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6th Grade Math Pacing Guide CCGPS Operations with decimal fractions positive rational numbers, factors, multiples, decompose, prime numbers, prime Addition and subtraction of common factorization, Fundamental Theorem of fractions and mixed numbers with Arithmetic, GCF, LCM, evaluate, surface unlike denominators such as area, metric system of measurement, 2,3,4,5,6,8,10, and 12 customary system of measurement,proportional relationships, Taught Continuously right rectangular prism, cylinder, pyramid, Skills to Maintain Terms/Symbols cone, geometric solid, net, geometric figures, line symmetry, rotational symmetry, Modeling multiplication of common fractions similar plane figures, scale factor, scale drawings, relations, varying quantities, ratio, Modeling percent direct proportion, proportions, proportional reasoning, frequency distributions, Graphing data pictographs, histograms, bar graphs, line Multiples and factors graphs, circle graphs, line plot, frequency Perimeter, capacity, and area of table, experimental probability, theoretical geometric figures probability, sampling, event, random sample, population, non-routine word Evaluating algebraic expressions problems. 1 6th Grade Math Pacing Guide CCGPS 1st 8 Weeks CCGPS Related GPS standards Resources Schedule MCC6.NS.2: Fluently divide multi-digit M6N1: Students will understand the meaning of 3 Weeks- 1 week numbers using the standard the four arithmetic operations as related to positve comp. fluency? 1 algorithm. rational numbers and will use these concepts to week decimals? 1 solve problems. week factor/multiples MCC6.NS.3 Fluently add, subtract, M6N1g. Solve problems involving fractions, McDougal Littell: Chapter and fractions? multiply, and divide multi-digit decimals, and percents. 2 resources decimals using the standard algorithm for each operation. Compute fluently with multi-digit M6N1a. Apply factors and multiples McDougal Littell: Chapter numbers and find common factors 4 lesson 2, 4 resources and multiples. MCC6.NS.4: Find the greatest M6N1c. Determine the greatest common factor McDougal Littell: Chapter common factor of two whole numbers (GCF) and the least common multiple (LCM) for a 4 lesson 2, 4 resources less than or equal to 100 and the set of numbers 1st 8 Weeks Unit 1: Number System Fluency least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor, (See standards for exampes) TRANSITION STANDARD- TAUGHT M6N1e. Multiply and divide fractions and mixed McDougal Littell: Chapter IN 5th and 6th FOR 2012-2013: numbers. 4 lesson 6, Chapter 5 MCC5.NF.6: Solve real world lesson 3, Consult with problems involving multiplication of 5th grade resources for fractions and mixed numbers, e.g., by modeling materials. using visual fraction models or equations to represent the problem. Apply and extend previous M6N1e. Multiply and divide fractions and mixed McDougal Littell: Chapter understandings of multiplication numbers. 5, lesson 4 and division to divide fractions by fractions 2 6th Grade Math Pacing Guide CCGPS MCC6.NS.1: Interpret and compute M6N1e. Multiply and divide fractions and mixed McDougal Littell: Chapter quotients of fractions, and solve word numbers. 5, lesson 4 problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. (See standards for examples) Understand ratio concepts and use M6A1: Students will understand the concept of 5 Weeks. 2 weeks ratio reasoning to solve problems. ratio and use it to represent quantitative Ratio/Rates? 1 week relationships. Percents? 2 weeks MCC6.RP.1: Understand the concept M6A1: Students will understand the concept of of a ratio and use ratio language to ratio and use it to represent quantitative describe a ratio relationship between relationships. two quantities. (see standards for examples) MCC6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. (see standards for examples) MCC6.RP.3: Use ratio and rate M6A2b. Use manipulatives or draw pictures to reasoning to solve real-world and solve problems involving proportional mathematical problems, e.g., by relationships. reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Using Equivalent Fractions 3 6th Grade Math Pacing Guide CCGPS MCC6.RP.3a: Make tables of M6A2e. Graph proportional relationships in the equivalent ratios relating quantities form y = kx and describe characteristics of the with whole-number measurements, graphs. find missing values in the tables, and Rate, Ratio and Proportional Reasoning, Using Equivalent Fractions plot the pairs of values on the coordinate plane. Use tables to compare ratios. Analyze and describe patterns arising from mathematical rules, tables, and graphs. MCC6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed. (see standards for examples) MCC6.RP.3c. Find a percent of a M6A2c. Use proportions (a/b=c/d) to describe quanitity as a rate per 100 (e.g. 30% relationships and solve problems, including of a quantity means 30/100 times the percent problems. quantity); solve problems involving finding the whole given a part and the percent. Explore and model percents using multiple representations. MCC6.RP.3d: Use ratio reasoning to M6M1: Students will convert from one unit to convert measurement unitsl another within one system of measurement manipulate and transform units (customary or metric) by using proportional appropriately when multiplying or relationships. dividing quantities. Students will convert from one unit to another within one system of measurement Unit 2: (customary or metric) by using proportional relationships. 4 6th Grade Math Pacing Guide CCGPS 2nd 8-Weeks CCGPS Related GPS standards Resources Schedule Apply and Extend previous M6A3: Students will evaluate algebraic understandings of arithmetic to expressions, including those with exponents, and algebraic expressions. solve simple one-step equations using each of the four basic operations. MCC6.EE.1: Write and evaluate M6A3: Students will evaluate algebraic numerical expressions involving expressions, including those with exponents, and whole-number exponents. solve simple one-step equations using each of the four basic operations. MCC6.EE.2 Write, read, and evaluate M6A3: Students will evaluate algebraic expressions in which letters stand for expressions, including those with exponents, and numbers. solve simple one-step equations using each of the four basic operations. MCC6.EE.2b. Identify parts of an M6A3: Students will evaluate algebraic expression using mathematical terms expressions, including those with exponents, and (sum, term, product, factor, quotient, solve simple one-step equations using each of the coefficient); view one or more parts of four basic operations. Unit 3 Expressions 2nd 8-Weeks an expression as a single entity. MCC6.EE.2c. Evaluate expressions M6A3: Students will evaluate algebraic at specific values for their variables. expressions, including those with exponents, and 3 Weeks. Include expressions that arise from solve simple one-step equations using each of the formulas in real-world problems. four basic operations. Perform arithmetic operations, including those involving those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). MCC6.EE.3 Apply the properties of M6A3: Students will evaluate algebraic operations to generate equivalent expressions, including those with exponents, and expressions. solve simple one-step equations using each of the four basic operations. 5 6th Grade Math Pacing Guide CCGPS MCC6EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). Unit 4: One-Step Equations and Inequalities M6A3: Students will evaluate algebraic 2nd 8-Weeks expressions, including those with exponents, and Reason about and solve one- solve simple one-step equations using each of the variable equations and inequalities four basic operations. MCC6.EE.5 Understand solving and equation or inequality as a process of M6A3: Students will evaluate algebraic answering a question: which values expressions, including those with exponents, and from a specified set, if any, make the solve simple one-step equations using each of the equation or inequality true. four basic operations. MCC6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem: understand that a variable can represent an M6A3: Students will evaluate algebraic unknown number, or, depending on expressions, including those with exponents, and the purpose at hand, any number in a solve simple one-step equations using each of the specified set. four basic operations. MCC6.EE7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = M6A3: Students will evaluate algebraic q and px = q for cases in which p, q, expressions, including those with exponents, and and x are all nonnegative rational solve simple one-step equations using each of the numbers. four basic operations. MCC6.EE.8 Write an inequality of the 5 weeks form x > c or x < c have infinitely M6A3: Students will evaluate algebraic many solutions; represent solutions of expressions, including those with exponents, and such inequalities on number line solve simple one-step equations using each of the diagrams. four basic operations. 6 5 weeks 6th Grade Math Pacing Guide CCGPS M6A3: Students will evaluate algebraic Represent and analyze quantitative expressions, including those with exponents, and relationships between dependant solve simple one-step equations using each of the and independent variables. four basic operations. MCC6.EE.9 Use variables to represent two quantities in a real- world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependant variable, in terms of the other quantity, thought of as the independant variable. Analyze the relationship between the M6A3: Students will evaluate algebraic dependant and independant variables expressions, including those with exponents, and using graphs and tables, and relate solve simple one-step equations using each of the these to the equation. four basic operations. Understand ratio concepts and use ratio reasoning to solve problems. MCC6.RP3a.b.c.d- State pacing Investigate state intent guide revisits standards from Unit 3 in in revisiting these the context of equations and standards- Frameworks? inequalities. Portal? 7 6th Grade Math Pacing Guide CCGPS 3rd 8-weeks Solve real-world and mathematical M6M2 Students wil use appropriate units of problems involving area, surface measure for finding length, perimeter, area, and area, and volume. volume and will express each quantity using the appropriate unit. M6M3d: Solve application problems involving the volume of fundamental solid figures. M6M4d: Solve application problems involving surface are of right rectangular prisms. MCC6.G.1 Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapesl apply these techniques in the context of solving real-world and mathematical Area and Volume problems. 3rd 8-weeks MCC6.G.2 Find the volume of a right M6M3 a.b.c.d (note- no longer finding volume of rectanglar prism with fractional edge cylinders or cones) 2 Weeks lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show tha the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 8 6th Grade Math Pacing Guide CCGPS MCC6.G.4 Represent three- M6M4 a,b,c,d (note- no longer finding surface dimensional figures using nets made area of cylinders or using nets beyond rectangular up of rectangles and triangles, and prisms) use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Develop understanding of statistical variability MCC6.SP.1 Recognize a statistical M6D1e. Relate the data analysis to the context of question as one that anticipates the questions posed. variability in the data related to the question and accounts for it in the answers. MCC6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. MCC6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions. Statistics MCC6.SP.4 Display numerical data in M6D1 b, Using data, construct frequency plots on a number line, including dot distributions, frequency tables, and graphs. 3 weeks plots, histograms, and box plots. 9 Statistics 6th Grade Math Pacing Guide 3 weeks CCGPS MCC6.SP5 Summarize numberical M6D1d. Use tables and graphs to examine data sets in relation to their context, variation that occurs within a group and variation such as by: a. Reporting the number that occurs between groups. of observations; b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. C. Giving quantitative measure of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered. Apply and extend previous understandings of numbers to the system of rational numbers. 10 s 6th Grade Math Pacing Guide CCGPS MCC6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 3rd 8-weeks ers and their Opposites 11 6th Grade Math Pacing Guide CCGPS MCC6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points 3rd 8-weeks on the line and in the plane with negative number coordinates .a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Given a point in the Rational Explorations: Numbers and their Opposites coordinate plane, determine the coordinates resulting from a reflection. c. Find and position integers and other reational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbrs on a coordinate plane. 3 weeks 12 Rational Explorations: Numbers and th 6th Grade Math Pacing Guide CCGPS 3 weeks MCC6.NS.7 Understand ordering and absolute value of rational numbers. A. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret - 3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3°C > -7° C to express the fact that -3°C is warmer than -7°C . c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of - 30 dollars, write /-30/ = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars. 13 6th Grade Math Pacing Guide CCGPS MCC6.NS.8 Solve real-world and mathematival problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. MCC6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find he length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 14 6th Grade Math Pacing Guide CCGPS Week by Week Pacing Guide * Note- this suggested week by week guide does not have much room for delay if the units draw long; particularly with getting all standards in prior to Benchmarks. There has been effort made to end neatly with breaks. This contains built- in CRCT review, however, any pushing back of 3rd quarter standards into this "free time" will miss content assessed by 3rd quarter benchmarks. (3 wks) Weeks 4-8 Weeks 1-3 Unit 1 Number System Fluency (5 wks) Unit 2 Rate, Ratio, and Proportional Reasoning; PLAN FOR THE Using Equivalent Fractions BENCHMARK PREP/POST TEST/PRE TEST WINDOW TO CUT OFF THE END OF THIS 5 WEEK UNIT 1st Quarter BENCHMARK (November 1-7 Post/Pre window) Weeks 9-11 (3 wks) Unit 3 Expressions THANKSGIVING BREAK (5 wks) Weeks 12-16 Unit 4 One-Step Equations and Inequalities **5 week unit overlaps and ends just after Christmas Break. CHRISTMAS BREAK ** Week 17-18 (2 wks) Unit 5 Area and Volume 15 6th Grade Math Pacing Guide CCGPS Week 19- 21 2nd Quarter BENCHMARK (January 14-17 Post/Pre window) (3 wks) Unit 6 Statistics If timed carefully, this chapter should end just prior to Mid-Winter Break MID WINTER BREAK (3 wks) Weeks 22-24 Unit 7 Rational Explorations: Numbers and their Opposites 3rd Quarter BENCHMARK (March 11-15 Post window) (4 wks) Weeks 25-28 CRCT REVIEW (Split in the middle by SPRING BREAK) 16