SEPTEMBER (Pacing Guide = 17 Days) - CHAPTER 1 Numerical Expressions and Factors Targeted Standard(s): CCSS 6.NS.2, 6.NS.4, 6.EE.1, 6.EE.2 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 1 instruction focuses on fluently dividing multi-digit numbers using the standard algorithm, finding common factors and multiples, writing and evaluating numerical expressions, and elements of the Standards for Mathematical Practice. Essential Questions: How do you know which operation to choose when solving a real-life problem? How can you use repeated factors in real-life situations? What is the effect of inserting parentheses into a numerical expression? Without dividing, how can you tell if a number is divisible by another number? How can you find the greatest common factor of two or more numbers? How can you find the least common multiple of two or more numbers? 1. Whole Numbers Operations 2. Powers and Exponents 3. Order of Operations 4. Prime Factorization 5. Greatest Common Factor 6. Least Common Multiple determine what operations to perform divide multi-digit whole numbers write expressions as powers find values of powers evaluate numerical expressions with whole number exponents use divisibility rules to find prime factorization of numbers use diagrams to identify common factors find greatest common factors use diagrams to identify common multiples find least common multiples add & subtract fractions solve real-life problems How to Use Your Math Book and Scavenger Hunt pgs. xxxvii & xxxix What You Learned Before pg. 1 For each lesson: o guided practice & problem solving o independent practice & problem Chapter Review pgs. 45-48 Cooperative learning Direct instruction Graphic organizers Multiple representations (visuals, Games & Puzzles Differentiated Instruction: Formative Assessments: o homework o exit tickets Summative Assessments: Classroom at BigIdeasMath.com; Apps for ebook, math videos, & math solutions via BigIdeasMath.com; math tool paper, manipulatives, four-function calculator with square root and percentage functions, scientific calculator Revised: December 1, 2015 Page 1
OCTOBER (Pacing Guide = 20 Days) - CHAPTER 2 Fractions and Decimals Targeted Standard(s): CCSS 6.NS.1, 6.NS.3 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 2 instruction focuses on dividing fractions and mixed numbers, computing with decimals efficiently, and elements of the Standards for Mathematical Practice. Essential Questions: What does it mean to multiply fractions? How can you divide by a fraction? How can you divide by a mixed number? How can you add and subtract decimals? How can you multiply decimals? How can you divide decimals? 1. Multiplying Fractions multiply fractions by fractions, What You Learned Before pg. 53 Formative Assessments: fractions by mixed numbers, and For each lesson: 2. Dividing Fractions mixed numbers by mixed numbers write reciprocals of numbers, divide 3. Dividing Mixed Numbers fractions by fractions, divide with o guided practice & problem solving o homework whole numbers & fractions 4. Adding and Subtracting Decimals divide mixed numbers 5. Multiplying Decimals add & subtract decimals Summative Assessments: multiply decimals Chapter Review pgs. 101-104 6. Dividing Decimals divide decimals Cooperative learning evaluate expressions Direct instruction use order of operations Graphic organizers solve real-life problems Multiple representations (visuals, Games & Puzzles Differentiated Instruction: Classroom at BigIdeasMath.com; Apps for ebook, math videos, & math solutions via BigIdeasMath.com; math tool paper, manipulatives, four-function calculator with square root and percentage functions, scientific calculator Revised: December 1, 2015 Page 2
NOVEMBER (Pacing Guide = 13 Days) - CHAPTER 3 Algebraic Expressions and Properties Targeted Standard(s): CCSS 6.NS.4, 6.EE.2a, 6.EE.2c, 6.EE.3, 6.EE.4 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 3 instruction focuses on writing and evaluating algebraic expressions; finding the greatest common factor in algebraic expressions; applying properties of addition and multiplication to show expressions are equivalent; and elements of the Standards for Mathematical Practice. Essential Questions: How can you write and evaluate an expression that models real-life? How can you write an expression that represents an unknown quantity? Does the order in which you perform an operation matter? How do you use mental math to multiply two numbers? 1. Algebraic Expression use order of operations to evaluate What You Learned Before pg. 109 Formative Assessments: expressions For each lesson: 2. Writing Expressions use variable to represent numbers in algebraic expressions 3. Properties of Addition & Multiplication write algebraic expressions o guided practice & problem solving o homework 4. The Distributive Property use properties of operations to generate equivalent expressions use the Distributive Property to find Summative Assessments: products Chapter Review pgs. 143-146 use the Distributive Property to Cooperative learning simplify algebraic expressions Direct instruction use the Distributive Property to Graphic organizers produce equivalent expressions Multiple representations (visuals, factor numerical and algebraic expressions Games & Puzzles solve real-life problems Differentiated Instruction: Revised: December 1, 2015 Page 3
DECEMBER (Pacing Guide = 13 Days) - CHAPTER 4 Areas of Polygons Targeted Standard(s): CCSS 6.G.1, 6.G.3 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 4 instruction focuses on finding areas of triangles, special quadrilaterals, and polygons; finding the distance between points with the same x- or y-coordinate; drawing polygons in the coordinate plane given vertices and finding lengths of sides; and elements of the Standards for Mathematical Practice. Essential Questions: How can you derive a formula for the area of a parallelogram? How can you derive a formula for the area of a triangle? How can you derive a formula for the area of a trapezoid? How can you find the lengths of line segments in a coordinate plane? 1. Areas of Polygons find areas of parallelograms What You Learned Before pg. 151 Formative Assessments: find areas of triangles For each lesson: 2. Areas of Triangles find areas of trapezoids find areas of composite figures 3. Areas of Trapezoids draw polygons in the coordinate o guided practice & problem solving o homework plane 4. Polygons in the Coordinate Plane find distances in the coordinate plane use order of operations Summative Assessments: solve real-life problems Chapter Review pgs. 181-184 Cooperative learning Direct instruction Graphic organizers Multiple representations (visuals, Games & Puzzles Differentiated Instruction: Revised: December 1, 2015 Page 4
JANUARY (Pacing Guide = 18 Days) - CHAPTER 5 Ratios and Rates Targeted Standard(s): CCSS 6.RP.1, 6.RP.2, 6.RP.3a, 6.RP.3b, 6.RP.3c, 6.RP.3d statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 5 instruction focuses on understanding ratios, rates, and unit rates; comparing ratios using tables; finding percent as a rate per 100; solving problems involving finding the whole, given a part and the percent; using ratio reasoning to convert measurement units; and elements of the Standards for Mathematical Practice. Essential Questions: How can you represent a relationship between two quantities? How can you find two ratios that describe the same relationship? How can you use rates to describe changes in real-life problems? How can you compare two ratios? What is the connection between ratios, fractions, and percents? How can you use mental math to find the percent of a number? How can you compare lengths between the customary and metric systems? 1. Ratios use ratios to describe the What You Learned Before pg. 189 Formative Assessments: relationship between two quantities For each lesson: 2. Ratio Tables use ratio tables to find equivalent ratios 3. Rates write unit rates o guided practice & problem solving o homework solve unit rate problems 4. Comparing and Graphing Ratios graph values from ratio tables write percents as fractions with 5. Percents denominators of 100 Summative Assessments: write fractions as percents Chapter Review pgs. 239-242 6. Solving Percent Problems find percents of numbers Cooperative learning find the whole given the part and the Direct instruction 7. Converting Measures percent Graphic organizers use conversion factors (rates) to Multiple representations (visuals, convert units of measurement use order of operations Games & Puzzles solve real-life problems Differentiated Instruction: Revised December 1, 2015 Page 5
FEBRUARY (Pacing Guide = 15 Days) - CHAPTER 6 Integers and the Coordinate Plane Targeted Standard(s): CCSS 6.NS.5, 6.NS. 6a, 6.NS.6b, 6.NS.6c, 6.NS.7a, 6.NS.7b, 6.NS.7c, 6.NS.7d, 6.NS.8 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 6 instruction focuses on describing quantities with positive and negative numbers; comparing and ordering integers and absolute value numbers; graphing ordered pairs in all four quadrants of the coordinate plane; and elements of the Standards for Mathematical Practice. Essential Questions: How can you represent numbers that are less than 0? How can you use a number line to order real-life events? How can you use a number line to compare positive and negative fractions and decimals? How can you describe how far an object is from 0? How can you graph and locate points that contain negative numbers in a coordinate plane? 1. Integers use positive and negative numbers What You Learned Before pg. 247 Formative Assessments: to describe real-life situations For each lesson: 2. Comparing and Ordering Integers graph integers on a number line use a number line to compare 3. Fractions & Decimals on the Number Line positive and negative integers o guided practice & problem solving o homework use a number line to order positive 4. Absolute Value and negative integers for real-life situations 5. The Coordinate Plane graph rational numbers on a number Summative Assessments: line Chapter Review pgs. 285-288 find the absolute value of numbers Cooperative learning use absolute value to compare Direct instruction numbers in real-life situations Graphic organizers describe the locations of points in Multiple representations (visuals, the coordinate plane plot points in the coordinate plane Games & Puzzles given ordered pairs Differentiated Instruction: find distance between point in the coordinate plane reflect points in the coordinate plane solve real-life problems Revised December 1, 2015 Page 6
LATE FEBRUARY TO MID-MARCH (Pacing Guide = 18 Days) - CHAPTER 7 Equations and Inequalities Targeted Standard(s): CCSS 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 7 instruction focuses on determining if a value is a solution; solving one-step equations; representing constraints with inequalities and recognizing they can have infinitely many solutions; solving one-step inequalities; and elements of the Standards for Mathematical Practice. Essential Questions: How does rewriting a word problem help you solve the word problem? How can you use addition or subtraction to solve an equation? How can you use multiplication or division to solve an equation? How can you write an equation in two variables? How can you use a number line to represent solution of an inequality? How can you use addition or subtraction to solve an inequality? How can you use multiplication or division to solve an inequality? 1. Writing Equations in One Variable write word sentences as equations What You Learned Before pg. 293 Formative Assessments: 2. Solving Equations Using Addition or use addition or subtraction to solve equations For each lesson: Subtraction use substitution to check answers use multiplication or division to solve o guided practice & problem solving o homework 3. Solving Equations Using Multiplication or equations Division identify independent and dependent variables 4. Writing Equations in Two Variables write equations in two variables Summative Assessments: use tables and graphs to analyze Chapter Review pgs. 345-348 5. Writing and Graphing Inequalities the relationship between two Cooperative learning variables Direct instruction 6. Solving Inequalities Using Addition or write word sentences as inequalities Graphic organizers Subtraction use a number line to graph the Multiple representations (visuals, solution set of inequalities 7. Solving Inequalities Using Multiplication or Division use inequalities to represent real-life Games & Puzzles situations Differentiated Instruction: use addition or subtraction to solve inequalities use multiplication or division to solve inequalities solve real-life problems Revised December 1, 2015 Page 7
LATE MARCH TO MID-APRIL (Pacing Guide = 12 Days) - CHAPTER 8 Surface Area and Volume Targeted Standard(s): CCSS 6.G.2, 6.G.4 statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 8 instruction focuses on finding areas of triangles, special quadrilaterals, and polygons; using nets made up of rectangles and triangles to find surface areas; finding the volumes of prisms with fractional edge lengths; and elements of the Standards for Mathematical Practice. Essential Questions: How can you draw three-dimensional figures? How can you find the area of the entire surface of a prism? How can you use a net to find the surface area of a pyramid? How can you find the volume of a rectangular prism with fractions edge lengths? 1. Three-Dimensional Figures draw three-dimensional figures What You Learned Before pg. 353 Formative Assessments: find the number of faces, edges, and For each lesson: 2. Surface Areas of Prisms vertices of solids use nets to represent prisms 3. Surface Areas of Pyramids find the surface area of prisms o guided practice & problem solving o homework use nets to represent pyramids 4. Volumes of Rectangular Prisms find the surface area of pyramids find the volume of prisms by using formulas Summative Assessments: solve real-life problems Chapter Review pgs. 381-384 Cooperative learning Direct instruction Graphic organizers Multiple representations (visuals, Games & Puzzles Differentiated Instruction: BigIdeasMath.com which may include lessons tutorials & presentations, online test practice, performance tasks, games, and additional resources; Dynamic Revised December 1, 2015 Page 8
MID-APRIL TO MID-MAY (Pacing Guide = 14 Days) - CHAPTER 9 Statistical Measures Targeted Standard(s): CCSS 6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5a, 6.SP.5c statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 9 instruction focuses on recognizing statistical questions as ones anticipating variability; understanding that data used to answer statistical questions has a distribution that can be described by center and spread; using measures of center to summarize all of the values in a data set with a single number; using measures of variation to summarize how all of the values in a data set vary with a single number; and elements of the Standards for Mathematical Practice. Essential Questions: How can you tell whether a question is a statistical question? How can you find an average value of a data set? In what other ways can you describe an average of a data set? How can you describe the spread of a data set? How can you use the distances between each data value and the mean of a data set to measure the spread of a data set? 1. Introduction to Statistics recognize statistical questions What You Learned Before pg. 389 Formative Assessments: use dot pots to display numerical For each lesson: 2. Mean data understand the concept of the mean 3. Measures of Center of data sets o guided practice & problem solving o homework find the mean of data sets 4. Measures of Variation compare and interpret the means of data sets 5. Mean Absolute Deviation understand the concept of measures Summative Assessments: of center Chapter Review pgs. 425-428 find the median and mode of data Cooperative learning sets Direct instruction find the range of data sets Graphic organizers find the interquartile range of data Multiple representations (visuals, sets check for outliers in data sets Games & Puzzles understand the meaning of mean Differentiated Instruction: absolute deviation find the mean absolute deviation of data sets solve real-life problems Revised December 1, 2015 Page 9
MID-MAY TO MID-JUNE (Pacing Guide = 13 Days) - CHAPTER 10 Data Displays Targeted Standard(s): CCSS 6. SP.2, 6.SP.4, 6.SP.5c, 6.SP.5d statistical thinking (http://www.corestandards.org/math/content/6/introduction/). In Chapter 10 instruction focuses on displaying data on a number line, including line (dot) plots, stem-and-leaf plots, histograms, and box-and-whisker plots; recognizing that a measure of center for a numerical data set summarizes all of its values with a single number and a measure of variation describes how its values vary with a single number; understanding that data used to answer statistical questions has a distribution that can be described by center, spread, and shape; choosing appropriate measures of center and variation based on shape; and elements of the Standards for Mathematical Practice. Essential Questions: How can you use place values to represent data graphically? How can you use intervals, tables, and graphs to organize data? How can you describe the shape of the distribution of a data set? How can you use quartiles to represent data graphically? 1. Stem-and-Leaf Plots make and interpret stem-and-leaf What You Learned Before pg. 433 plots For each lesson: 2. Histograms make histograms 3. Shapes of Distribution use histograms to analyze data describe shapes of distributions o guided practice & problem solving 4. Box-and-Whisker Plots center and variation to represent o independent practice & problem data sets make and interpret box-and-whisker plots Chapter Review pgs. 467-470 choose appropriate measure of compare box-and-whisker plots Cooperative learning solve real-life problems Direct instruction Graphic organizers Multiple representations (visuals, Games & Puzzles Differentiated Instruction: Formative Assessments: o homework o exit tickets Summative Assessments: Revised December 1, 2015 Page 10