Successful completion of Math 7 or Algebra Readiness along with teacher recommendation.


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1 MODESTO CITY SCHOOLS COURSE OUTLINE COURSE TITLE:... Basic Algebra COURSE NUMBER:... RECOMMENDED GRADE LEVEL: ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT: per semester MEETS GRADUATION REQUIREMENTS:... Algebra REQUIRED FOR GRADUATION:... No CBEDS CODE:... MEETS UC AND CSU ENTRANCE REQUIREMENTS:... No REPLACES:... N/A Course Description: Basic Algebra covers about 15 of the key standards of Algebra and grade 6 &7 standards found on the CASHEE exam. Units of instruction include order of operations, integers, solving equations, graphing linear equations, systems of linear equations, inequalities, exponents, quadratic equations, radicals and polynomials. Recommended Prerequisites: Successful completion of Math 7 or Algebra Readiness along with teacher recommendation. *Course work of transfer students will be evaluated for equivalency. Date Matched Against State Framework:... May 2008 Board Approved:... PENDING REQUIRED TEXTBOOK: Burger, C.H.K. (2008). Algebra. Holt. Other resources: Teacher created material to add extra support for specific standards.
2 Course Philosophy The object of this course is to teach algebra to noncp students, in an effort to prepare them for a more rigorous course of study. This course is designed to spiral the key algebra skills  integer operations, solving equations, graphing lines, and polynomial operations  throughout the course. Each chapter test should be designed to enable the students to show what they have learned. The first 3 chapter tests should have more openended questions, but as the difficulty of the course increases, there should be more reliance on multiple choice and true/false questions. Students enrolled in this course will take the Algebra CST. The goal for each student is to score 380 on the CAHSEE (if in the 10 th grade) and score basic on the algebra CST. Additional Resources Several sections of this course outline requires teachers to supplement with material not in the actual textbook. Please use the following resources to help: Holt intervention materials Review For Mastery Workbook Practice A handouts Teacher created material (Please visit the District Math SharePoint site to access resources created by other teachers and to upload your own creations for the benefit of the community).
3 Algebra Standards 112 and Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the 4 basic arithmetic operations. 2. Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and rising to a fractional power. They understand and use the rules of exponents. 3. Students solve equations and inequalities involving absolute values. 4. Students simplify expressions prior to solving linear equations. 5. Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 6. Students graph a linear equation and compute the x and yintercepts. They are also able to sketch the region defined by linear inequality (e.g., 2x+6y<4). 7. Students verify that a point lies on a line, given an equation of the line. Students are able to derive equations of lines. 8. Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. 9. Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. 10. Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. 11. Students apply basic factoring techniques to second and simple thirddegree polynomials. These techniques include finding a common factor, recognizing the difference of two squares, and recognizing perfect squares of binomials. 12. Students simplify a rational expression by factoring and reducing it to the lowest terms. 15. Students apply algebraic techniques to solve rate problems & work problems. 16 &18. Students understand the concepts of a relation and a function. They should also know whether a given relation defines a function or whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function. 17. Students determine the domain of independent variables and the range of dependent variable defined by a graph, a set of ordered pairs, or a symbolic expression. 19 & 20. Students know the quadratic formula and are familiar with its proof by completing the square. Students should solve quadratic equations using the formula. 21. Students graph quadratic functions and know that their roots are the xintercept.
4 Chapter 1: Order of Operations (3 weeks) Convert verbal description to math symbols...grade 7 AF Intro to number lines (whole numbers)...grade 5 NS Intro to Exponents...Grade 7 NS , 1.4 Order of Operations...Grade 7 NS Evaluate Expressions...Grade 7 AF Complete tables...grade 7 AF Supplement Rate problems (1step)...Grade 7 AF Example 2 Rate problems (multiplestep)...algebra Example 2 Intro domain and range...algebra Example 2... Supplement The order of operations will appear throughout the course and is an extremely important skill for the student to master. This chapter only includes whole numbers. Rate problems are on both the CAHSEE and the CST algebra tests. The students should be able to do multistep problems. This chapter also introduces the students to exponents. Make sure they have practice with a wide variety of problems such as Evaluate Evaluate 20 x 2 if x= 4 Evaluate b 2 4ac if a=2, b=7 and c=3 Although chapter 6 is the Inequality chapter, it might be useful to introduce inequalities right away. They should be able to graph x = 4 and x > 6 (for example) on a number line.
5 Chapter 2: Integers (23 weeks) Integer Operations... Grade 7 NS Supplement Intro Absolute Value... Grade 7 NS Supplement Expand number line to Integers... Grade 6 NS Supplement Intro distributive property... Grade 6 AF Simplifying Expressions... Algebra Need to continue practice with the following skills: Complete tables domain and range graphing on number line The Operations of Integers must be drilled over and over. Students should be aware of the basic ideas a + b = a (b) and a +( b) = a b. In many ways you are repeating what you taught in chapter one, except now with integers.
6 Chapter 3: Solving Equations (3 weeks) Reciprocal & opposites... Algebra , 1.3 Simplifying Equations... Algebra , 2.2, 2.3 Solve 1step equations... Grade 6 AF Solve 2step equations... Grade 7 AF Solve up to 4step equations (mostly 3step)... Algebra , 2.4 Percent Review... Grade 7NS 1.3, 1.6, Convert verbal description to math symbols... Grade 7 AF supplement Scale models... Grade 7 MG Proportions... Grade 6 NS Distributive Property... Grade 6 AF supplement There will be time for the students to improve solving equations later in the semester. It is strongly recommended that you have students solve their equations stepbystep, vertically down their paper, lining up the equal signs. Have the students write their steps alongside their equations showing what they are trying to do. Students are required on state tests to analyze and correct sample problems and identify which step contained the error. Sample: 2 + 3(x + 4) = 7 Dist. Prop 2 + 3x + 12 = 7 Simplify 3x + 14 = 7 sub 14 3x = 7 div by 3 x = 7/3 Provide plenty of practice for proportion word problems and scale model problems. This is an important standard for the students to master for the CAHSEE.
7 Chapter 4: Graphing Linear Equations (3 weeks) Graph linear equation... Algebra Example 1 Determine if a point is on a given line... Algebra Example 2 Plotting points using x, y table... Grade 7 AF supplement Interpreting Graphs... Grade 7 AF supplement Slopeintercept form... Algebra Know definition, calculate slope... Grade 7 AF Intro to functions... Algebra 16 & , 4.2, 4.3 Graphing is a skill the students must master, but keep in mind that you can use chapters 5 and 6 to reinforce and spiral graphing concepts. The goal is for the students to master slopeintercept form. Next chapter, standard form will be taught. Giving Mastery Quizzes on graphing in slopeintercept form is strongly encouraged. Teach the slope formula, and although the hope is the stronger students will memorize it, it is not required. It is suggested that the same philosophy is used when it comes to the quadratic formula in chapter 8. Continue to have student complete x, y tables. This allows the students to continue to improve their Order of Operations skills. Also, the use of the x, y tables opens the way toward teaching domain, range, and functions.
8 Chapter 5: Systems of Equations (3 weeks) Graph linear equation... Algebra Finding intercepts, graphing from standard form... Algebra Slope... Algebra Graphing by SlopeIntercept Form... Algebra Concept of parallel lines... Algebra Does a given point solve a system?... Algebra Example 1 Solve systems of equations graphically... Algebra Example 2 Review solving ax + b = cx + d... Algebra 5... supplement The main methods you are teaching to solve a system are by graphing and by plugging possible answers back into the systems. The only systems that the students will solve with algebra are the types when both equations in the system are in slopeintercept form. Therefore, you will need to review solving equations of the form ax + b = cx + d. You are reviewing graphing, but adding the concept of graphing using intercepts. Students should know that there could be none or 1 solution to a system (The infinite case does not need to be stressed). Another key idea here is that the students should be able to figure out which equation (out of 4 choices) has certain attributes, most notably  given a slope and a point on the line, what is the equation of the line?
9 Chapter 6: Inequalities (3 weeks) Solve up to 3step inequalities (1variable).... Algebra Graphing 1variable inequalities... Grade 5 NS Graph linear inequalities Slopeintercept form... Algebra Standard form... Algebra Graph systems of inequalities... Algebra This chapter should mostly be seen as a way to review many standards of the previous chapters. Completing this chapter is similar to preparing for a comprehensive summative final exam. For a system of inequalities, students can show understanding of the concept by having the lines predrawn, and then having to decide which of the 4 regions should be shaded by checking a possible point within each region. Another variation could be to shade a region and ask the students to check if it is correct. *It is recommended that Chapters 1 6 be completed during the first semester and that a comprehensive summative final exam be given in an effort to continually spiral the algebra content.
10 Chapter 7: Exponents (3 weeks) Exponent Rules... Algebra , 7.3, 7.4 Zero and Negative Exponents... Grade 7NS Scientific Notation... Grade 7NS Monomial Operations... Algebra supplement The 3 basic rules of exponents (product, quotient, and power rules) should be taught over and over as they are on both the CST and the CAHSEE. Also, the students should be comfortable with the concept of negative exponents (also on both tests).
11 Chapter 8: Quadratic Equations and Radicals (4 weeks) Evaluate and Approximate radicals... Grade 7NS Rational vs. Irrational... Algebra Graph Simple quad and cubic equations... Grade 7NS supplement Graph quadratic equations... Algebra Evaluate radical expressions (e.g., 5 16 )... Algebra Know and apply quadratic formula... Algebra 19 & Domain and range... Algebra supplement This is probably the most difficult chapter in that it involves using the quadratic formula, graphing quadratic and cubic equations, and includes more advanced ideas of domain and range. When it comes to solving quadratic equations, students need to differentiate between problems with, and without, multiplechoice solutions. They also need to be aware whether the multiplechoice solutions are integers or irrational solutions. For example, if the given quadratic equation has only integers as possible multiplechoice solutions, then the student should be trained to simply put the integral solutions back into the equation. If the solutions are irrational, then the student should be trained to determine the a, b, and c values and plug the values into the quadratic formula. The course does not require the student to memorize the quadratic formula for class exams, but you should try to encourage memorization because the STAR test requires it.
12 CAHSEE Preparation (1 week) *If there are only 9th graders in the course, this week can be skipped. But, it is a great chance for spiral review and differentiated remediation. There should be at least a week of time to review for the CAHSEE. Download practice problems from the state website. Also, there is a CAHSEE teacher guide that would be of use. You can count the results of the CAHSEE as a chapter test. There are some topics on the CAHSEE that we have not covered in the course. Geometry is a good topic to review since it is almost ignored in this course. Other strong candidates for practice are meanmedianmode, probability, fractions, and you can introduce some Pythagorean theorem problems if time. The CAHSEE particularly emphasizes percent increases and decreases. You could use circle graphs for other percent practice such as: 80 students took a test with the given circle graph as a result showing the percentages of A, B, C, D and F grades. What percent of the students got at least a C? How many students got an A? and so on.
13 Chapter 9: Polynomials (3 weeks) Combine like terms... Grade 7 AF supplement Polynomial operations... Algebra Factor into binomials & common factor... Algebra Simplify Rational expressions by factoring... Algebra Examples 2 &3 Multiply binomials is key in this chapter since without this skill the students will not know how to factor or to reduce rational expressions by factoring. A suggestion is to start with the Distributive Property (FOIL) method almost right away; they need practice this repeatedly over time. A Mastery quiz on multiplying binomials is also strongly suggested. It is suggested that you introduce factoring over several days working in the fraction problems early so they get used to them. One day you might practice factoring only quadratic trinomials 2 ax bx c with only positive coefficients (a =1). The next day you might practice only with c negative. Then you might switch into common factoring; this is where you can begin having the students reduce rational expressions with common factors. Thereafter, include some rational expression factoring as part of your factoring problems. It is suggested you only use multiple choice problems for the case where a 1. It is recommended that you don t spend a lot of time with 2step factoring (common factor and trinomial factoring), because many students struggle a great deal with the various 1step factoring. But, you need to do some for the stronger students. This is a good time to review order of operations and integer operations. Have them simplify expressions such as 5(3x 2 4x + 2) 3(x 2 + 2x 6) 2x(4x + 7) + 3(x 1)
14 Algebra CST Preparation (1 week) You should have about a week prior to the STAR exam to review. A review of solving equations and stepbystep simplification of polynomials such as 4(2x + 2) + 4(3x 1) would be good practice. You can also use perimeter problems of polygons with side lengths of 2x + 1 for more practice. I also emphasize the skill of substituting multiplechoice solutions back into the linear or quadratic equations. At this time you might also review the notions of domain, range, and x and y intercepts. Reemphasize that the xintercepts can also be called a roots, zeros or solutions. You might also embed instruction to teach them what a counterexample is. (It is listed within the standards). Part of the preparation is psychological. They need to know that they did not cover all the standards and therefore they cannot possibly know how to do all the problems. Their job is to find the problems they recognize and focus on doing those problems correctly.
15 Chapter 10: Review and Preview (4 weeks) Now that the CAHSEE and Algebra CST are over, you should have about 3 4 weeks to go back and review any material that the students struggled with. Emphasis on integer operations, factoring and graphing linear equations would be key. There are many resources in the Holt curriculum that can be used to review past learning. Continue to spiral past learning. Remember, students that have excelled in this course are to be balloted the following year for CP Algebra. Those students that are still struggling or that did not pass the CAHSEE are to move into Basic Geometry. The emphasis is to get students to be proficient in algebra. This course provides many of the basics they will need to be successful in a more rigorous Algebra course of study. *It is recommended that Chapters 7 10 be completed during the second semester and that a comprehensive summative final exam be given in an effort to continually spiral the algebra content.
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