| Jefferson County | ||||
| 8th Grade Pre-Algebra Curriculum | ||||
| I - Introduced Skill D - Developing Skill A - Assessed Skill M - Mastered & Maintained Skill | ||||
| P - Preview Lesson F - Follow-Up Lesson PS - Prerequisite Skill GS - Getting Started RM - Reading Math | ||||
| The pre-algebra curriculum was adapted from the Glencoe Pre-Algebra content standards by a consortium of Jefferson County mathematics educators on July 1, 2006. The curriculum was aligned with the Tennessee standards for eighth grade mathematics, the Jefferson County Schools curriculum gradebook for eighth grade mathematics, and Pre-Algebra, 2005 edition, Glencoe Publishing. | ||||
| Number and Operations | Student Edition Lesson(s) | Resources | ||
| Content Standard 1.0 - The students will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving. | ||||
| 8.1.1 | Understand numbers, ways of representing numbers, relationships among numbers, and number systems. | |||
| a. | recognize the place value of a given digit; (M) | 5-2, PS6 | ||
| b. | use exponents to express a monomial written in expanded form; (I) | 4-2 | ||
| c. | determine the square root of perfect squares; (A) | 9-1 | ||
| d. | use a variety of models to demonstrate the relationships within the real number system (e.g., Venn diagrams, webs); (D) | 9-1, 9-2 | ||
| e. | work flexibly with fractions, decimals, and percents to solve problems; (A) | Addressed throughout the text in Chapters 4-13 | ||
| f. | compare and order fractions, decimals, and percents; (A) | 4-8, 5-1, 5-6, 6-4, 9-2, PS5 | ||
| g. | connect whole numbers, fractions, decimals, percents, and integers to locations on the number line; (A) | 2-1, 5-1, 5-6, 9-2 | ||
| h. | develop meaning for percents greater than 100 and less than one; (D) | 6-4, 6-6, 6-8 | ||
| i. | use appropriate mathematical language and symbols to express numerical relationships (e.g., <, >, =, ≤, ≥); (M) | 1-1, RM1, 1-2, 1-3, 1-4, 1-5, RM2, 3-3P, 3-3, 3-4, 3,5, RM3, 3-6, 6-1, 6-2, 7-1P, 7-1, 7-2, RM7, 7-3, 7-4, 7-5, 7-6, GS8, 8-2, RM8, 8-7, 8-9, 8-10, 8-10F, GS9, GS10, 13-5, 13-6, PS5 | ||
| j. | understand and use ratios and proportions to represent quantitative relationships; (A) | 6-1, RM6, 6-2, 6-2F, 6-3, 6-5, 9-8P, 9-8 | ||
| k. | recognize and use exponential, scientific and calculator notation to represent large numbers in real-world situations; (A) | 4-2, 4-8, 9-1, 9-8, 10-7 | ||
| l. | demonstrate understanding of opposites, reciprocals, integers, and absolute value; (A) | 2-1, 2-2P, 2-2, 2-3, GS3, 3-3P, 3-3, 3-4, 3-5, 3-6, 4-7, 5-4, 5-5, 5-9 | ||
| m. | identify the opposite of a rational number; (A) | 2-1, 2-2P, 2-2, 2-3, 5-5, 5-9 | ||
| n. | use concrete, pictorial, and symbolic representations of integers; (M) | 2-1, 2-2P, 2-2, 2-3, 2-4, 2-5, 3-3P, 7-1P, 13-1F, 13-2, 13-4P | ||
| o. | apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime). (D) | 2-1, 2-2P, 2-2, 2-3, 2-4, 2-5, 4-1, 4-3, 4-4, 4-5, 4-6, GS5, RM5, 5-6, 5-7, GS6, GS10 | ||
| 8.1.2 | Understand operations and how they relate to one another. | |||
| a. | understand the meaning and effects of arithmetic operations with rational numbers; (D) | Addressed throughout the text | ||
| b. | apply the associative and commutative properties of addition and multiplication to simplify computations with rational numbers; (M) | 1-4, 2-2P, 2-2, 2-4, 10-5 | ||
| c. | apply the distributive property to simplify computations with rational numbers; (A) | 3-1, GS4, 4-4, 7-2, GS13, 13-4 | ||
| d. | apply order of operations in computing with rational numbers using parentheses and exponents; (A) | 1-2, 1-4, GS4, 4-2 | ||
| e. | understand and use inverse relationships (e.g., addition and subtraction, multiplication and division, squaring, and finding square roots) to simplify computations and solve problems. (D) | Addresses throughout the text. | ||
| 8.1.3 | Solve problems, compute fluently and make reasonable estimates. | |||
| a. | select and use appropriate methods and tools for computing with whole numbers, fractions, decimals, percents and integers in problem-solving situations (e.g., mental computation, estimation, calculators, computers, paper and pencil); (A) | GS1, 1-1, 1-3F, 1-4, 1-5, 2-2, 3-1, 3-2, 3-5, 3-6, 4-1, 4-3, 5-1, 5-5, 5-7, 6-4, 6-6, 9-1, 9-4, 9-8, 11-2, 11-6, PS7, PS9, PS11, PS12 | ||
| b. | develop and analyze procedures for computing with fractions, decimals, and integers; (M) | 1-4, 2-2P, 2-2, 2-3, 2-4, 2-5, 3-1, 4-1, 4-2, 4-3, 4-4, 4-5, 4-7, 4-8, 5-1, 5-3, 5-4, 5-5, 5-6, 5-7, 6-1, 6-2, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 9-1, PS7, PS8, PS9, PS10, PS11, PS12 | ||
| c. | develop and use strategies to estimate the results of rational number computations in real-world situations using inductive reasoning, deductive reasoning, and conjectures; (A) | 1-1, 1-4, 3-5, 5-5, 5-9, 6-6, 9-1, 11-2, PS7, PS9, PS11, PS12 | ||
| d. | determine whether the results of rational number estimates and computations are reasonable; (A) | GS1, 1-1, 2-3, 3-3, 3-4, 3-5, 3-6, 4-8, 5-1, 5-3, 5-4, 5-5, 5-7, 5-9, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 7-1, 7-2, 7-4, 7-5, 7-6, 8-2, 8-3, 8-7, 8-9, 8-10, 9-1, 9-4, 9-7, 10-2, 10-7, 10-8, 12-7, 13-4, PS7, PS9, PS11, PS12 | ||
| e. | solve one-step real-world problems involving whole numbers, fractions, decimals, and percents; (M) | Addressed throughout the text. | ||
| f. | raise rational numbers to whole number powers; (I) | 4-2, 9-5, GS9 | ||
| g. | solve multi-step real-world problems involving whole numbers, fractions, decimals, and percents; (D) | Addressed throughout the text. | ||
| h. | develop, analyze, and explain methods for solving problems involving ratios and proportions (e.g., scaling, finding equivalent ratios); (A) | 6-2, 6-2F, 6-3, 6-5, 9-7, 11-6P, 11-6 | ||
| i. | calculate rates involving cost per unit to determine the best buy. (A) | 6-1 | ||
| Algebra | Student Edition Lesson(s) | Resources | ||
| Content Standard 2.0 - The student will understand and generalize patterns as they represent and analyze quantative relationships and change in a variety of contexts and problems using graphs, tables, and equations. | ||||
| 8.2.1 | Understand patterns, relations, and functions | |||
| a. | represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible, symbolic rules;(A) | 1-1, GS2, 4-4, 5-10, 5-10F | ||
| b. | develop understanding for arithmetic and geometric sequences;(D) | 5-10, 5-10F | ||
| c. | relate and compare different forms of representation for a relationship; (A) | 1-6, 1-7, GS8, 8-1P | ||
| d. | identify functions as linear or nonlinear, and evaluate functions; (D) | 8-2, 8-3, 8-6F, 8-7, 13-5, 13-6 | ||
| e. | compare and contrast properties of functions from tables, graphs, or equations. (I) | 8-1, 8-2P, 8-2, RM8, 8-3, 8-6F, 8-7, 13-5, 13-6 | ||
| 8.2.2 | Represent and analyze mathematical situations and structures using algebraic symbols. | |||
| a. | formulate multi-step equations that represent relationships and real-world situations; (A) | Addressed throughout the text | ||
| b. | develop understanding of intercept and slope; (I) | 8-3, 8-4P, 8-4, 8-5P, 8-5, 8-6, 8-6F, 8-7 | ||
| c. | use symbolic algebra to represent situations and solve problems; (A) | Addressed throughout the text | ||
| d. | use a variety of forms to represent linear relationships; (I) | 1-7P, 1-7, 8-1P, 8-1, 8-2, RM8, 8-3, 8-5, 8-6, 8-6F, 8-7, 8-8, 8-9, 8-10 | ||
| e. | recognize and generate equivalent forms for simple algebraic expressions; (A) | 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, GS4, 4-5, GS7, 7-1P, 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, GS9, GS10, GS13 | ||
| f. | evaluate an algebraic expression given values for two or more variables, up to exponential values of 3; (A) | 1-3, 1-4, GS2, 2-3, GS4 | ||
| g. | solve one-and two-step linear equations involving integers and fractions; (A) | 3-3P, 3-3, 3-4, 3-5, 3-6, GS7, 7-1P, 7-1, 7-2, 8-1, 8-2, GS9, GS10 | ||
| h. | use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper); (A) | 3-3P, 3-3, 3-4, 3-5, 3-6, GS7, 7-1P, 7-1, 7-2, 8-1, 8-2, GS9, GS10 | ||
| i. | apply given formulas to solve real-world problems; (A) | 3-7, 6-5, 6-7, 6-9, 8-2, 8-3, 9-6, 10-7, 11-2, 11-3, 11-4, 11-5, 12-7, 13-4, 13-6 | ||
| j. | solve multi-step linear inequalities; (A) | 7-3, 7-4, 7-5, 7-6 | ||
| k. | identify the graph of a linear equation; (A) | 8-2, 13-5 | ||
| l. | identify the graphical representation of the solution to a one-variable linear inequality; (I) | 7-3, 7-4, 7-5, 7-6 | ||
| m. | develop understanding for particular values of patterns, relationsips, and linear functions, (e.g., x-and y-intercepts and slope); (I) | 8-1P, 8-1, 8-2P, 8-2, 8-3, 8-4P, 8-4, 8-5P, 8-5, 8-6, 8-6F, 8-7, 13-5 | ||
| n. | develop understanding for and identify the vertex, maximum/minimum value, and line of symmetry for quadratic functions. (I) | Use graphing calculator or pictoral representations of quadratic functions | ||
| 8.2.3 | Use mathematical models to represent and understand quantitative relationships. | |||
| a. | use a variety of representations to solve real-world problems (e.g., graphs, tables, equations). (D) | Addressed throughout the text | ||
| 8.2.4 | Analyze change in various contexts. | |||
| a. | compare linear relationships to non-linear relationships; (I) | 8-2, 13-5 | ||
| b. | develop understanding of rate of change in real-world situations. (A) | 8-4P, 8-4, 8-5P, 8-5 | ||
| 8.2.5 | Students will recognize and apply operations to algebraic expressions involving monomials and polynomials | |||
| a. | identify algebraic expressions as monomial, binomial, or trinomial; and give their degree(I) | 4-1, 13-1 | ||
| b. | simplify algebraic expressions (e.g., combining like terms); (I) | 3-2 | ||
| c. | simplify polynomial expressions (e.g, adding or subtracting binomials, and trinomials); (I) | 13-2, 13-3 | ||
| d. | multiply a monomial by a monomial; (I) | 4-6 | ||
| e. | multiply a polynomial expression by a monomial using the distributive property and exponent rules; (I) | 13-4 | ||
| f. | multiply a binomial by a binomial using the FOIL method. (I) | Glencoe Mathematics Algebra I TeacherWorks CD-ROM - text - section 8-7, example 2; study guide & intervention page 491; skills practice page 493 1-18 | ||
| Geometry | Student Edition Lesson(s) | Resources | ||
| Content Standard 3.0 - The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures. | ||||
| 8.3.1 | Analyze characteristics and properties of two- and three-dimensional geometric figures. | |||
| a. | define, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties; (A) | 3-7, RM9, 9-3, 9-4, 10-1, 10-1F, 10-2, 10-3P, 10-4, RM10, 10-6, 10-7, 11-1 | ||
| b. | understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (A) | 9-3, 10-1 | ||
| c. | solve problems using angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (A) | 10-1 | ||
| d. | determine the measure of an angle of a triangle given the measures of the other two angles; (A) | 9-4 | ||
| e. | understand relationships among the angles and side lengths of similar geometric figures; (A) | 9-7, 10-3F, 11-6 | ||
| f. | determine congruence of line segments, angles, and polygons by direct comparison of given attributes; (D) | 9-3, 9-4, 9-6, 10-1, 10-1F, 10-2, 10-3, 10-6 | ||
| g. | develop understanding of the Pythagorean Theorem (A) | 9-5P, 9-5 | ||
| 8.3.2 | Specify locations and describe spatial relationships using coordinate geometry and other representational systems. | |||
| a. | graph points in the coordinate system. (A) | 1-6, 1-7P, 1-7, 2-6, 8-2, 8-3, 8-4, 8-5, 8-6, 8-6F, 8-8, 8-9, 8-10, 8-10F, 10-3 | ||
| 8.3.3 | Apply transformations and use symmetry to analyze mathematical situations. | |||
| a. | describe sizes, positions and orientations of shapes under transformations (e.g. rotations, translations, reflections, dilations,); (D) | 10-3P, 10-3, 10-3F | ||
| b. | relate symmetry and congruence to reflections about a line, including a review of quadratic graphs.. (D) | 10-3P, 10-3 | ||
| 8.3.4 | Use visualization, spatial reasoning, and geometric modeling to solve problems. | |||
| a. | use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, angle measure); (D) | 9-3, 9-4, 9-5P, 9-5, 9-8P, 10-1, 10-1F, 10-3, 10-3F, 10-6, 10-6F, 11-1P, 11-2P, 11-6 | ||
| b. | build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa; (D) | 11-1P, 11-1, 11-2, 11-3, 11-4, 11-5, 11-6 | ||
| c. | use visualization and spatial reasoning to solve real-world problems; (A) | 11-1P, 11-1, 11-2, 11-3, 11-4, 11-5, 11-6 | ||
| d. | recognize and appy geometric ideas and relationships such as tessellations in areas outside the mathematics classroom (e.g., art, science, everyday life). (A) | 10-6, 10-6F | ||
| Measurement | Student Edition Lesson(s) | Resources | ||
| Content Standard 4.0 - The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems. | ||||
| 8.4.1 | Understand measurable attributes of objects and the units, systems, and processes of measurement. | |||
| a. | understand both metric and customary systems of measurement; (M) | 5-3, 11-7, PS13, PS14 | ||
| b. | convert from one unit to another within the same system; (A) | 5-3, GS6, PS13, PS14 | ||
| c. | select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. (A) | 3-7, 7-2, 9-3, 10-5P, 10-5, 10-6, 10-7, 10-8, 11-2P, 11-2, 11-3, 11-4, 11-5, 11-6P, 11-6, 11-7 | ||
| 8.4.2 | Apply appropriate techniques, tools, and formulas to determine measurements. | |||
| a. | estimate length, perimeter, circumference, area, and volume using a variety of strategies; (A) | 3-7, 7-2, 9-3, 10-5P, 10-5, 10-6, 10-7, 10-8, 11-2P, 11-2, 11-3, 11-4, 11-5, 11-6P, 11-6 | ||
| b. | select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision; (A) | 3-7, 7-2, 9-3, 10-5P, 10-5, 10-6, 10-7, 10-8, 11-2P, 11-2, 11-3, 11-4, 11-5, 11-6P, 11-6, RM11, 11-7 | ||
| c. | apply formulas and/or other strategies to solve problems involving perimeter of polygons and circumference of circles; (A) | 3-7, 7-2, 9-3, 10-5P, 10-5, 10-6, 10-7, 10-8, 11-2P, 11-2, 11-3, 11-4, 11-5, 11-6P, 11-6 | ||
| d. | apply formulas and/or other strategies to solve problems involving area of circles and polygons; (A) | 3-7, 7-2, 9-3, 10-5P, 10-5, 10-6, 10-7, 10-8, 11-2P, 11-2, 11-3, 11-4, 11-5, 11-6P, 11-6 | ||
| e. | find area of complex and irregular shapes; (A) | 10-8 | ||
| f. | apply given formulas to find volume of selected prisms and cylinders; (I) | 11-2P, 11-2, 11-3 | ||
| g. | compare and contrast the volumes of a variety of geometric solids; (D) | 11-2P, 11-2, 11-3 | ||
| h. | solve problems involving rate/time/distance (i.e., d=rt); (A) | 3-7 | ||
| i. | solve problems involving scale factors using ratio and proportion; (A) | 6-3, 11-6P, 11-6 | ||
| j. | solve real-world problems using the Pythagorean Theorem, and determine if a triangle is a right triangle; (A) | 9-5P, 9-5 | ||
| k. | construct tables and graphs to represent rates of change; (A) | 8-4P, 8-4, 8-5P, 8-5 | ||
| l. | find measures using proportional relationships and properties of similar figures; (D) | 9-7, 11-6P, 11-6 | ||
| m. | determine the measure of angles by applying angle relationships (e.g., complimentary, supplementary, interior, exterior, vertical, corresponding). (D) | 10-1 | ||
| Data Analysis and Probability | Student Edition Lesson(s) | Resources | ||
| Content Standard 5.0 - The student will understand and apply basic statistical and probability concepts as they organize and analyze data, and to make predictions and conjectures. | ||||
| 8.5.1 | Formulate questions that can be addressed with data and collect, organize, and display revelant data to answer questions. | |||
| a. | formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g. random samlping, simulations); (D) | 4-6F, 5-8p, 5-10F, 6-2F, 6-9P, 6-9F, 8-1P, 8-4P, 8-5P, 11-2P, 11-6P, 12-6F, 12-9F | ||
| b. | select, create, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, scatterplots). (A) | 1-7P, 1-7, 4-6F, 5-8P, 5-10F, 6-2F, 6-9P, 6-9F, 8-1P, 8-4P, 8-5P, 8-8, 9-3F, 11-2P, 11-6P, 12-1, 12-2, 12-3, 12-3F, 12-4, 12-4F, 12-5, 12-6F, 12-9F, PS15 | ||
| 8.5.2 | Select and use appropriate statistical methods to analyze data. | |||
| a. | find, use, and interpret measures of center and spread (e.g. mean, interquartile range); (A) | 5-8, 5-8F, GS12, 12-1, 12-2, 12-3, 12-3F | ||
| b. | develop meaning for frequency, distribution, and outliers; (l) | 12-3, 12-4 | ||
| c. | discuss, understand, and interpret the relationship between data sets and their graphical representations (e.g. bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots). (A) | 1-7P, 1-7, 8-8, 12-1, 12-2, 12-3, 12-3F, 12-4, 12-4F, 12-5, PS15 | ||
| 8.5.3 | Develop and evaluate inferences and predictions that are based on data. | |||
| a. | make conjectures and predictions based on data; (A) | 1-1, 1-7P, 1-7, 5-8P, 5-8, 6-9, 6-9F, 8-8, 12-6F, 12-8, 12-9, 12-9F | ||
| b. | recognize misleading presentations of data; (A) | 12-5, RM12 | ||
| c. | develop meaning for lines of best fit; (l) | 8-8 | ||
| d. | determine an appropriate sample to test a hypothesis; (A) | 1-7P, 4-6F, 5-8P, 5-10F, 6-2F, 6-9P, 6-9, 8-1P, 8-4P, 8-5P, 11-2P, 11-6P, RM12, 12-6F 12-9F | ||
| e. | make conjectures to formulate new questions for future studies. (l) | 1-2, 1-3F, 1-5, 1-6, 1-7P, 2-2P, 3-7F, 4-2, 4-6, 4-6F, 5-1, 5-4, 5-10F, 6-2F, 6-7F, 8-1P, 8-4P, 8-5P, 8-5, 9-2, 9-4, 9-8P, 10-3F, 11-2, 11-6P 12-6F, 13-6F | ||
| 8.5.4 | Understand and apply basic concepts of probability. | |||
| a. | develop meaning of mutually exclusive events; (l) | 12-9 | ||
| b. | connect the symbolic representation of a probability to an experiment; (A) | 6-9, 6-9F, 12-9F | ||
| c. | use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models); (D) | 12-6, 12-6F, 12-7, 12-9, 12-9F | ||
| d. | distinguish between theoretical and experimental probability; (l) | 6-9 | ||
| e. | find the probability of dependent and independent events. (D) | 12-9 | ||