PreAlgebra Pacing Guide 2006 - 2007
1st Semester
Day 1 Day 11 Begin August 8th Begin Chapter 1
8.1.1.i. use appropriate mathematical language and symbols to express numerical relationships (e.g., <, >, =, ≤, ≥); (M)
8.1.2.b. apply the associative and commutative properties of addition and multiplication to simplify computations with rational numbers; (M)
8.1.2.d. apply order of operations in computing with rational numbers using parentheses and exponents; (A)
8.1.3.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)
8.2.1.a. represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible, symbolic rules;(A)
8.2.1.c. relate and compare different forms of representation for a relationship; (A)
8.2.2.f. evaluate an algebraic expression given values for two or more variables, up to exponential values of 3; (A)
8.3.2.a. graph points in the coordinate system. (A)
8.5.2.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, scatter plots). (A)
8.5.3.a. make conjectures and predictions based on data; (A)
Day 12 August 23rd Chapter 1 Assessment
Day 13 Day 20 Begin August 24th Begin Chapter 2
8.1.1.g. connect whole numbers, fractions, decimals, percents, and integers to locations on the number line; (A)
8.1.1. l. demonstrate understanding of opposites, reciprocals, integers, and absolute value; (A)
8.1.1. m. identify the opposite of a rational number; (A)
8.1.1. n. use concrete, pictorial, and symbolic representations of integers; (M)
8.1.3.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)
8.1.3. b. develop and analyze procedures for computing with fractions, decimals, and integers; (M)
8.2.2. f. evaluate an algebraic expression given values for two or more variables, up to exponential values of 3; (A)
8.3.2. a. graph points in the coordinate system. (A)
8.5.3. e. make conjectures to formulate new questions for future studies. (l)
Day 21 September 6th Chapter 2 Assessment
Day 22 Day 32 Begin September 7th Begin Chapter 3
8.1.1.l. demonstrate understanding of opposites, reciprocals, integers, and absolute value; (A)
8.1.2.c. apply the distributive property to simplify computations with rational numbers; (A)
8.2.2.e. recognize and generate equivalent forms for simple algebraic expressions; (A)
8.2.2.i. apply given formulas to solve real-world problems; (A)
8.4.1.c. select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. (A)
8.4.2.a. estimate length, perimeter, circumference, area, and volume using a variety of strategies; (A)
8.4.2.b. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision; (A)
8.4.2.c. apply formulas and/or other strategies to solve problems involving perimeter of polygons and circumference of circles; (A)
8.4.2.d. apply formulas and/or other strategies to solve problems involving area of circles and polygons; (A
8.4.2.h. solve problems involving rate/time/distance (i.e., d=rt); (A)
Day 33 September 22nd Chapter 3 Assessment
Day 34 Day 45 Begin September 25th Begin Chapter 4
8.1.1. b. use exponents to express a monomial written in expanded form; (I)
8.1.1. k. recognize and use exponential, scientific and calculator notation to represent large numbers in real-world situations; (A)
8.1.1. o. apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime). (D)
8.1.2. d. apply order of operations in computing with rational numbers using parentheses and exponents; (A)
8.1.3. f. raise rational numbers to whole number powers; (I)
8.2.2. e. recognize and generate equivalent forms for simple algebraic expressions; (A)
8.5.1. a. formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g. random sampling, simulations); (D)
8.5.3. d. determine an appropriate sample to test a hypothesis; (A)
Day 46 October 13th Chapter 4 Assessment
Day 47 Day 61 Begin October 16th Begin Chapter 5
8.1.1. a. recognize the place value of a given digit; (M)
8.1.1. f. compare and order fractions, decimals, and percents; (A)
8.1.1. g. connect whole numbers, fractions, decimals, percents, and integers to locations on the number line; (A)
8.1.1. m. identify the opposite of a rational number; (A)
8.1.1. o. apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime). (D)
8.1.3. b. develop and analyze procedures for computing with fractions, decimals, and integers; (M)
8.1.3. 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)
8.2.1. a. represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible, symbolic rules ;( A)
8.2.1. b. develop understanding for arithmetic and geometric sequences ;( D)
8.5.2. a. find, use, and interpret measures of center and spread (e.g. mean, interquartile range); (A)
8.5.3. a. make conjectures and predictions based on data; (A)
Day 62 November 6th Chapter 5 Assessment
Day 63 Day 75 Begin Nov. 8th Begin Chapter 6
8.1.1.f. compare and order fractions, decimals, and percents; (A)
8.1.1.h. develop meaning for percents greater than 100 and less than one; (D)
8.1.1.j. understand and use ratios and proportions to represent quantitative relationships; (A)
8.1.3.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)
8.1.3.b. develop and analyze procedures for computing with fractions, decimals, and integers; (M)
8.1.3.h. develop, analyze, and explain methods for solving problems involving ratios and proportions (e.g., scaling, finding equivalent ratios); (A)
8.1.3.i. calculate rates involving cost per unit to determine the best buy. (A)
8.4.2.i. solve problems involving scale factors using ratio and proportion; (A)
8.5.1.a. formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g. random sampling, simulations); (D)
8.5.3.a. make conjectures and predictions based on data; (A)
8.5.3.d. determine an appropriate sample to test a hypothesis; (A)
8.5.4.b. connect the symbolic representation of a probability to an experiment; (A)
8.5.4.d. distinguish between theoretical and experimental probability; (l)
Day 76 November 30th Chapter 6 Assessment
Day 77 Day 85 Begin December 1st Begin Chapter 7
8.1.1. i. use appropriate mathematical language and symbols to express numerical relationships (e.g., <, >, =, ≤, ≥); (M)
8.2.2. j. solve multi-step linear inequalities; (A)
8.2.2. l. identify the graphical representation of the solution to a one-variable linear inequality; (I)
Day 86 December 14th Chapter 7 Assessment
2nd Semester
Day 88 Day 102 Begin January 3rd Begin Chapter 8
8.2.1. c. relate and compare different forms of representation for a relationship; (A)
8.2.1. e. compare and contrast properties of functions from tables, graphs, or equations. (I)
8.2.2. b. develop understanding of intercept and slope; (I)
8.2.2. d. use a variety of forms to represent linear relationships; (I)
8.2.2. g. solve one-and two-step linear equations involving integers and fractions; (A)
8.2.2. h. use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper); (A)
8.2.2. k. identify the graph of a linear equation; (A)
8.2.2. m. develop understanding for particular values of patterns, relationships, and linear functions, (e.g., x-and y-intercepts and slope); (I)
8.2.4. b. develop understanding of rate of change in real-world situations. (A)
8.4.2. k. construct tables and graphs to represent rates of change; (A)
8.5.2. 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)
8.5.3. a. make conjectures and predictions based on data; (A)
8.5.3. c. develop meaning for lines of best fit; (l)
Day 103 January 25th Chapter 8 Assessment
Day 104 Day 117- Begin January 26th Begin Chapter 9
8.1.1.c. determine the square root of perfect squares; (A)
8.1.1.d. use a variety of models to demonstrate the relationships within the real number system (e.g., Venn diagrams, webs); (D)
8.1.1.g. connect whole numbers, fractions, decimals, percents, and integers to locations on the number line; (A)
8.1.3.f. raise rational numbers to whole number powers; (I)
8.2.2.i. apply given formulas to solve real-world problems; (A)
8.3.1.b. understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (A)
8.3.1.d. determine the measure of an angle of a triangle given the measures of the other two angles; (A)
8.3.1.e. understand relationships among the angles and side lengths of similar geometric figures; (A)
8.3.1.g. develop understanding of the Pythagorean Theorem (A)
8.3.4.a. use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, angle measure); (D)
8.4.1.c. select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. (A)
8.4.1.j. solve real-world problems using the Pythagorean Theorem, and determine if a triangle is a right triangle; (A)
8.4.2.l. find measures using proportional relationships and properties of similar figures; (D)
8.5.3.e. make conjectures to formulate new questions for future studies. (l)
Day 118 February 15th Chapter 9 Assessment
Day 119 Day 131 Begin February 20th Begin Chapter 10
8.2.2. i. apply given formulas to solve real-world problems; (A)
8.3.1. b. understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (A)
8.3.1. c. solve problems using angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (A)
8.3.1. f. determine congruence of line segments, angles, and polygons by direct comparison of given attributes; (D)
8.3.3. a. describe sizes, positions and orientations of shapes under transformations (e.g. rotations, translations, reflections, dilations,); (D)
8.3.3. b. relate symmetry and congruence to reflections about a line, including a review of quadratic graphs. (D)
8.3.4. a. use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, angle measure); (D)
8.3.4. d. recognize and apply geometric ideas and relationships such as tessellations in areas outside the mathematics classroom (e.g., art, science, everyday life). (A)
8.4.1. c. select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. (A)
8.4.2. a. estimate length, perimeter, circumference, area, and volume using a variety of strategies; (A)
8.4.2.b. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision; (A)
8.4.2. c. apply formulas and/or other strategies to solve problems involving perimeter of polygons and circumference of circles; (A)
8.4.2. d. apply formulas and/or other strategies to solve problems involving area of circles and polygons; (A)
8.4.2. m. determine the measure of angles by applying angle relationships (e.g., complimentary, supplementary, interior, exterior, vertical, corresponding). (D)
Day 132 March 9th Chapter 10 Assessment
Day 133 Day 136 Begin March 12th Begin Chapter 11 (11-1 thru 11-3)
8.2.2. i. apply given formulas to solve real-world problems; (A)
8.3.1. a. define, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties; (A)
8.3.4. c. use visualization and spatial reasoning to solve real-world problems; (A)
8.4.1. c. select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. (A)
8.4.2.b. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision; (A)
8.4.2. f. apply given formulas to find volume of selected prisms and cylinders; (I)
8.4.2. g. compare and contrast the volumes of a variety of geometric solids; (D)
Day 137 March 16th Chapter 11 Assessment (11-1 thru 11-3)
Day 138 Day 139 Begin March 26th Continue Chapter 11 (11- 4 and 11 5)
8.2.2. i. apply given formulas to solve real-world problems; (A)
8.3.4. c. use visualization and spatial reasoning to solve real-world problems; (A)
8.4.1. c. select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. (A)
8.4.2.b. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision; (A)
Day 140 March 28th Chapter 11 Assessment (11- 4 thru 11 5)
Day 141 Day 145 - Begin March 29th Begin Chapter 12 (12 1 thru 12 5)
8.5.1.b. select, create, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, scatter plots). (A)
8.5.2.a. find, use, and interpret measures of center and spread (e.g. mean, interquartile range); (A)
8.5.2.b. develop meaning for frequency, distribution, and outliers; (l)
8.5.2.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, scatter plots). (A)
8.5.3.b. recognize misleading presentations of data; (A)
Day 146 April 5th Chapter 12 Assessment (12 1 thru 12 5)
Day 147 Day 151 TCAP Review
Day 152 Day 156 TCAP Testing
Day 157 Day 159 - Begin April 23rd Continue Chapter 12 (12 6 thru 12 9)
8.5.3.d. determine an appropriate sample to test a hypothesis; (A)
8.5.4.a. develop meaning of mutually exclusive events; (l)
8.5.4.b. connect the symbolic representation of a probability to an experiment; (A)
8.5.4.c. use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models); (D)
8.5.4.e. find the probability of dependent and independent events. (D)
Day 160 April 26th Chapter 12 Assessment ( 12 6 thru 12 9)
Day 161 Day 172 - Begin April 30th Begin Chapter 13
8.2.1.d. identify functions as linear or nonlinear, and evaluate functions; (D)
8.2.1.e. compare and contrast properties of functions from tables, graphs, or equations. (I)
8.2.2.k. identify the graph of a linear equation; (A)
8.2.2.m. develop understanding for particular values of patterns, relationships, and linear functions, (e.g., x-and y-intercepts and slope); (I)
8.2.4.a. compare linear relationships to non-linear relationships; (I)
8.5.3.e. make conjectures to formulate new questions for future studies. (l)
Day 173 May 16th Chapter 13 Assessment