8th+Grade+Parent+Letters

March 16, 2010 Dear Parents, We have just completed our sixth chapter in algebra, which introduced students to solving systems of linear equations and inequalities. Student learned several ways to find the solution to a system of linear equations. These methods included graphing, using substitution, and using the strategy of elimination. They learned that by classifying systems they can determine if two lines intersect providing one solution, are parallel providing no solution, or are the same line providing an infinite number of solutions. They also worked with systems of linear inequalities, graphing the inequalities and shading to find the solutions of those systems. We were able to complete the chapter just in time to celebrate pi day last Friday. As part of that celebration, some of the eighth graders wore t-shirts they had created for the occasion. Students participated in activities that included watching video clips from Project Mathematics discussing the early history of pi and the computation of the value of pi. Students also listened to a pi day rap created by high school students in Vancouver and constructed a paper chain using links of different colors to represent the digits of pi. A highlight of each class was a contest held to see who could recite the most digits of pi. We were all blown away by Kelly Galakatos, who recited 65 digits of pi, and by Marty Schwarze, who recited pi to 84 places! Each class was concluded by students eating pie. We will be taking a break from graphing and solving equations in Chapter 7. Students will study the properties of exponents as well how to classify, add, subtract, and multiply polynomials. Although the concept of exponents is not new to the eighth graders, they will learn how to simplify expressions containing negative exponents, as well as the value of an expression with an exponent of zero. We will be reviewing the concept of scientific notation as we work with very large and very small numbers. We will also be extending the rules that your student has learned for integer exponents, using those rules to simplify exponential expressions containing multiplication and division. The chapter continues with the study of polynomials, dealing with topics such as the degree of a polynomial, writing a polynomial in standard form, and learning basic operations with polynomials such as addition, subtraction, and multiplication.

February 19, 2010 Dear Parents, We are beginning our sixth chapter in Algebra. The chapter we just completed was a continuation of learning how to identify and graph linear functions, then applying those skills. The chapter included several important formulas used to represent these equations. They learned that the standard form of a line can be used to find x and y-intercepts and that it can be used to identify whether an equation is linear. They learned how to write the equations of lines given two points; or a point and a slope. They studied parallel and perpendicular lines, learning how to identify them by looking at their slopes. We graphed equations by hand and using a graphing calculator; learning how the slope and y-intercept of an equation affects its position on a graph. This knowledge helped students identify and create transformations; including translations, rotations, and reflections. In general, I was pleased with the performance of students on this test. Part of the requirements for this chapter included memorizing the different forms of a linear equation and knowing how to apply those formulas. Learning formulas and vocabulary as they are presented, and studying the notes and handouts will help students improve their grade. In Chapter 6, we will be studying systems of linear equations and inequalities. A system of linear equations is a set of two or more linear equations containing two or more variables. A solution to the system is a point that makes all of the equations true. Students will learn several ways to find the solution to a system of linear equations and to classify systems as //consisten//t (at least one solution), //inconsistent// (no solutions), //independent// (exactly one solution), or //dependent// (infinitely many solutions). We will also be working with systems of linear inequalities - sets of two or more linear inequalities containing two or more variables. Students will engage in a real-life application as they solve a system of linear equations after researching and graphing average salaries of baseball and basketball players over a ten year period.

December 11, 2009 Dear Parents, We finished our fourth chapter in Algebra just in time for exams. The big concept for this chapter was functions, and how they are represented through graphs. As you know from the news, media, and maybe your own career, graphs are used to represent many different situations. In this chapter, we made and interpreted graphs that showed how two variables were related. Students also learned the difference between a continuous graph and a discrete graph, how to identify the domain and the range of a relation, and how to write equations using function notation. This chapter also presented the concept of scatter plots and their use for comparing two sets of data. Students learned to interpret the possible relationships of two things being compared by using a trend line. They also learned how to determine if data being compared has a positive or negative correlation; or perhaps no correlation at all. We will continue working with functions in chapter 5. During this chapter, students will learn how to identify and graph linear functions. This will give them opportunity to continue learning and applying graphing skills. They will learn to use the standard form of a line as well as the slope-intercept form. They will learn how the slope and y-intercept of an equation affects its position on a graph. We will also be working with transformations; including translations, rotations, and reflections. I am pleased with the progress we have made so far. We will continue using skills already learned as we continue our algebra curriculum.

November 24, 2009 Dear Parents, I am pleased to say that we are already into our fourth chapter of algebra. Chapter 3, Inequalities, allowed students to practice many of the same skills they learned for solving equations. Students learned that for both of these concepts, finding a solution involved isolating the variable by using inverse operations in the reverse order. However they learned one major difference: when you multiply or divide both sides of the inequality by a negative number, you must reverse the inequality sign. We ended the chapter by working with compound inequalities, which are formed when two inequalities are combined using the words AND or OR. Students learned that these two types of inequalities are called conjunctions and disjunctions. We also took class time to model and solve real-world problems using inequalities. Providing practice in this area is important, as modeling and solving real world problems using algebra is an important application of the subject. In Chapter 4, your student will make and interpret graphs that show how two variables are related. We will be identifying special relationships called functions, and using functions to model real-world data. Vocabulary will continue to be extremely important, and as you can see, the skills we learn in each lesson build upon previous work. Remember to use the publisher’s website (found on my class page) as a resource tool.

November 5, 2009 Dear Parents, We have just completed our second chapter in Algebra. I was pleased with the results of your students’ tests. Most scored much higher than on their Chapter 1 test, even though new material was introduced that was much more challenging. As we progress, students are becoming more focused, understanding the need to apply themselves in class and on homework. In addition to presenting a variety of skills needed to solve equations in one variable, Chapter 2 covered the important concepts of working with ratios, proportions, and percents. . In Chapter 3, we will be learning to solve inequalities in one variable. Solving an inequality involves many of the same skills used in solving equations - you isolate the variable by using inverse operations in the reverse order. However there is one major difference: when you multiply or divide both sides of the inequality by a negative number, you must reverse the inequality sign. You can see why this is true with a simple example: 8 > -2. When you multiply both sides by -3: 8(-3) and -2(-3), the result is -24 < 6. For this inequality to remain true, > changed to <. With this one exception, solving one-step inequalities, multi-step inequalities, and inequalities with variables on both sides follows the same process as solving an equation.

Vocabulary will continue to be extremely important, and as you can see, the skills we learn in each lesson build upon previous work. Remember to use the publisher’s website (which I have as a link on my homework page) as a resource tool. The parent resources can be found by entering the keyword MA7 Parent.

September 23, 2009

Dear Parents,

We have just completed our first chapter in algebra. Although this chapter contains many important concepts that are foundations for algebra, most of the objectives dealt with topics that were introduced and practiced in sixth and seventh grade. Some of the concepts we covered were: writing and evaluating algebraic expressions, operations with positive and negative numbers, simplifying expressions using the order of operations, and graphing points in the coordinate plane. During this chapter we also studied powers and square roots, including square roots that are equal to decimals that never end and never repeat. These numbers are irrational, belonging to one of the classifications of real numbers. Students were asked to identify and classify other types of numbers as well. The other classifications for real numbers are natural numbers, whole numbers, integers, and rational numbers. The end of the chapter covered the importance of the Commutative, Associative, and Distributive Properties and their use in simplifying and combining like terms. It also presented lessons in graphing functions by generating ordered pairs. Ordered pairs are generated by picking a value for x(input), substituting it into the function, and then finding the value of y (output).

I have stressed to the eighth graders that this course will require more effort than just coming to class and doing homework. The vocabulary and properties in algebra are extremely important, and the skills we learn in each lesson build upon previous work. Encourage your student to look over the examples presented in each day’s lesson, memorize the vocabulary, and use the online study tools presented with the lesson. The textbook offers some excellent resources on the publisher’s website, including video tutorials, extra practice, and a help site for parents. I encourage you to visit this site (found at go.hrw.com). The parent resources can be found by entering the keyword MA7 Parent.

I recently returned the summer packet that your student completed. Those students that showed their work clearly and completely did very well. Points were deducted for missing or incomplete work, and for not attempting or missing a problem containing concepts learned in a previous grade.

In Chapter 2, your child will solve a variety of equations in one variable, including equations that result from proportion and percent problems. They will also work with evaluating and solving formulas for given values.

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