Steve Rogers - Algebra 2 and Geometry

srogers@tmpsantafe.org • 505-660-8160

Welcome to Algebra 2!

Review, class philosophy, extension of existing knowledge.

Complex fractions and dimensional analysis are the topics of the week.  Both of these topics require sophisticated uses of fractions.

Continue to work with fractions in various forms.  This week we will look at all of the arithmetic operations on rational expressions.  Rational expressions are fractions with variables in the numerator and especially the denominator.  We will also extend our knowledge of the order of operations, which has something to do with fractions.

The week begins with the addition and subtraction of rational expressions.  We then dive into exponents – review of the rules of exponents, look closely at negative exponents, and begin work with fractional exponents.

This week will be a week of exponents, including rational exponents and applying the rules of exponents to rational exponents.

One more week working with exponents.  This week we will look at simplifying radicals and rationalizing radical denominators.

I will be out on October 1, so one of our fellow teachers will be substituting.

During this week we will complete our current work with exponents and take a quiz on this material.  We will begin working with solving equations to lead to work with 2-dimensional linear equations.

All this week we will be working on solving equations.  We will work with linear equations in one variable, rearranging formulas, and move into linear equations in two variables.

Continue solving equations with more work on formula.  Will also work on factorization.  Part of our work with solving equations will lead to solutions that are the square root of -1, aka imaginary numbers.  This will evolve into an introduction of complex numbers.

Continue work with complex numbers and review all of the material since the last quiz.  Quiz will be given on Thursday.

This week we will look at inequalities and ways to show their solutions with inequalities, graphing on a number line, and interval notations.

Complete our work with inequalities with a final look at absolute value inequalities and examples of their uses.

Introduce the idea of function and begin working with linear equations with 2 variables.

Work with functions and function notation.  This will require a number of definitions, especially function, domain, range, independent variable, dependent variable, continuous, discrete.

More work with functions and introduction to linear functions.

Quiz on Tuesday before our break.

A week of linear equations including rate of change (aka slope, m) and writing linear equations for data and situations.

Another week of linear equations including work with parallel and perpendicular lines and graphing of lines.

Welcome to Geometry!

Class philosophy and introduce geometric terms and concepts.

Continuation of learning basic definitions of geometric terms and labels.  Learning more geometric constructions (compass and straight edge only).  Begin to look at Postulates and Theorems.

Work with Postulates and Theorems to begin to analyze various geometric figures.  We begin this by looking at the accuracy of our measurements.

This week we will calculate the midpoint of line segments in one dimension and two dimensions.  We will continue to review all of the materials we have learned so far and end the week with a quiz covering it all.

After the quiz we begin working with angle postulates.

This week we leave lines and their parts and move onto angles.  In addition, we will look at our first formal proofs.  The Vertical Angle Theorem will be proven as well the Pythagorean Theorem.  The Pythagorean Theorem will be proven visually.

We will also have a pop quiz on geometric constructions – notes are allowed.

Finish up with angles and move onto polygons.

I will be missing on Thursday, October 1, so one of our fellow teachers will be substituting for me.

This week will be all about polygons – general ideas, triangles, and quadrilaterals.  We will learn definitions, algebraic traits, draw and construct.

This is a week of triangles.  We will look at inequalities in triangles, especially how the sides and angles relate to each other.

Additional work on inequalities in triangle sides and angles.  We will then begin reviewing the material we have worked with since the last quiz.  There will be a quiz one day next week.

Continue reviewing the usages of postulates and theorems related to angles and triangles.  Apply formula for area and perimeter of different polygons.  Review all of the material covered since the last quiz.

A quiz will be given in class on Thursday.

This week we will be working with transversals – a line that intersects 2 or more lines.  We will begin with any other lines and then look at the special case if the intersected lines are parallel to each other.

This will require each student to remember the linear pair postulate, the definition of supplemental angles, and the vertical angle theorem.

Continue working with parallel lines intersected by a transversal.  Introduce the converse of a theorem.  Continue to work on showing that a solution is true and that a theorem true.

Continue working with intersecting lines, especially parallel lines and a transversal.

Will introduce the converse of theorems and postulates.

Will continue to work on formal proofs in an informal manner.

Additional work on lines and points, especially the distance from a point to a line and perpendiculars.

Quiz on Tuesday before the break.

Work on formal proofs.  Begin with inductive reasoning to deductive reasoning and 2-column proofs of geometric ideas.

More formal proofs of conjectures written by the students.  Writing proofs in flow chart form.