Geometry: How do we solve for angles & sides of isosceles & equilateral triangles?

Geometry:  

What is the relationship between the base angles of an isosceles triangle? What are the definitions of equilateral and equiangular? Review the converse of theorems about isosceles & equilateral triangles. Set up algebraic equations to solve for missing angles and sides using these theorems. 

1. Assignment: p. 239 - 240 / 1 - 9, 17, 18, 19, 22, 23
   

Math 2A: More Practice with Graphing Quadratics

Math 2A:  

Complete selected Regents type questions on graphing quadratic equations. What are some test taking strategies to find the vertex and axis of symmetry of quadratic equations? Treat this like an open-book quiz!

Alg2/Trig E: What are the sum & product of the roots of a quadratic?

Alg2/Trig E:  
What are some more relationships between the coefficients of a quadratic equation in standard form? How do we calculate the sum & product of the roots? Use the sum and product of the roots to write a quadratic equation. Complete an Exit Card and Think, Pair, & Share (for extra credit).

Geometry: How can we prove two triangles are congruent?

Geometry:  

Good job on your quiz! Let's prove triangles are congruent using the Hypotenuse-Leg Postulate. Careful you may only use this for right triangles. Also, what do you know about the other corresponding parts of congruent triangles? Are they congruent after you prove two triangles are congruent?

1. Assignment: Worksheet.
   

Math 2A: How can we graph quadratics?

Math 2A:  

Good job on your quiz! Let's graph a quadratic and determine other interesting parts of a parabola besides the roots (or x-intercepts). For example what is the lowest or highest point of a parabola (vertex) and the line (axis) of symmetry? What does changing the coefficients of a quadratic do to the graph?  Make sure you copy the table and show all work!

1. Assignment: Worksheet.

Alg2/Trig E: How do we describe the nature of roots using the Discriminant?

Alg2/Trig E:  
Calculate the discriminant of a quadratic equation. What does this number say about the roots of an equation without actually solving for them? If the discriminant is less than zero, we know the roots are imaginary; is a perfect square, they are rational; or is equal to zero, they are equal. What do the graphs of the quadratics convey about the nature of the roots?

1. Assignment: Worksheet.
2. Quiz on Thursday!
   

Alg2/Trig E: Let's review quadratic functions.

Alg2/Trig E:  
Work in pairs to review concepts about quadratic functions. What are the vertex, axis of symmetry, and x-intercepts of a quadratic equation? Also, how do we solve quadratic equations algebraically (ex: factoring or Quadratic Formula) or graphically?

Geometry: How can we prove two triangles are congruent?

Geometry:  

Station Activity: Work in groups and rotate to each station with your recording sheet. In Station A, complete two-column proofs with SSS or SAS; in Station B, with ASA or AAS; and in Station C, complete critical thinking questions about corresponding parts of congruent triangles.

1. Quiz on Tuesday!
   

Math 2A: How do we solve quadratic equations with factoring?

Math 2A:  

Let's use your factoring skills to solve quadratic equations. Since we cannot use strategies like the Distributive Property, combining like-terms, or inverse operations, let's use factoring and the zero property to solve equations. Why are there two solutions? What do our algebraic solutions represent graphically?

1. Assignment: Worksheet.

Alg2/Trig E: How do we solve quadratic equations with the Quadratic Formula?

Alg2/Trig E:  
What if you don't remember or cannot factor a quadratic equation before solving? Use the Quadratic Formula... You can use it to find roots that are real or imaginary, rational or irrational, and equal or unequal. Always write your solutions in simplest form.

1. Assignment: p. 267 – 268 / 54 – 60 (even) and p. 295 – 296 / 18, 20, 40, 46

Geometry: How can we prove two triangles are congruent?

Geometry:  

Let's add two more postulates to help use prove two triangles are congruent: A.S.A. and A.A.S. Complete two-column proofs using definitions and relationships between certain angles in the triangles. Analyze diagrams and decide whether there is enough information to prove two triangles congruent; if so, could you use S.S.S., S.A.S., A.S.A., or A.A.S.

1. Assignment: p. 223 / 5, 6, 8 - 13 and p. 210 / 1 - 4
   

Alg2/Trig E: How do we use factoring to help us solve quadratic equations?

Alg2/Trig E:  
Let's review how to factor expressions completely and trinomials (a not = to 1). Using the zero property and your handy checklist, you will be able to solve any quadratic equation that is factorable. On Thursday, you will learn a method for when you cannot factor the quadratic.

1. Assignment: Worksheet.
   
2. Project due: Tuesday, 11/10/09
   

Math 2A: How can we factor expressions completely?

Math 2A:  

Use a graphic organizer to factor expressions completely. After you take out the GCF, figure out if the expression in the parentheses is a binomial or trinomial. If it is a binomial, Ms. Maida will help you; if it is a trinomial, I will help you. Then you will have a chance to be the binomial or trinomial.

1. Assignment: Worksheet.

Geometry: How can we prove two triangles are congruent?

Geometry:  

Let's practice more proofs where we can use the S.S.S. or S.A.S. Postulates. Work with a partner and complete a two-column proof by matching statements with reasons. Always pay attention to what you know to be true and what you may be assuming to be true. Check your partner's work and share your solutions!

1. Assignment: Two-column proofs.
   

Alg2/Trig E: How do we use factoring to help us solve quadratic equations?

Alg2/Trig E:  
Let's review how to factor the GCF, trinomials (a = 1), and binomials (DOTS). What is the zero property and how can we use it to solve quadratic equations? What do our algebraic solutions represent on a graph? And why do we set quadratics equal to 0 when we want to solve?

1. Project due: Tuesday, 11/10/09
   

Math 2A: More Practice with Factoring Expressions

Math 2A:  

In group of 4 or 5 rotate to each station to work with each teacher on factoring problems. In Station A, you will practice how to factor with a GCF; Station B, practice how to factor trinomials (a = 1) & binomials (DOTS); and Station C, factor completely using the GCF and one other method (This is new, so I will help you at this station). Have fun and ask questions at each station.

Geometry: How can we prove two triangles are congruent?

Geometry:  

How do we prove two triangles are congruent? If you know three corresponding sides are congruent, then you can use the Side-Side-Side Postulate. If you know two corresponding sides and the included angle are congruent, then you can use the Side-Angle-Side Postulate. There is a HUGE difference between what we know (ex: Definition of midpoint, Reflexive Property, etc.) and what we accidentally assume.

1. Assignment: p. 216 - 217 / 12 - 17, 20, 21
   

Alg2/Trig E: What does a quadratic function look like and what are the basic characteristics of a parabola?

Alg2/Trig E:  
How do we graph a quadratic and what characteristics can you identify by looking at the graph? What are the vertex, axis of symmetry, and x-intercepts of various parabolas? Where are the "roots" of a quadratic and how does that relate to our next chapter about solving quadratics?

1. Assignment: p. 253 – 254 / 22 (on graph paper), 27, 29, 32, 33, 39, 40, 51*
2. Project due: Tuesday, 11/10/09
   

Math 2A: More Practice with Factoring Expressions

Math 2A:  

Let's work together to try to solve a matching puzzle for factoring. Each square has four sides with polynomial expressions or factored expressions. Match the sides that have equivalent forms and solve the puzzle! There is only one answer.

1. Assignment: Final Four Worksheet.
   
2. Quiz on Friday.
   

Math 2A: How can we factor a trinomial (where a = 1)?

Math 2A:  

Good work with the graphic organizer! You should always start in the first box and ask yourself, "Is there a GCF?" and factor that if possible. Today we will also check whether it is a factorable trinomial... Use one of the methods learned in class (ex: diamond puzzle or two column checking) to factor the trinomial expression.

1. Assignment: Worksheet.
2. Quiz on Friday.
   

Geometry: What are the congruence properties for congruent triangles?

Geometry:  

Can we use the definition of congruent and identify corresponding parts of congruent triangles? What are some examples of the reflexive, symmetric, and transitive properties given congruent triangles? Let's review the interior angle sum of a triangle and the Exterior Angle Theorem

1. Assignment: Practice 4.2 A.
   
2. Quiz on Thursday!
   

Alg2/Trig E: Does anyone ever really use complex numbers?

Alg2/Trig E:  
How are complex used in the field of electrical engineering? In a series circuit there are several formulas where complex numbers are used to measure two characteristics at one time (ex: E = IZ and Total Impedance). Read through the passages and answer the questions thoughtfully. You may not work with a partner.

1. Project due: Tuesday, November 10, 2009.

Alg2/Trig E: Let's review complex numbers!

Alg2/Trig E:  
Let's review the concepts of complex numbers. With a partner, use dice to randomly create various complex number problems. Then switch your sheet with another pair and try to solve the problems they created for you! Be careful with how "cruel" you are when creating problems... You might get the same treatment in return.

1. Assignment: Worksheet
2. Project due: Tuesday, November 10, 2009.
   
3. Quiz on Wednesday! 

Math 2A: How can we factor the difference of two squares (DOTS)?

Math 2A:  

What are perfect squares and how many do you know? What does it mean to take the square root of a number? Let's use a graphic organizer to factor expressions. This will help us find the quickest path to factoring an expression!

1. Assignment: Worksheet.

Geometry: What is the definition of congruent? What are the corresponding parts of congruent triangles?

Geometry:  

Let's review the interior angle sum of a triangle. Can you set up an algebraic equation to solve for x if x represents the measure of an interior angle of a triangle? What if x represents the measure of an exterior angle of a triangle? What is the definition of congruent and how can you use notation or symbols to identify corresponding parts? Example: List the corresponding congruent parts of the two triangles below.

1. Assignment: See worksheet.
   

Math 2A: More Practice with Factoring the GCF

Math 2A:  

Let's practice factoring expressions with the GCF. It is very important that you always look for a GCF between the terms in a polynomial expression first! Then divide by the GCF to find the other factor of an expression. Complete problems around the room about factoring with a GCF.

1. Assignment: None.

Alg2/Trig E: What is the absolute value of complex numbers?

Alg2/Trig E:  

What is the definition of absolute value in the Real Number System? How can we apply this definition to complex numbers? The absolute value of a complex number is the distance away from the origin in the complex plane. Think back to Geometry, and try to remember how to calculate distance.

1. Assignment: Worksheet
2. Quiz on Wednesday! 

Geometry: How do we classify triangles by their sides & angles?

Geometry:  

What is your first name and last name and how does your name define you? Apply this idea to a particular triangle. Classify triangles by giving them first and last names after analyzing their sides and angles. What makes a triangle isosceles, equilateral or scalene? Acute, right, obtuse, or equiangular?

1. Assignment: Practice 4.1 A Worksheet