Mark D. Martin

Instruction Outline 8^th Grade Math Using State Standards

Text, Prentice Hall Pre-Algebra (2004)

Introduction- Stella Maris Academy follows California State Standards and the diocesan standards. The California Standards are more specific, although generally consistent with the diocesan standards. The focus in this document is hence on the California Standards. The diocese typically continues pre-algebra through 8^th grade. The pre-algebra California State Standards for 7^th grade therefore continue to apply to the 8^th grade math class. Advanced students who did exceptionally well in 7^th grade math take the advanced algebra course to which the grades 8-12 Algebra 1 State Standards apply.

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 straightforward. 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.

Pre-Algebra is tough. Concepts build upon those in all prior grades. Concepts come at a much higher pace than in the lower grades. More abstract concepts are covered. Mastering the concepts is crucial to success in Algebra in high school. Additionally, these math concepts are some of the most useful in daily life. Most people indeed use fractions, decimals, percents, proportions, volume, area, probability, etc. in our daily lives even though we have forgotten how to, and don’t need to, factor polynomials, write geometric proofs, or do calculus. (Those things are vitally important to advancing math, science, engineering, technology and society in general. Most of us do not use them in our daily lives, however.)

Most of the concepts were introduced last year. The goal this year is to ensure mastery as well as kick things up a notch. For example, while we covered scientific notation last year, we did not multiply or divide numbers expressed in scientific notation. While we covered exponents last year, we did not multiply or divide numbers with the same base raised to powers. Students in this class who work hard should be well prepared for high school Algebra I next year.

In the following chart the California State Standards sections are referred to by the following abbreviations: NS= Number Sense, A = Algebra and Functions, MG = Measurement and Geometry, S = Statistics, Data Analysis and Probability, MR = Mathematical Reasoning. Brief descriptions of the standards are given, but refer to the actual standard for a complete description. The 7^th Grade Math Standards are at: http://www.cde.ca.gov/be/st/ss/mthgrade7.asp. The Mathematical Reasoning Standards are meet throughout all topics and therefore are not separately set forth below.

	Topics	California State Standards	Notes
Qtr 1	Algebraic Expressions and Integers (Chapter 1) Variables and expressions “Translating” from “English” to “Algebra” Order of operations (PEMDAS) Evaluating expressions Integers and absolute value Adding integers Subtracting integers Multiplying and dividing integers	NS1.2 decimal and integer operations NS2.5 absolute value A1.3 associative and commutative properties of + and x, identity properties of + and x, distributive property, inverse operations	-Integer operations are reviewed from last year. Students are expected to memorize the following rules: -Addition * Same sign- add absolute values, give result sign of that the numbers have * Different signs – subtract absolute values, give result sign of the number with the greater absolute value. -Subtraction – add the opposite -Multiplication (two numbers) *same sign, product is positive *different signs, product neg -Division – same rules as multiplication
	One-Step Equations and Inequalities (Chapter 2) Properties of numbers Commutative + & - Associative + & - Additive identity Multiplicative identity Zero properties Distributive property Simplifying variable expressions Variables and equations Definitions, sentence, equation, open sentence Writing equations from words Solution of an equation Solving equations by adding or subtracting Inverse operations Additive property of equality Solving equations by multiplying or dividing Division property of equality Multiplication property of equality Inequalities and their graphs Solving one-step inequalities by adding or subtracting Subtraction property of inequality Addition property of inequality Solving one-step inequalities by multiplying or dividing Division properties of inequality Multiplicative properties of inequalities	A1.1 writing equations A1.3 properties A1.4 algebraic terminology A4.1 two step equations and inequalities A4.2 multi step problems	Properties of numbers have been taught in prior years including seventh grade. In 8^th grade the terminology becomes more formal. Students also solved equations and inequalities last year, but this year the equations become somewhat more complex.
	Decimals and Equations (Chapter 3) Rounding and estimating Mean, median and mode Using formulas Solving equations by adding or subtracting decimals Solving equations by multiplying or dividing decimals Using the metric system Length, capacity (volume) and mass Choosing appropriate units Estimating Converting metric units (King Hector died Monday drinking chocolate milk.) Precision and significant digits	NS1.2 decimal operations A1.1 writing equations A4.1 two step equations and inequalities A4.2 multi step problems MG1.1 measurement conversions	Decimal operations are reviewed with a greater emphasis on solving equations with decimals. Round, estimating, measures of central tendency and metric conversions are also reviewed in greater detail
Qtr 2	Factors, Fractions and Exponents (Chapter 4) Divisibility rules for 2, 3, 4, 5, 6, 9 and 10 Exponents Prime factorization and greatest common factor (GCF) Simplifying fractions using GCF Rational numbers Exponents and multiplication Multiplying powers with the same base Finding a power of a power Exponents and division Dividing powers with the same base Simplifying expressions with integer exponents (including 0) Negative exponents Scientific notation Calculating with scientific notation	NS1.1 Scientific Notation NS1.3 decimal fraction conversions NS1.4 and 1.5 rational and irrational numbers NS2.1 Exponents including operations with common base A2.1 and 2.2 exponents including exponent operations	Factoring is reviewed from last year. In addition to factoring numbers, students are also expected to factor variable expressions. Exponents and scientific notation were also explored last year. This year we kick it up a notch with operations involving exponents and scientific notation. Students are also expected to gain mastery over negative exponents this year.
	Fraction Operations (Chapter 5) Comparing and ordering fractions Finding LCM using prime factorization Finding LCM of variable expressions Number line Fraction and decimals Adding and subtracting fractions by finding the LCD Adding and subtracting mixed numbers Multiplying and dividing fractions and mixed numbers Conversion of customary units Dimensional analysis Solving equations by adding or subtracting fractions Solving equations by multiplying fractions Powers of products and quotients	NS2.2 Add subtract fractions with uncommon denominators NS2.3 multiply, divide and simplify rational numbers using exponent rules MG1.1 measurement conversion	Fraction operations again are reviewed, now with a greater emphasis of dealing with fractions in equations. More complex problems involving adding and subtracting mixed numbers are also given this year. Finally, again while exponents were studied last year, this year we do operations involving the multiplication and division of exponents.
	Ratios, Proportions and Percents (Chapter 6) Ratios and unit rates Proportions and cross products Similar figures and scale drawings Probability and odds Fractions, decimals and percents Percent proportion Solving percent problems using equations Percent of change Markup and discount	A4.2 multi step problems involving rate MG1.1 Measurement conversions MG1.2 scaled drawings MG1.3 unit rates, dimensional analysis	This year we try and explore in more detail some of the practice uses of ratios, proportions and percents.
Qtr 3	Solving Equations and Inequalities (Chapter 7) Solving two-step equations Solving multi-step equations Multi-step equations with fractions and decimals Writing equations (“translating” from “English” to “Algebra”) Solving equations with variables on both sides Solving two-step inequalities Transforming formulas Simple interest Compound interest	A1.1 writing equations A1.3 properties A1.4 algebraic terminology A4.1 two step equations and inequalities A4.2 multi step problems S1.6 percent increase or decrease (i.e. percent of change) NS1.7 discounts, markups, commissions, profits	In this chapter we solve equations and inequalities involving multiple steps.
	Functions and Graphing (Ch 8 & 1-10, 13-1, 13-2) Graphing equations with two variables using a table Slope Intercepts Slope-intercept form of equation Wring rules for linear functions Functions Scatter plots Interpreting graphs Solving systems of linear equations Meaning of solution of systems of equations Graphing linear inequalities Graphing systems of linear inequalities Graphing non-linear functions	A1.5 represent quantitative relationships graphically and interpret graphs A3.1 graph functions to second and third powers A3.2 reserved until 8th grade A3.3 graph linear functions and determine slope A3.4 plotting A4.2 solve multi step problems involving rate, average speed, distance time or a direct variation MG3.2 plot figures, translations, reflections	Students were introduced to graphing last year. This year the process is more formalized and students are expected to be able to quickly find slope from either a given ordered pair, or from a graph. We go further into the interpretation of graphs and what slope and y-intercept may tell us in the real world. We also explore more non-linear functions including graphing non-linear functions on computer using the Grapher application on the lab iMacs.
	Spatial Thinking (Chapter 9) Definitions – points, line, plane, segments, rays. Intersecting, parallel and skew lines. Drawing and measuring angles Angle relationships and parallel lines Classifying polygons Sum of interior angles of polygons Congruent figures Circles – radius, diameter, chord, circumference, central angle, C=Pd, circle graphs Construction of angle bisector, perpendicular bisector, congruent angles using a straight-edge and compass Translations Symmetry and reflections Rotations	MG3.1 identifications, constructions, etc. MG3.4 Congruent figures MG3.6 elements of 3D objects, plane intersections, skew lines, etc.	We review many of the geometry concepts we learned last year. We have more time to more closely examine translation, symmetry, reflections and rotations on the coordinate plane, a topic that may only be briefly introduced in the 7^th grade class. We review constructions from last year.
Qtr 4	Area and Volume (Chapter 10) Area of parallelograms Area of triangles Area of trapezoids Area of irregular figures Area of circles Naming three-dimensional figures – prisms, pyramids, cylinders, cones and spheres Describing three-dimensional figures from two-dimensional “nets” Surface are of prisms and cylinders Surface area of pyramids, cones and spheres Volume of prisms and cylinders Volume of pyramids, cones and spheres	MG2.1to 2.4 area, volume, surface area, etc. MG3.5 2-D nets of 3-D objects	Students in 8^th grade are expected to master these area and volume concepts which involve a degree of memorization as well as the ability to visualize and keep track of a variety of surfaces.
	Right Triangles in Algebra (Chapter 11) Square roots and irrational numbers Pythagorean theorem Distance and midpoint formulas Square roots of expressions with variables Sine, cosine and tangent ratios	NS2.4 roots MG3.3 Pythagorean Theorem	Square roots, irrational numbers and ratios are explored in the context of geometry.
	Data Analysis (Chapter 12 part) Frequency tables and line plots Box-and-whisker plots including quartiles Stem and leaf plots	S1.1 data display S1.2 scatter plots S1.3 box and whisker plots – quartiles	These topics may be only briefly introduced in 7^th grade. In 8^th grade they can be more closely examined and mastered.