignored, failed, or sent to a "special" math class.  If you have ever spent time in the remedial math classes, it's often an even worse situation. 

When I was in middle school (in the 70's), I got pretty good grades in math until I reached financial math and pre-algebra, then things got tough.  When I look back, there are certain skills that were not emphasized as important when I was preparing for high school.  One of them is word problems.  All of my teachers – ALL of them – had a policy that if the students did well on the "regular" problems (usually 50-60 equation drills of some sort) then we were permitted to skip the word problems.  BIG MISTAKE!

When students prepare to take the ACT, the SAT, or other college entry exams, you can bet that every single math problem on those tests is a word problem.  If a student has little experience with word problems, it's like reading a foreign language.  For visual students such as myself, financial math and equations with x's and y's were confusing and pointless.  Does this sound like something your child would say?

When it came time for me to teach my kids, creativity was essential to not only help them understand but so that I could finally understand.  I was able to discover numerous methods to engage them, and later used those same methods to teach other kids.  I have helped a number of students to adequately prepare for Algebra, and they have gone on to do very well in higher maths.

I have spent a great deal of time with expert math instructors who are equally frustrated with the school textbooks and the "new math" that administrators are making them teach.  This is primarily because the new math is trying to teach math in illogical order.  

They explained to me the EXACT order that math needs to be taught for the best possible outcome and to properly prepare them for higher math and college.  The list is highly accurate, and I have used this method to remediate many students who were struggling because they didn't have the basics.  I would even be as bold to say – if you use my list, and then google free resources for worksheets, you will never have to buy a math curriculum.  Ever.

I have placed this amazing resource in the member Toolbox.  It is available for all membership levels, including our Basic (free) level.  Simply login with your member credentials, and the Toolbox link will appear in the navigation menu at the top of the website.  Click on the Math section, then Pre-Algebra and take a look!