Algebra I Unit 3: Linear Equations

Our last unit focused on modeling functions, which means translating real life problems into math equations. We mostly used the worksheet from the On-Core book, Chapter 2. These were the topics:

Algebra I Unit 2: Algebra Modeling and Unit Analysis

These lessons still had quite a bit of review from pre-algebra, but it turned out to be much needed review. We switched back and forth between the On Core book (all of chapter 1) and the super old Algebra book (chapter 2):

- Balancing one variable equations (one and two step solutions)
-  Simplifying expressions
-  Distributive property
-  Writing and modeling functions
-  Using dimensional analysis to check equations (here's an explanation)
-  Math lab: Hooke’s Law (results produce a straight line with the spring constant = to the slope)
-  Random reviews:  proportions, balancing equations with fractions, and converting between units

After this unit, my son was much more comfortable with fractions and dimensional analysis, both of which could have (and still may) caused trouble in future units.  This unit took the rest of September. Next we’ll finish tying up all the loose ends of linear equations and get set-up to start solving systems of equations.

Algebra I Unit 1: Review

This first unit took two weeks, or actually 9 days, since we took off for Labor Day. It was pretty straight forward:

- Graphing (plotting ordered pairs)

- Modeling relationships with variables (i.e. making up variable for real life situations)

- Order of operations

- Adding, subtracting, multiplying and dividing positive and negative integers

- Real and rational numbers

- Experimental probability

This year, Friday’s math class is a Random Review. This is a worksheet that is extra practice for a skill. It could be something my son struggled with that week or may need to review for next week’s lessons. It is always timed, but only for the purpose of practicing for standardized tests. The reviews for this unit were math facts with larger numbers.

The lessons included the first chapter in the super old version of a Prentice Hall textbook.  The next unit is Algebra Modeling and Unit Analysis.

Math: Algebra I

Math is my favorite subject to teach, which usually means I run on and on and bore any interest out of my son. So, I’m trying to back off a bit this year and let him work more on his own. He had a solid pre-Algebra year in 7^th. This year’s focus is making sure we avoid the problems I see too often in high school students.

Working with positive and negative terms:

5 – 6 = 5 + -6 = -1

Correctly distributing and not loosing track of terms or signs:

(2x + 3)(x - 5) = 2x² -7x -15

Being able to quickly factor a polynomial:

x² + 5x + 4 = (x + 1)(x + 4)

Using dimensional analysis to check if the problem is correctly set up in the beginning: 20 miles/hour * 1 hour/60 min * 1 min/60 sec * 5280 feet/mile = 29.3 feet/sec

Starting Math

Math is not my kids’ favorite subject. That would be science. But, math is by far the easiest one for them. Since I’m a former public school math teacher and my son never seriously struggled with math, my first instinct was to skip all pre-made workbooks and create my own. Then, I started thinking about all the work involved in making up problems, so I punted and headed to the local curriculum store for workbooks. I’m still designing what is taught when and how, but the pre-made worksheets are a huge time saver.

Eventually, my son will return to public school. To make that transition easier on the academic side, I am trying to include all the objectives required for his grade.  The store had one set of workbooks that were specifically tied to the new common core standards for math. Since we’re compacting 7th and 8th grade together, I bought the sets for both years. They came with separate teacher’s and student’s books. An old fashion Pre-algebra workbook completed the math library.

School Skills – Math Fluency

Just like fluency in reading, fluency in math refers to how accurately and quickly you can work. I spent the first week of home school assessing my son for potential problems. We’d been told that he was weak in math fluency, but it didn’t make sense, because he could work complicated problems just fine in a reasonable amount of time.

Step 2 Content, con’t.

At this point, I had read through the entire published objectives for 7th graders in North Carolina. I had them sorted into charts with the notes from the unpacked PDFs, which gave me a general picture of what we should be teaching in order to stay on pace with public school. I had also looked over the objectives for the next few grades to see where we needed to be at the end.