Mark D



Mark D. Martin

Instruction Outline 8th Grade Algebra Using State Standards

Text, Prentice Hall Algebra (1998)

Introduction- Stella Maris Academy follows California State Standards and the diocesan standards. The California Standards are more specific, although consistent with the diocesan standards. The focus in this document is hence on the California Algebra Standards, . Mr. Martin in general follows the topics as they are presented in the text for consistency and to ensure students have sufficient background knowledge to understand new topics. Where necessary, Mr. Martin deviates from that order, and frequently supplements materials, to ensure students are learning what is required in the State Standards. Tests are almost always hand designed by Mr. Martin to accurately assess students understanding of the concepts in the State Standards. The outline here, of course, is just that – a brief outline. In the notes column I have tried to highlight some of the key concepts or areas of difficulty. The timeline is approximate. Teaching is a day-by-day process constantly evaluating how the students are doing.

Instruction is clear and straight-forward. I introduce practical examples and applications as much as practical. I also try to include a sense of humor. Students are shown how to do small chunks of concepts consistent with their background knowledge. Alternately, and preferably, they are given situations or problems to help them discover a concept new to them consistent with their background knowledge. They are then given sufficient practice so that concept becomes part of their long-term memory. Part of that practice is homework. I try to make homework short enough to not be unduly burdensome while giving sufficient practice. Homework is posted on my class Web site.

The Algebra class is only offered to those students who have excelled in 7th grade math. Students who qualify are urged to take the class but are not required to. They may take the regular 8th grade math course instead. The Algebra class is paced so as to complete the California Algebra 1 Standards for grades 8-12 and is designed to be equivalent to a high school level Algebra 1 course. Students unable to perform at that pace may be required to transfer to the 8th grade math course. Whether students are permitted to skip Algebra 1 in high school depends on the high school. Many high schools require students pass an Algebra exam before they can take Geometry or other advance subject. Some will require summer school if the score is not sufficient.

The Algebra class starts at 7:40 a.m., prior to the regular school starting time. It finishes at 8:15 a.m. Students are required to do their “homework” during the study period time which is usually in the library during the regular 8th grade math class. You must complete all your math work during that time before doing anything else. If you finish your math work prior to the end of the study period you must do work from other classes. The computers in the library are not available during the study period unless Mr. Martin gives you an Algebra assignment requiring the use of the computers. Exemplary behavior is required in the Algebra class and during the study period. A student may be required to transfer to the 8th grade math class if there are any significant behavior problems.

| |Topics |California State Standards |Notes |

| | |(24.0 logical argument used throughout) | |

|Qtr 1 |Tools of Algebra (Chapter 1) |1.0, 1.1 properties |Much of this is review from last year, but essential to success this year. In algebra students learn to |

| |Order of operations |25.0 properties, justification, etc. |use the properties to justify each step they take. This is one reason I require students to show all their|

| |Adding and subtracting integers | |work. They are not only getting an answer. They are showing that answer is correct according to the |

| |Multiplying and dividing integers | |accepted rules of mathematics and algebra. This will also help them when they do formal proofs in geometry|

| |Real numbers and irrational numbers | |in high school. Additionally, I require students to show their work because they are less likely to make |

| |Properties including commutative, associative and identity properties of + & x | |errors, it helps them maintain the concepts in long term memory and helps me ensure that it is their work.|

| |Algebraic Concepts and Simple Equations (Ch 3) |4.0 simplifying expressions before solving |Much of this is also review from last year, but again essential to success in Algebra. It is vital to |

| |Goal – isolate variable | |always keep the goal in mind – i.e. to isolate the variable. The basic rule is whatever you do to one |

| |Rule – Whatever you do to one side of the equation, you must do to the other side| |side, you do to the other side. I sometimes call this the Golden Rule of Algebra. (I also stress the other|

| |Inverse operations | |Golden Rule in class also!) Another important point about the “Golden Rule of Algebra” is that whatever |

| |Solving addition and subtraction equations | |you are doing, you are doing to the whole side. I also require students to show their work in a very |

| |Solving multiplication and division problems | |systematic fashion. They must show what they are doing to each side and what the result of that operation |

| |Solving two step equations | |is. They work vertically down the page. |

| |Combining like terms to solve equations | | |

| |Distributive property | | |

| |Rational numbers and equations (equations involving fraction – multiplying by | | |

| |reciprocal and multiplying by LCD to eliminate fractions) | | |

| |Percent equations | | |

| |Percent of change | | |

| |Equations and Inequalities (Chapter 4) |3.0 absolute value equations | Some of this is review but students are required now to solve increasingly more complex equations and |

| |Proportions |4.0 simplifying expressions before solving equations |inequalities. They are also required to solve absolute value equations and compound inequalities both of |

| |Cross products |5.0 Students solve muti-step problems, including word |which are new concepts, and sometimes challenging, concepts to them. |

| |Scaled drawings |problems, involving linear equations and linear | |

| |Percent proportion |inequalities in one variable and provide justification | |

| |Equations with variables on both sides |for each step | |

| |Solving absolute value equations | | |

| |Transforming formulas | | |

| |Solving inequalities using addition and subtraction | | |

| |Solving inequalities using multiplication and division | | |

| |Solving multiple step inequalities | | |

| |Compound inequalities | | |

| |Solving inequalities given a replacement set | | |

|Qtr 2 |Word Problems |5.0 Students solve muti-step problems, including word |This is a mini unit on solving classic Algebra 1 word problems. These are the dreaded problems that |

| |Distance, rate, time |problems, involving linear equations and linear |usually begin with something like: |

| |Work |inequalities in one variable and provide justification |Two trains leave the station at the same time, one traveling ... |

| |Unit rates |for each step |At the 8th grade fun raiser, hot dogs are selling at $1.50 and hamburgers are selling at $2.50 each. A |

| |Percent mixture |15. 0 Students apply algebraic techniques to solve rate |total of . . . |

| | |problems, work problems, and percent mixture problems. |How many liters of 40% acetic acid solution must I mix with . . . |

| | | |I have $5 in dimes and quarters. If I have . . . |

| | | |Two bicyclists are traveling on the same path in the same direction. One is traveling at 12 miles per hour|

| | | |and the other is . . . |

| | | |Sally leaves home at 6:30 a.m. traveling at 60 miles per hour. Sally’s husband discovers she forgot her |

| | | |briefcase and takes off in the car traveling at . . . |

| | | |Students today usually also get these problems in an Algebra II class. I deal with them with the 8th |

| | | |grade Algebra students in an organized, systematic process so that students are on their way to mastering |

| | | |them. This not only gives them a leg up in the future, but also begins to help them see how algebra can be|

| | | |used describe and solve problems. (Okay, not quite real life problems in Algebra 1, but it’s a start.) It |

| | | |also helps them in their logical thinking. |

| |Graphing and Functions (Chapters 2 and 5) |6.0 Students graph a linear equation and compute the x |Students were introduced to formal graphing concepts last year, but now these concepts are explored in |

| |Graphing a line using a table |and y intercepts (e.g., graph 2x + 6y = 4). They are also|much more depth and form the backbone of students’ future mathematical studies in Algebra II, |

| |Slope and Intercepts |able to sketch the region defined by linear inequality |Pre-Calculus, Calculus and beyond in high school and college. I deviate from the order in text moving |

| |Slope intercept form of line, y=mx + b |(e.g. they sketch the region defined by 2x + 6y < 4) |around in what I consider to be a more logical order for the students to understand the concepts. You can |

| |Given Equation in Slope Intercept Form, Graph Line |7.0 Students verify that a point lies on a line, given an|see further examples of some of what we do in the PowerPoint presentation at |

| |Given a line, write equation for the line in slope intercept form |equation of the line. Students are able to derive linear |. One can see by the number of standards that graphing and |

| |Write equation of line through a given point with a given slope |equations by using the point-slope formula |functions are important concepts for students to grasp. Since we have access to the iMac computers in the |

| |Write equation of line in slope intercept form given two points |8.0 slopes parallel and perpendicular lines. “[F]ind |lab we use the Grapher program to help understand many of these concepts. While it is also vitally |

| |Standard form of line, Ax +By = C |equation of a line perpendicular to a given line that |important for students to be able to graph by hand, use of the computer helps use to look at many |

| |Given Equation in Standard Form, Find Slope and y intercept |passes through a given point. |different scenarios in a short amount of time. Mr. Martin also uses the Grapher program and other programs|

| |Drawing Line by finding x and y intercepts |16.0 Students understand the concepts of a relation and a|to demonstrate concepts to students using the LCD projector and SmartBoard. Students in computer class can|

| |Writing an Equation in Standard Form Given the Slope and One Point |function, determine whether a given relation defines a |also use Excel for graphing. |

| |Slope of Horizontal and Vertical Lines |function, and give pertinent information about given | |

| |Lines with same slope are parallel |relations and functions. | |

| |Lines whose slopes are the negative reciprocal of each other are perpendicular |17.0 Students determine the domain of independent | |

| |Slope as rate of change |variables and the range of dependent variables defined by| |

| |Input-Output introduction to functions |a graph, a set of ordered pairs, or a symbolic | |

| |Relations, domain, range, independent and dependent variables |expression. | |

| |Definition of function |18.0 determining whether a relation is a function | |

| |Vertical line test | | |

| |Three view of a function – rule, table of values, graph | | |

| |Families of functions – linear, quadratic, absolute value | | |

|Qtr 3 |Systems of Equations and Inequalities (Chapter 6) |9.0 Students solve a system of two linear equations in |This chapter builds on students’ knowledge of graphing. If students do not learn the prior chapter well, |

| |Solving systems of equations by graphing |two variables algebraically and are able to interpret the|they will struggle now. |

| |Number of solutions possible: one, none or infinite |answer graphically. Students are able to solve a system | |

| |Solving systems of equations by substitution |of two linear inequalities in two variables and to sketch| |

| |Solving systems of equations using elimination |the solution sets. | |

| |Adding, subtracting. Multiplying one or both equations before multiplying or | | |

| |subtracting | | |

| |Solving word problems using systems of equations | | |

| |Linear inequalities | | |

| |Systems of linear inequalities | | |

| |Systems of nonlinear inequalities | | |

| |Quadratic Equations and Functions (Chapter 7) |19.0 Students know the quadratic formula and are familiar|We approach quadratic functions by having students graph the function using a table. Students explore the |

| |Definition, properties of and graphing quadratic functions, y=ax2+by+c |with its proof by completing the square |shape of the curve, the axis of symmetry, whether the curve points up or down, whether it is wide or |

| |Parabola |20.0 Students use the quadratic formula to find the roots|narrow. They can then use much of what they learn to graph the quadratic functions much more quickly. |

| |Axis of symmetry |of a second-degree polynomial to solve quadratic |Students then learn that if they can express a quadratic equation in the form of 0=ax2+by+c they can solve|

| |Standard form |equations. |that equation by using the quadratic formula, [pic] . This, as well as a few other things in class, they |

| |a>0 opens up; a ................
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