- GeneralWelcome to Mrs. Brown's Algebra 2 class. The documents that introduce the class and the class topics and supplies that will be needed are listed in Topic 1 for Week 1. The Graded Course of Study is included below.
- Chapter 1- Algebra Review
Chapter 1- Algebra ReviewTuesday, August 29th
1. The rules for integers and order of operations will be reviewed.
2. Students will add the SmartNotes 2.1.4 to their folders and complete problems 1-7 on simplifying expressions.
3. Students will investigate algebraic expressions and equations and solve real-world problems included in the guided notes.
4. Unit cubes will be used to model a hot tub tile problem both numerically and algebraically.
5. The homework is to complete worksheet over Using Arithmetic Order of Operations to find solutions for problems 1-12.
Thursday, August 31st
1. Students will put the homework from Monday on the board for the 12 problems using the arithmetic order of operations.
2. Students will watch the video "Is PEMDAS wrong?"
3. Students will continue with their review of Algebra by simplifying, evaluating and solving numeric and algebraic expressions and equations.
4. Students will review the Order of Operations and Evaluating Expressions power point.
5. The homework is to Evaluate the Expressions for given values, problems 1-10.
Tuesday, September 5th
1. Students will go over SmartBoard Notes 1.2 on Number Properties and Expressions after going over the Homework on the board from the previous week.
2. They will complete the mixed review problems 1-14 and go over them with the class.
3. Students will review the SmartBoard Notes over Open Sentences and complete the problems.
4. Students will take a quiz over Chapter 1 of the Algebra 1 review.
Thursday, September 7th
1. After reviewing the homework of evaluating algebraic expressions as models, the students will move to using the properties to solve algebraic equations.
2. Students will use the math triangle to solve literal equations involving three variable linear equations.
3. Students will continue by solving linear equations and explore problem solving strategies. They will be able to identify errors in incorrect problem solutions.
4. Students will review algebraic proofs as any problem solved geometrically could also be solved algebraically.
4. The lesson presentation and guided notes will cover consecutive integers, the math triangle and literal equations.
5. Students will watch the Tarver Video "Solving Equations for the Variable."
4. Students will complete the homework Solving Algebraic Equations problems 1-9 all.
Students will take the Chapter 1 Test at the next class.
- Chapter 5- Quadratics
Chapter 5- Quadratics
1. Students will review the table and graph of the parent function of a quadratic equation and standard form of transformed quadratic equations.
2. Students will investigate the factored form of a quadratic when the coefficient of a is 1.
3. Students will use the distributive property to multiply and make sure that the factored form of the quadratic equation is correct.
4. The reason quadratic equations are factored is to be able to use the zero product property to find the x-intercepts of the quadratic equation.
5. The students will factor trinomials on Worksheet 5.2 1-14. They must bring all terms to one side of the equation in standard form so the equation equals zero, then factor the trinomial, then use the Zero-Product Property and set each factor equal to zero, solve each resulting equation for the variable, and finally check their solution in the equation.
6. The homework is Worksheet 5.1 problems 1-16 all.
5.1 Solving for roots in quadratic equations
1. Students will solve directly for quadratic equations by using square roots which are the inverses of quadratics. This is another method to solve for x when there is no linear term in the quadratic equation because it is more direct. An example is problem number 2 on worksheet 5.2 practice problems. Students will complete guided notes page 4 from 5.1.
2. Students will use the principal square root which is often the most reasonable answer in a quadratic equation.
3. Students will understand that the roots of a quadratic equation is where it crosses the x axis and is therefore an x-intercept and a solution of the quadratic equation.
4. Students will complete the guided notes page 4 of 5.1 and will try practice problems on page 233 problems 5-22.
5. Parabolas from falling objects will be investigated and real world problems involving a pendulum and objects is space will be explored as well as prize money and company profits. (p. 234 problems 29, 30, and 32.)
6. The homework is Worksheet 5.3 problems 1-18 all. To solve for x take the square roots of both sides of the equation.
1. The students will understand that the axis of symmetry and the x point of the vertex of a parabola is halfway between the x-intercepts.
2. The formula for the x-intercepts will be derived from this understanding and used to find the x-coordinate of the vertex of the quadratic equation.
3. Once the x-intercept is found, it can be substituted for x in the quadratic equation and y can be found. This is the y-coordinate of the quadratic equation.
4. The class will discuss problems 1-10 and walk through the steps and students will complete the guided notes 1-3 of 5.2.
5. The parabola opens up or down depending on whether the coefficient a is positive or negative.
6. The homework is to find the vertex in order to sketch the graphs of problems 29-34 on page 240 using colored pencils for the graphs of the different problems.
1. Students will review methods for factoring quadratics: Finding the greatest common factor, finding difference of squares, looking for a perfect trinomial square, using the method to find factors that multiply to give the first and last term and add or subtract to give the middle term. They will complete the guided notes 5.3 1-5 all.
2. Students will factor the quadratic equation using patterns in order to derive the solutions. Students will complete the
3. Algebra tiles will be used to complete the square.
4. Mathematics Illuminations on the computer will also be used to factor quadratic equations and find the zeroes of the function.
5. Students will expand equations manually using multiplication and the distributive property.
6. The final method of factoring will be completing the square using
The homework is Worksheet 5.4 Problems 1-10 factoring by completing the square.
1. Now that students have learned how to factor a quadratic equation using completing the square they will learn why it is called the Graphing Form.
2. Students will work in groups to find the transformations of quadratic equations from the parent function.
3. Students will work in groups to investigate vertical stretches and compressions and horizontal and vertical shifts.
4. The collaborative groups will make the table and graph of the transformed function.
5. They will explain to the class what transformations occur and why.
6. The graphing calculator will be used to check the transformations of the functions.
7. The homework is Posters of Quadratic Transformations with summary explanations.
5.4 The Quadratic Formula
1. Some quadratic equations cannot be factored using the methods previously learned. The students will determine if an equation cannot be factored.
2. Students will use the discriminant to determine if there is one solution, two solutions, or no real solutions to a quadratic equation.
3. The students will use the quadratic formula to solve quadratic equations but first complete the guided notes page 8 from 5.3.
4. Students will practice putting the quadratic equation in standard form for problems 1-4 on page 255.
5. Students will identify the coefficients a,b, and c on problems 21 and 22 of page 255 to substitute in the quadratic formula and solve.
6. The homework is Worksheet 5.5 problems 1-10.
5.5 Complex Numbers
1. Sometimes quadratic equations do not have exact (decimal) or real number solutions.
2. If the radicand has a negative number inside it is an imaginary number.
3. Students will be able to write numbers using the imaginary unit i.
4. Students will simplify expressions and solve equations using imaginary numbers.
5. Students will perform the operations of addition, subtraction, multiplication and division using imaginary numbers.
6. The homework is pages 262-263 1-55 odd.
5.6 Writing Equations given the Zeros
1. Students have factored equations and found the zeros in order to graph the Quadratics.
2. Students will now be given the zeros and from that they can substitute and expand using reverse thinking and find the quadratic equation.
3. Once they have the equation they can find the midpoint for the x of the vertex and substitute that in the derived equation to find the y of the vertex.
4. Now their graph and equation is complete.
5. They can identify shifts from the parent equation from the vertex form.
6. The homework is Worksheet 5.6 problems 1-6 all.
1. Today the students will review for the examination on Quadratic Equations.
2. They will complete the review packet for Chapter 5.
3. The review packet covers factoring quadratics, solving quadratics with no linear term using square roots, completing the square, using the quadratic formula, finding the vertex and axis of symmetry and the graphing form to graph quadratic equations.
4. The second part of the review packet has given zeros so that they can be graphed using the zero-product property and factoring quadratics to find the zeros and solve for the x-intercepts in order to graph the equation
5. The test over Chapter 5 Quadratic Equations will be at the next class session.