Summer algebra

I have a stack of about 2 dozen Algebra I books from the library. None of these are suitable for use by a student. These would work really well for a parent who assigns their child algebra to do at home and the parent is stuck...

Summer algebra
The right Algebra I book

I have a stack of about 2 dozen Algebra I books from the library. None of these are suitable for use by a student. These would work really well for a parent who assigns their child algebra to do at home and the parent is stuck.

The content of these books varies widely, but they all include many topics that are not under the heading 'Algebra I'. Here's what I found inside.

  • Pre-algebra - negatives, fractions and parentheses
  • Functions, especially linear functions, which is a course in between pre-algebra and Algebra I.
  • Most but not all Algebra I topics
  • Algebra II topics
  • Advanced post-algebra topics like complex numbers, exponents and logs.
  • Post calculus topics like linear algebra and series, with some statistics thrown in.

What are these authors thinking? They write algebra books for a struggling high school student and then throw in a few optional chapters on topics after BC calculus.

The right Algebra I book is a list of problems for the child and one of these spoon-feeding books for the parent in case you're asked to help. From this list, which problems are the best ones for your child? Any problem she can do in 30 minutes.

Algebra I topics
Equation Manipulation

Step 1 in algebra is the transition from 3 + __ = 15 to 3 + x = 15. This is followed by more complicated version of this equation. As I explained in the last issue, there's no magic in solving simple algebriac equations, just a little hard work and experimentation.

Khan is a good place for sample problems but you have to use google search because the Khan website itself is useless in finding anything. There are plenty of Algebra I and Algebra II high school tests available, and the first few sections cover this topic.

Geometry and Trig

Once your child knows how to solve for x, it opens the door to a diversion into geometry and trig. We are now coming back to Algebra I to clean up all of the gaps.

Pre-Algebra Practice

Algebra problems are a good place to practice pre-algebra skills. We're very rusty on our pre-algebra skills because we skip pre-algebra and backtrack whenever a pre-algebra concept appears in an algebra problem.

We also found a gap in linear functions. Apparently my 20 minute linear function starter course did not stick, even when given twice. I think I'm going to assign an 8th grade linear functions book as a backtracking exercise.

The best starter problems for Algebra I are word problems. Verbal math requires 3 times the thinking as equational math, and as a bonus word problems are usually multi-step. The third best way to practice Algebra I is just to move on to trig and geometry, but as I found it leaves a lot of gaps.

Advanced topics

The focus of Algebra I is performing the 4 basic manipulations (add, subtract, multiply and divide each side of the equation) properly in the presense of negatives and parentheses.

At some point, I'll introduce a 5th operation, which will be to multiple one element of one side of the equation, or the whole side, by one. One in this case can take the form of 5/5 or (1/5)/(1/5), or (1 + x) / (1 + x).

The last topic will be finding the roots of simple quadratic equations without a formula.

During this tour of basic Algebra, we'll encounter, learn and practice a variety of math topics. When we get to 2nd degree polynomials, it will be time to move on to Algebra II, but not before next year. In between Algebra I and Algebra II, we'll use our new found equation manipulation skills on geometry and trig. Again.

My Algebra I course
Problem selection

A good Algebra I problem has 3 parts:

  • Some confusion and complication that disguises the equation to be solved so it takes the child a few minutes to realize that this is the same exact routine as the last exercise, mainly solving for x.
  • A series of equation manipulations fraught with pre-algebra topics that takes a few attempts to find the right approach. Do we start by adding 3 to each side or dividing by 5? Let's find out.
  • A 3 or 4 step solution process independent of the equation manipulation that requires some logic. By this I mean something more than 'find the value of x', like 'will Sue go to the movie based on solving the value of x in each scenario?'

Algebra I books themselves are horrible, as is Khan Academy, because they focus on a single step to practice a single topic, repeated over and over again in problems, with no confusion, until it's programmed into the child's brain, and then move on to the next spoon feeding topic. To make matters worse, in case the child isn't in the mood to think at all, Algebra I books and online material explains in nauseating detail how to do the problem step-by-step.

This isn't going to a child to do homework in 4 AP course by 8 p.m. each night. This is the prescription for a college essay that reads 'I spent 8 hours a night doing AP homework because I never learned how to think before I got to high school and that's why my admissions scores on 'personality' and 'liveliness' are zeros.

Practice Problems

After a month of research, I've settled on the NY Regents exams in Algebra 1. I'll supplement these with released tests from Virginia and maybe Texas. The level of the material in most is suitable for elementary school, and the harder problems will develop thinking.

The NY library has Algebra I exams going back to 1955. The 1955 version is a riot. Here's the first page.

With the exception of the concept of 'x' appearing in these problems, my exiting 4th grader has seen all of these topics in school except for question 8. Question 8 requires special mention because it involves factoring nth degree polynomials, a topic that has been moved to modern Algebra II courses, representing a skill as useful as using a slide rule or churning butter. I will be investigating strategies to test out of Algebra II in high school simply to skip this annoying topic. (I will also be investigating strategies to test out of geometry and trigonometry because this is Competitive Parent Magazine).

The Best Way to Do Algebra

The 2nd best way to learn Algebra I is to do algebra word problems, but these are so lame that my 7th grader's math journal is full of answers to homework problems that read 'Joe would not consider apples to begin with because he likes Doritos, so this problem is lame.' I read through a year's homework answers because he brought home the contents of his locker. I don't know what the questions were, but there's no doubt his non-answers are 100% correct. Joe wouldn't eat apples and I'm sure the problem is lame.

The best way to learn a super-set of advanced Algebra I skills and all of the thinking and problems solving skills and Grit which should be the real objective of doing Algebra I work - is to program video games. The best video games would be the original Pong or Atari games like Asteroids and Space invaders, but these have already been rejected by my kids as Ancient Lamoness. Modern video games are suitable for both boys and girls, whereas I think my old school approach was more for a boy who has been trapped in a cave for the last 40 years.

I'm going to supplement my Algebra course with a step-by-step tutorial on how to set up a web page, add javascript and jQuery, and add Canvas. Canvas is a way to plot x and y, draw shapes, and make them move on a web page. I'm competing with Alice and Scratch, but Alice and Scratch take away the work to move a point on an x/y grid.

I know from experience that a child will emerge from a visual programming exercise midway in the Algebra II realm with higher skills and less effort. If anyone is interested, I'll share. I started this blog a month ago, and it takes about 2 years for readers to notice, so I'll probably be finished before I get the first comment.