Required Vocabulary for Algebra One
 
The student needs to master every word on the list below.  The list includes a working vocabulary.  That means the student needs to know the meaning of the word or phrase and how to apply it if it indicates some kind of action (for example the word solve).  Working vocabulary words or phrases are in bold.  New words and phrases will constantly be added to the list.
 
 

Equations
  constant
  variable
  coefficient
  term
  expression
  equation
  quantity
  left-side (of an equation)
  right-side (of an equation)
  like-terms
  simplify (combine like-terms)
  solve for
  isolate
  remove/move (a term)
  remove/move (a coefficient or divisor)
  flip/reverse (the equation)
  change the signs of every term (in the equation)
 

Expressions
  Substitute (a number for a variable)
  Evaluate (a numerical expression)
  Simplify (an expression by properly removing all parentheses and combining like terms)
 

Problem Solving
  What is the question?
  Define the variable(s)
  Translate from English into Algebra
  Translate from Algebra into English
  State the solution
  Presentation Form
 

polynomials
  monomial
  binomial
  like binomials
  trinomial
  polynomial
  power
  exponent
  Index (indices)
  base
  degree of a variable
  degree of a monomial
  degree of a polynomial
  distributive rule
  double-distributive rule
  multiply monomials (uses the multiplication rule for monomials)
  raise a monomial to a power (uses the power rule for monomials)
  multiply a term times a quantity (using the distributive rule)
  simplify (by distributing a minus sign) 
  simplify (by distributing a term)
  F(OI)L
  factor out a sign
  factor out a number
  factor out a variable
  factor into a product of binomials
Geometry
  point
  line
  horizontal
  vertical
  slanted line
  graph (noun, meaning picture representing data)
  graph (verb, meaning draw a graph)
  number line
  x-axis
  y-asis
  origin
  draw/mark a point
  draw/mark a point (on graph paper)
  T-chart
  Evaluate y for x = (some number)
  Find y when x = (some number)
  increasing
  rising
  decreasing
  falling
  angle
  vertex
  rectangle
  triangle
  side
  perimeter
  area
  Find the perimeter
  Find the area of the rectangle
  Find the area of the triangle
 

Mathematics for the Intuitive Learner

Math 8 (MYP3)
Home | Math 6 (MYP1) | Math 8 (MYP3) | Completing the Square | Drill Sheets

Everyone, please read the note at the bottom of the home page!

Week of November 3 (and after)

Assignment for Thursday, Friday, week of Nov. 3, 2013

In your textbook, read chapter 7, sections A-C.  Try the problem sets in each section: Exercises 7A, 7B and 7C.  Look for the problems that are algebraic in nature.  You should be able to work almost any of these problems -- check your answers in the back of the book.  If your can't make sense of it, ask me in class at the beginning of the period.

Expect a quiz.

Assignment for Monday, Nov. 3, 2014:
Do the worksheet at
You should be able to do any problem on this worksheet.

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The class is taught in strands.  Each class period, the students are presented two to three topics (strands) that are not mutually dependent.  In other words, they don't need to know one subject to understand the other one.

This approach avoids boredom and brain meltdown.  It also allows me to revisit each topic more frequently, giving the students more opportunities to ask questions and catch on.
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Current Topics

Solving Linear Equations:
  We are finishing up with solving linear equations (with denominators) efficiently.

We are just starting intuitive geometry:  Recognizing the fundamental theorems of geometry using our own intuition.  The students will see algebraic problems resulting from those principles.

Graphing linear equations from their description.  Students should be able to graph a linear equation with any of the following information:
  A point and a slope.
  A point and a description (vertical, horizontal, parallel to __, perpendicular to __.)
 

Students will be expected to memorize "The Equation Maker", a rule for creating the equation of a line from a point and a slope.  [This topic will be coming soon.]

Completed Topics

Multiplying fractions efficiently*.

Converting fractions and decimal numbers to percentages.

Reading data and extracting information which will be correctly presented as percentages.

Solving Linear Equations:
  Solving linear equations (with no denominators) efficiently.*

Multiplying monomials and reducing fractions with monomial numerators and denominators.

Distributing monomials over polynomials.

Applying the Double-Distributive Rule.

Describing the graph of a given linear equation.  Students should be able to extract:
  Sample points
  Intercepts and Slope (both by two-point method and from converting the equation to slope-intercept form).

  Students should be able to recognize the equations of horizontal and vertical lines.

Graphing linear equations from their description.  Students should be able to graph a linear equation with any of the following information:
  Two points (either of which could be intercepts)

 

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*efficiently is used here to mean without the usual written-out carryings, borrowings and various others thinking steps traditional to grade-school arithmetic.  When multiplying fractions, this also means reducing in place.