7th Grade Pacing Guide

7th Grade Pacing Guide 2011-2012 Section Section Title page Brain Pop SPI GLE CFU Vocabulary CHAPTER 1: EXPRESSIONS & PATTERNS EXPRESSIONS 1-1a Powers & Exponents 25 Numbers & Operations: Exponents 2.1 Simplify numerical expressions involving rational numbers. 2.3 Use rational numbers and roots of perfect squares/cubes to solve contextual problems 2.5 Understand and work with squares, cubes, square roots and cube roots. 2.2 Develop and analyze algorithms and compute efficiently with integers and rational numbers base, cubed, evaluate, exponent, exponential form, factors, powers, squared, standard form 1-1b Numerical Expressions 29 Numbers & Operations: Order of Operations 2.1, 2.3 2.2 Understand and work with the properties of and operations on the system of rational numbers., 1.7 Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world. 2.2 numerical expession, order of operations 1-1c Algebraic Expressions 33 3.1 Evaluate algebraic expressions involving rational values for coefficients and/or variables. 2.2 3.2 Represent and analyze mathematical situations using algebraic symbols. algebra, algebraic expression, coefficient, define a variable, variable 1-1d Properties 38 Number & Operations: Associative Property, Commutative Property, Distributive Property 2.1, 2.3 2.2, 3.1 Recognize and generate equivalent forms for simple algebraic expressions. 2.3 Recognize that rational numbers satisfy the commutative and associative laws of addition and multiplication and the distributive law. equivalent expressions, properties Page 1

PATTERNS Section Section Title page Brain Pop SPI GLE CFU Vocabulary 1-2a PSI: Look for a Pattern 42 Number & Operations: Fibonacci Sequence 1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words., 2.3 1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. 1.5 Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions. 1-2b Sequences 44 1.2 1.4 Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies., 1.5, 1.7 3.2 arithmetic sequence, geometric sequence, sequence, term 1-2c EXTEND: Sequences 50 1.2 1.3 Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas., 1.5 3.2 SQUARE ROOTS 1-3a EXPLORE: Perfect Squares 52 2.3 1.3, 1.8 Use technologies/ manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts., 2.5 Page 2

1-3b Squares & Square Roots 53 Numbers & Operations: Square Roots, Rational & Irrational Numbers 2.3 1.8, 2.5 perfect square, radical sign, square, square root Les. 18 Simplify Square Roots 820 2.12 Recognize mn = m n and ( m) 2 = m. 1-3c Estimate Square Roots 57 2.3, 2.4 Determine the approximate location of square/cube roots on a number line. 1.2, 1.8, 2.5 2.9 Efficiently compare and order rational numbers and roots of perfect squares/cubes; determine their approximate locations on a number line, 2.10 Recognize that when a whole number is not a perfect square, then its square root is not rational and cannot be written as the ratio of two integers., 2.11 Estimate square/cube roots and use calculators to find approximations. Les. 19 Cube Roots 822 2.3 CHAPTER 2: INTEGERS INTEGERS & THE COORDINATE PLANE 2-1b Integers & Absolute Value 77 Numbers & Operations: Absolute Value 2.1 2.2 2.4 Understand that a and -a are additive inverses and are located the same distance from zero on the number line; relate distance from zero to absolute value. absolute value, graph, integer, negative integer, positive integer 2-1c The Coordinate Plane 81 Geometry & Measurement: The Coordinate Plane NA (needed for future sections) 1.4, 1.7 coordinate plane, quadrant, ordered pair, origin, x-axis, x-coordinate, y-axis, y- coordinate Page 3

ADD & SUBTRACT INTEGERS Section Section Title page Brain Pop SPI GLE CFU Vocabulary 2-2b Add Integers 88 2.1, 2.5 Solve contextual problems that involve operations with integers. 1.8, 2.1 Extend understandings of addition, subtraction, multiplication, and division to integers., 2.2 2.2, 2.3, 2.4, 2.6 Use the number line to demonstate addition and subtraction with integers. additive inverse, opposites 2-2d Subtract Integers 95 2.1, 2.5 1.8, 2.1, 2.2 2.2, 2.6 2-3a PSI: Look for a Pattern MULTIPLY & DIVIDE INTEGERS 100 1.2 1.2, 1.5 2-3c Multiply Integers 104 2.1, 2.5 1.4, 2.1, 2.2 2.2, 2.3, 2.5 Understand that -(-a) = a for any number a. 2-3d Divide Integers 109 2.1, 2.5 1.8, 2.1, 2.2 2.2 CHAPTER 3: RATIONAL NUMBERS RATIONAL NUMBERS 3-1c Compare & Order Rational Numbers 133 2.2 Compare rational numbers using appropriate rational numbers. 1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning., 1.7, 1.8, 2.2 1.1 Recognize common abbreviations (such as gcd/gcf and lcd)., 2.1 Understand that the set of rational numbers includes any number that can be written as ratio of two integers in which the denominator is not zero. common denominator, least common denominator (LCD), rational numbers Les. 20 Relative Error 824 Data Analysis: Rounding, Geometry & Measurement: Estimating 1.2 Recognize round-off error and the inaccuracies it introduces., 2.15 Report results of calculations appropriately in a given context (i.e. using rules of rounding, degree of accuracy, and/or significant digits.) round-off error Page 4

ADD & SUBTRACT FRACTIONS Section Section Title page Brain Pop SPI GLE CFU Vocabulary 3-2a Add & Subtract Like Fractions 139 Numbers & Operations: Fractions, Reducing Fractions, Adding & Subtracting Fractions 2.1, 2.3 2.2 2.2 like fractions 3-2c Add & Subtract UnLike Fractions 146 2.1, 2.3 1.8, 2.2 1.3 Check answers both by estimation and by appropriate independent calculations, using calculators or computers judiciously., 2.2 unlike fractions 3-2d Add & Subtract Mixed Numbers 152 3-3b Multiply Fractions 160 Numbers & Operations: Mixed Numbers Numbers & Operations: Multiplying & Dividing Fractions 2.1, 2.3 1.2, 2.2 1.3, 2.2 MULTIPLY & DIVIDE FRACTIONS 2.1, 2.3 1.7, 2.2 1.1, 2.2, 2.3 3-3c PSI: Draw a Diagram 166 2.1, 2.3 1.2 3-3d Divide Fractions 168 2.1, 2.3 1.2, 2.2 1.3, 2.2 reciprocal Les. 21 Algebraic Expressions & Rational Numbers 826 3.1 MONOMIALS 3-4a Multiply & Divide Monomials 176 Algebra: Multiplying & Dividing Exponents 2.1 3.1 3.1 Perform basic operations on linear expressions (including grouping, order of operations, exponents, simplifying, and expanding.) monomial 3-4b Negative Exponents 181 2.1 2.6 Introduce the concept of negative exponents. 2.13 Use the meaning of negative exponents to represent small numbers, translate between scientific and standard notation. negative exponent Page 5

3-4c Scientific Notation 185 Numbers & Operations: Standard & Scientific Notation 2.1 1.4, 2.6, 2.7 Understand and use scientific notation. 1.11 Translate from calculator notation to scientifc/ standard notation. 2.13, 2.14 Express numbers in scientific notation and recognize its importance in representing the magnitude of a number. scientific notation END FIRST NINE WEEKS CHAPTER 4: EQUATIONS & INEQUALITIES ADDITION & SUBTRACTION EQUATIONS 4-1a PSI: Work Backward 202 2.3 1.2 4-1d Solve One-Step Addition & Subtraction Equations 208 Algebra: Equations with Variables 3.7 Translate between verbal and symbolic representations of realworld phenomena involving linear equations. 1.4, 1.8, 3.7 Use mathematical models invovling linear equations to analyze real-world phenomena., 3.8 Use a variety of strategies to efficiently solve linear equations and inequalities. 1.10 Model algebraic equations with manipulatives, technology and pencil and paper. equation, equivalent equations MULTIPLICATION & DIVISION EQUATIONS 4-2b Solve One-Step Multiplication & Division Equations 215 3.7 1.4, 1.8, 3.7, 3.8 1.10, 3.2 coefficient, formula 4-2d Equations with Rational Coefficients 221 3.6 Solve linear equations with rational coefficients symbolically or graphically., 3.7 1.8, 3.7, 3.8 1.10, 3.2 multiplicative inverse,reciprocal 4-3b Solve Two-Step Equations 230 Algebra: Two-Step Equations 3.6, 3.7, 3.8 Solve contextual problems involving two-step linear equations. MULTI-STEP EQUATIONS 3.7, 3.8 1.10, 3.2 two-step equation Page 6

Les. 8 More Two-Step Equations ( This would be a good place to add some work on simplifying polynomials.) 783 Algebra: Polynomials 4-3d Solve Equations with Variables on Both Sides 236 3.7, 3.8 3.8 3.2 At this point, teachers may want to add a lesson on manipulating formulas. (If so, Brain Pop -Algebra: Distance, Rate, & Time may be helpful.) INEQUALITIES 4-4b Solve Inequalties by Addition or Subtraction 244 Algebra: Inequalities, Graphing & Solving Inequalities 3.9 Solve linear inequalities in one variable with rational coefficients symbolically or graphically. 1.8, 3.8 3.2 4-4c Solve Inequalties by Multiplication or Division 249 3.9 3.8 3.2, 3.14 Understand that when solving linear inequalities, multiplication or division by a negative reverses the inequality symbol. Les. 9 Solve Two-Step Inequalities 787 two-step inequality CHAPTER 5: Proportions & Similarity PROPORTIONS 5-1b Rates 266 Data Analysis: Comparing Prices 2.6 Express the ratio between two quantities as a percent, and a percent as a ratio or fraction., 2.7 Use ratios and proportions to solve problems. 2.3 Develop an understanding of and apply proportionality., 2.4 Use ratios, rates, and percents to solve single- and multi-step problems in various contexts. 2.8 Apply ratios, rate, proportions and percents (such as discounts, interest, taxes, tips, distance/rate/time, and percent increase or decrease.), 3.10 Solve problems involving unite rates (e.g., miles per hour, words per minute). rates, unit rate 5-1c Proportional & Nonproportional Relationships 272 1.3, 2.6, 2.7 2.3, 2.4 2.8 nonproportional, proportional Page 7

5-1d Solve Proportions 276 Les. 2 Graphing Proportional Relationships 765 Ratio, Proportions, & Percent: Proportions 1.1 Use proportional reasoning to solve mixture/concentration problems., 2.7 2.3, 2.4 SCALE DRAWINGS & MODELS 5-2a PSI: Draw a Diagram 282 2.7 1.2, 2.3, 2.4 2.7 Write number sentences to solve contextual problems involving ratio and percent., 2.8 cross products. equivalent ratios, proportion ordered pair, coordinate plane, x- coordinate, y-coordinate, origin, x-axis, y- axis, quadrants 5-2b Scale Drawings 284 Ratio, Proportions, & Percent: Scale Drawings 1.4 Use scales to read maps., 2.7 1.4, 1.7, 2.3, 4.4 Understand and use ratios, derived quantities, and indirect measurement. 1.7 Explain and demonstrate how scale in maps and drawings shows relative size and distance., 1.8 Recognze the applications of scale factor by exploring blueprints, shadow measuring, and scale models. scale, scale drawing, scale factor, scale model SIMILARITY & PROPORTIONAL REASONING 5-3a Similar Figures 293 Geometry & Measurement: Similar Figures 4.1 Solve contextual problems., 4.2 Use SSS, SAS, and AA to determine if two problems are similar. 1.1, 1.3, 4.1 Understand the application of proportionality with similar triangles., 4.4 4.1 Solve problems involving indirect measurement such as finding the height of a building by comparing its shadow with the height and shadow of a known object., 4.2 Use similar triangles and proportionality to find the lengths of unknown line segments in a triangle., 4.4 Compare angles, side lengths, perimeters and areas of similar shapes. corresponding angles, corresponding sides, indirect measurement Les. 22 Similar Triangles 828 4.2 SSS Similarity, SAS Similarity, AA Similarity Page 8

5-3b Perimeter & Area of Similar Figures 299 4.1, 4.3 Apply scale factor to solve problems involving area and volume. 2.3, 4.1, 4.3 Understand and use scale factor to describe the relationships between length, area, and volume. 4.3 Understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related,and the cube of the scale factor describes how corresponding volumes are related. CHAPTER 6: Percent PERCENTS 6-1b Percent of a Number 320 2.6 1.7, 2.4 2.7 6-1c Percent and Estimation 325 2.6 1.2, 2.4 2.7, 2.8 6-2b 6-2d The Percent Proportion PSI: Determine Reasonable Answers PROPORTIONS & EQUATIONS 332 2.6, 2.7 2.3, 2.4 2.7 percent proportion 342 NA 1.2, 2.4 APPLYING PERCENTS 6-3b Percent of Change 346 2.7 1.8, 2.4 2.8 percent of change, percent of decrease, percent of increase 6-3c Sales Tax and Tips 351 Ratio, Proportions, & Percent: Taxes 2.7 1.7, 2.4 2.7, 2.8 sales tax, tip, gratuity 6-3d Discount 355 2.7 1.4, 2.4 2.7, 2.8 discount Page 9

6-3e Simple Interest 359 Ratio, Proportions, & Percent: Interest, Mortgages 2.7 2.4 2.8 principal, simple interest CHAPTER 7: Linear Functions RATES & FUNCTIONS 7-1a EXPLORE: Relations & Functions 377 3.2 Determine whether a relation (expressed in various ways) is a function. 3.2 Understand and compare various representations of relations and functions, 3.3 Understand the concept of function as a rule that assigns to a given input one and only one number (the output). 3.3 Identify a function from a written description, table, graph, rule, set of ordered pairs, and/or mapping. 7-1b Equations & Functions 378 3.3 Given a table if inputs x and outputs f(x), identify the function rule and continue the pattern., 3.5 Represent proportional relationships with equations, tables, and graphs. 3.2, 3.3, 3.4 Use function notation where f(x) represents the output that the function f assigns to the input x. 3.4 Make tables of inputs x and outputs f(x) for a variety of rules that include rational numbers (including negative numbers) as inputs. dependent variable, domain, function, function notation, function rule, function table, independent variable, range, relation 7-1c Functions & Graphs 385 Algebra: Graphing Linear Equations 3.5 1.5, 3.2, 3.5 Understand and graph proportional relationships., 3.7 3.4, 3.5 Plot points to represent tables of linear function values., 3.6 Understand that the graph of a linear function f is the set of points on a line representing the ordered pairs (x, f(x)), 3.11 Relate the features of a linear equation to a table and/or graph of the equation. linear function 7-1d EXTEND: Graphing Technology: Graphing Relationships 400 3.3, 3.5, 3.7 1.3, 3.2 1.10, 3.11 Page 10

END 2ND NINE WEEKS Section Section Title page Brain Pop SPI GLE CFU Vocabulary SLOPE 7-2a EXPLORE: Rate of Change 391 3.4 Interpret the slope of a line as a unit rate given the graph of a proportional relationship., 3.5 1.5, 3.5, 3.6 Conceptualize the meanings of slope using various interpretations, representations and contexts. 1.6 Develop meaning of intercept and rate of change in contextual problems., 3.9 Identify a function exhibiting a constant rate of change as a linear function and identify the slope as a unit rate. 7-2b Constant Rate of Change 392 3.4, 3.5 1.5, 2.4, 3.6 1.6, 3.8 Understand slope as the ratio of vertical change to horizontal change., 3.9 constant rate of change, nonlinear function, rate of change 7-2c Slope 396 Algebra: Slope & Intercept 3.4 1.5, 3.5, 3.6, 3.7 1.6, 3.8, 3.9, 3.10 slope 7-2d EXTEND: Graphing Technology: Compare Graphs 400 3.5 1.8, 3.2 1.10, 3.11 VARIATION 7-3a PSI: Use a Graph 402 3.5 1.2,1.5, 3.2 Page 11

7-3b EXPLORE: Proportional & Nonproportional Relationships 404 1.3 Recognize whether information given in a table, graph, or formula suggests a directly proportional., linear, inversely proportional, or other nonlinear relationship., 3.5 1.5, 1.8, 3.5, 3.6 3.7 Distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x). 7-3c Direct Variation 405 1.3, 3.4 1.5, 3.5 1.5 Understand that a linear function I which f(0) = 0 is called a directly proportional relationship., 3.7, 3.12 Use linear equations to solve problems and interpret the meaning of slope, m, and the y-intercept, b, in f(x) = mx + b in terms of the context., 3.13 Given a graph that exhibits the intersection of a line and the y-axis, write a linear function in slopeintercept form; y = mx + b. constant of variation, direct variation slopeintercept form, y-intercept 7-3d EXPLORE: Inverse Variation 411 1.3 1.5 1.4 Recognize quantities that are inversely proportional (such as the relationship between the lengths of the base and the side of a rectangle with fixed area). Page 12

7-3e Inverse Variation 412 1.3 1.7, 3.5 1.4 inverse variation Les. 24 Identify Relationships 834 1.3 CHAPTER 8: Probability & Predictions PROBABILITY 8-1a Probability & Simple Events 429 Probability: Basic Probability NA 1.1, 1.7, 5.5 Understand and apply basic concepts of probability. complementary event, geometric probability, outcome, probability, random, simple event 8-1b Sample Spaces 435 5.5 5.7 Use a tree diagram or organized list to determine all possible outcomes of a simple probability experiment. odds in favor, sample space, tree diagram 8-1c Count Outcomes 440 5.5 5.7 Fundamental Counting Principle COMPOUND EVENTS 8-2a EXPLORE: Independent & Dependent Events 449 NA 1.8, 5.5 8-2b Independent & Dependent Events 450 Probability: Compound Events, Independent & Dependent Events NA 5.5 compound events, dependent events, disjoint events, independent events Page 13

PREDICTIONS Section Section Title page Brain Pop SPI GLE CFU Vocabulary 8-3a Theoretical & Experimental Probability 458 5.4 Use theoretical probability to make predictions. 1.4, 5.5 5.4 Use proportional reasoning to make predictions about results of experiments and simulations. experimental probability, theoretical probability 8-3b EXTEND: Simulations 463 5.4 1.8, 5.5 5.4 8-3c PSI: Predictions 464 1.2, 5.5 8-3d EXPLORE: Fair & Unfair Games 5.5 Evaluate the design of an experiment. 466 5.4 1.3, 1.8, 5.5 5.5 8-3e Fair & Unfair Games 466 5.4 1.3, 1.8, 5.5 5.5 fair game, unfair game 8-3f Use Data to Predict 468 5.3 Formulate questions and design studies to collect data about a characteristic shared by two populations, or different characteristics within one population., 5.5 population, sample, survey CHAPTER 9: Statistical Displays MEASURES OF CENTRAL TENDENCY 9-1b Measures of Central Tendency 491 Probability: Mean, Median, & Mode 1.7, 5.1 Collect, organize, and 5.3 Calculate and interpret analyze both single- and twovariable data. 5.4 Use the mean, median, upperquartile, lower-quartile, and proportional reasoning to make interquartile range of a set predictions about results of of data. experiments and simulations. mean, measures of central tendency, median, mode 9-2a Measures of Variation MEASURES OF VARIATION 498 5.3 5.4 interquartile range, lower quartile, measures of variation, outlier, quartile, range, upper quartile Page 14

9-2b Box-and-Whisker Plots 504 5.3 5.1, 5.2 Select, create, and use graphical representations of data., 5.4 5.1 Create and interpret box-andwhisker plots and stem-and-leaf plots., 5.2 Interpret and solve problems using information presented in various visual forms. box-and-whisker- plot STATISTICAL DISPLAYS 9-3b Circle Graphs 514 Data Analysis: Graphs 5.1, 5.2 5.1, 5.2, 5.4 5.5 circle graph 9-3c Histograms 520 5.1, 5.2 5.1, 5.2 5.5 cumulative relative frequency, histogram, relative frequency 9-3e Stem-and-Leaf Plots 526 5.1, 5.2, 5.3 5.1, 5.2, 5.4 9-4a PSI: Use a Graph 532 5.1, 5.2 1.2, 5.2 9-4b Scatter Plots & Lines of Best Fit MORE STATISTICAL DISPLAYS back-to-back stem-and-leaf plot, stem, stem-and-leaf plot 534 5.1, 5.2 1.4, 5.1, 5.2 line of best fit, scatter plot 9-4c Select an Appropriate Display 540 5.1, 5.2 1.7, 5.1, 5.2 5.1, 5.2, 5.5 END 3RD NINE WEEKS CHAPTER 11: Measurement & Proportional Reasoning CONVERT MEASUREMENTS 11-1b Convert Customary Units 626 1.4, 4.2 Apply proportionality to converting among different units of measurements to solve problems involving rates such as a motion at a constant speed., 4.4 dimensional analysis, unit ratio Page 15

11-1c Convert Metric Units 631 4.2, 4.4 accuracy, gram, kilogram, liter, meter, metric system 11-1d Convert Between Systems 635 1.7, 4.2, 4.4 11-1e Convert Rates 639 4.2, 4.4 4.5 11-1f 11-2b 11-2c Convert Units of Area & Volume Explore: Changes in Scale Changes in Dimensions 643 4.2, 4.4 SIMILAR SOLIDS 652 4.3 1.3, 4.3 4.3, 4.4 654 4.3 1.3, 4.3 4.3, 4.4 similar solids During the rest of 4th nine weeks: 1. Finish any uncovered topics. 2. Review for TCAPS. 3. Additional topics at teacher's discretion. (Suggest selections from chapters 10, 12 that will be relevant preparation for 8th grade.) Page 16