MOUNTAIN VIEW SCHOOL DISTRICT

SIXTH GRADE

MATH

Sixth Grade Math

Common Core State Standard

CC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Arkansas Frameworks(NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technology(A.7.4.1) Analyze Change: Identify, describe and generalize relationships in which quantities change proportionallyQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to non-complex fractions.)

Arkansas FrameworksAR.6.NO.3.6 (NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technologyQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Arkansas Frameworks(A.6.5.1) Algebraic Models and Relationships: Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs(A.7.5.1) Analyze Change: Model and describe quantities that change using real world situationsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Arkansas Frameworks(A.7.8.1) Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost)(A.4.6.1) Patterns, Relations and Functions: Solve problems by finding the next term or missing term in a pattern or function table using real world situations(G.10.7.1) Coordinate Geometry: Plot points in the coordinate plane(A.4.5.1) Patterns, Relations and Functions: Solve problems by finding the next term or missing term in a pattern or function table using real world situations(A.4.7.2) Patterns, Relations and Functions: Identify and extend patterns in real world situations(A.5.7.2) Expressions, Equations and Inequalities: Solve simple linear equations using integers and graph on a coordinate plane(A.6.6.1) Algebraic Models and Relationships: Complete, with and without appropriate technology, and interpret tables and line graphs that represent the relationship between two variables in quadrant I(A.6.7.1) Algebraic Models and Relationships: Use tables and graphs to represent linear equations by plotting, with and without appropriate technology, points in a coordinate plane(G.10.6.1) Coordinate Geometry: Use ordered pairs to plot points in Quadrant IQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Arkansas Frameworks(A.7.6.1) Analyze Change: Identify and compare situations with constant or varying rates of change(A.7.7.1) Analyze Change: Use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of change(NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technologyQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.

Arkansas Frameworks(NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technology(NO.1.6.1) Rational Numbers: Demonstrate conceptual understanding to find a specific percent of a number, using models, real life examples, or explanations(NO.3.6.7) Application of Computation: Determine the percent of a number and solve related problems in real world situations(NO.1.5.1) Rational Numbers: Use models and visual representations to develop the concepts of the following:---Fractions: parts of unit wholes, parts of a collection, locations on number lines, locations on ruler (benchmark fractions), divisions of whole numbers;---Ratios: part-to-part (2 boys to 3 girls), part-to-whole (2 boys to 5 people);---Percents: part-to-100(NO.1.5.3) Rational Numbers: Identify decimal and percent equivalents for benchmark fractions(NO.1.6.2) Rational Numbers: Find decimal and percent equivalents for proper fractions and explain why they represent the same value(NO.3.7.6) Application of Computation: Solve, with and without technology, real world percent problemsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Arkansas Frameworks(NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technology(M.12.5.2) Attributes and Tools: Make conversions within the customary measurement system in real world problems.(M.12.6.2) Attributes and Tools: Make conversions within the same measurement system in real world problems(M.12.7.2) Attributes and Tools: Understand relationships among units within the same system(M.12.8.2) Attributes and Tools: Describe and apply equivalent measures using a variety of units within the same system of measurementQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Arkansas Frameworks(NO.3.6.4) Estimation: Estimate reasonable solutions to problem situations involving fractions and decimals(NO.3.6.2) Computational Fluency: Develop and analyze algorithms for computing with fractions (including mixed numbers) and decimals and demonstrate, with and without technology, computational fluency in their use and justify the solution(NO.2.6.5) Understand Operations: Model multiplication and division of fractions (including mixed numbers) and decimals using pictures and physical objects(NO.2.8.5) Understand Operations: Model and develop addition, subtraction, multiplication and division of rational numbersQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.2 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently divide multi-digit numbers using the standard algorithm.

Arkansas Frameworks(NO.3.4.3) Computational Fluency-Multiplication and Division: Attain, with and without appropriate technology, computational fluency in multiplication and division using contextual problems using:-- two-digit by two-digit multiplication (larger numbers with technology),-- up to three-digit by two-digit division (larger numbers with technology),-- strategies for multiplication and dividing numbers,-- performance of operations in more than one way,-- estimation of products and quotients in appropriate situations, and-- relationships between operations(NO.3.5.1) Computational Fluency: Develop and use a variety of algorithms with computational fluency to perform whole number operations using addition and subtraction (up to five-digit numbers), multiplication (up to three-digit x two-digit), division (up to two-digit divisor) interpreting remainders, including real world problems(NO.3.6.1) Computational Fluency: Apply, with and without appropriate technology, algorithms with computational fluency to perform whole number operations (+, -, x, /)Qtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.NS.3 Compute fluently with multi-digit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Arkansas Frameworks(NO.2.6.5) Understand Operations: Model multiplication and division of fractions (including mixed numbers) and decimals using pictures and physical objects(NO.2.8.5) Understand Operations: Model and develop addition, subtraction, multiplication and division of rational numbers(NO.3.7.3) Estimation: Determine when an estimate is sufficient and use estimation to decide whether answers are reasonable in problems including fractions and decimalsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples. Find the greatest common factor of two whole numbers less than or equal to 100 and the 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. For example, express 36 + 8 as 4 (9 + 2).

Arkansas Frameworks(NO.3.6.5) Application of Computation: Find and use factorization (tree diagram) including prime factorization of composite numbers (expanded and exponential notation) to determine the greatest common factor (GCF) and least common multiple (LCM)(NO.2.5.3) Number theory: Identify the distributive property by using physical models to solve computation and real world problems(NO.2.6.2) Number theory: Apply the distributive property of multiplication over addition to simplify computations with whole numbers(NO.3.7.4) Application of Computation: Apply factorization, LCM, and GCF to solve problems using more than two numbers and explain the solution(NO.2.4.2) Number Theory: Apply number theory:-- determine if any number is even or odd,-- use the terms 'multiple,' 'factor,' and 'divisible by' in an appropriate context,-- generate and use divisibility rules for 2, 5, and 10,-- demonstrate various multiplication & division relationshipsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. 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.

Arkansas Frameworks(NO.1.7.5) Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number line(NO.1.7.6) Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers)(M.12.2.5) Temperature: Compare temperatures using the Fahrenheit scale on a thermometer(M.12.3.3) Temperature: Distinguish the temperature in contextual problems using the Fahrenheit scale on a thermometer(M.13.4.6) Temperature: Read temperatures on Fahrenheit and Celsius scalesQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. 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 on the line and in the plane with negative number coordinates.

Arkansas Frameworks(NO.1.7.5) Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number line(NO.1.7.6) Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers)(NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)(NO.1.8.4) Rational Numbers: Understand and justify classifications of numbers in the real number system(G.10.7.1) Coordinate Geometry: Plot points in the coordinate planeQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.NS.6a 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.

Arkansas Frameworks(NO.1.7.5) Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number line(NO.1.7.6) Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers)(NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)(NO.1.8.4) Rational Numbers: Understand and justify classifications of numbers in the real number systemQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.6b 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.

Arkansas Frameworks(G.9.7.2) Symmetry and Transformations: Perform translations and reflections of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper)(G.10.7.1) Coordinate Geometry: Plot points in the coordinate plane(G.9.8.2) Symmetry and Transformations: Draw the results of translations and reflections about the x- and y-axis and rotations of objects about the originQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Arkansas Frameworks(G.10.7.1) Coordinate Geometry: Plot points in the coordinate plane(NO.1.7.5) Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number lineQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers.

Arkansas Frameworks(NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)(NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology(NO.1.6.5) Rational Numbers: Recognize and identify perfect squares and their square rootsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.7a 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.

Arkansas Frameworks(NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)(SEI.2.AI.4) Solve and graph simple absolute value equations and inequalitiesQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.7b 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.

Arkansas Frameworks(NO.1.7.5) Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number line(NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)Qtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.NS.7c 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.

Arkansas Frameworks(NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology(SEI.2.AI.4) Solve and graph simple absolute value equations and inequalitiesQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.7d 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.

Arkansas Frameworks(NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology(SEI.2.AI.4) Solve and graph simple absolute value equations and inequalitiesQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. Solve real-world and mathematical 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.

Arkansas Frameworks(NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)(NO.1.8.4) Rational Numbers: Understand and justify classifications of numbers in the real number system(NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technologyQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving whole-number exponents.

Arkansas Frameworks(A.5.5.3) Expressions, Equations and Inequalities: Select, write and evaluate algebraic expressions with one variable by substitution(A.5.6.3) Expressions, Equations and Inequalities: Evaluate algebraic expressions with one variable using appropriate properties and operations (+, -, x, /)(A.5.7.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using positive rational numbers(A.5.8.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using rational numbers(NO.3.5.5) Application of Computation: Use factors of numbers:-- to introduce exponents,-- to find common factors of two numbers,-- to simplify fractions to the lowest termsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and evaluate expressions in which letters stand for numbers.

Arkansas Frameworks(A.5.5.2) Expressions, Equations and Inequalities: Write expressions containing one variable (a letter representing an unknown quantity) using rules for addition and subtraction(A.5.6.2) Expressions, Equations and Inequalities: Write simple algebraic expressions using appropriate operations (+, -, x, /) with one variable(A.5.5.3) Expressions, Equations and Inequalities: Select, write and evaluate algebraic expressions with one variable by substitution(A.5.6.3) Expressions, Equations and Inequalities: Evaluate algebraic expressions with one variable using appropriate properties and operations (+, -, x, /)(A.5.8.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using rational numbersQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

Arkansas Frameworks(A.5.5.2) Expressions, Equations and Inequalities: Write expressions containing one variable (a letter representing an unknown quantity) using rules for addition and subtraction(A.5.6.2) Expressions, Equations and Inequalities: Write simple algebraic expressions using appropriate operations (+, -, x, /) with one variable(A.5.6.3) Expressions, Equations and Inequalities: Evaluate algebraic expressions with one variable using appropriate properties and operations (+, -, x, /)Qtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

Arkansas Frameworks(A.5.7.3) Expressions, Equations and Inequalities: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like termsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.

Arkansas Frameworks(NO.2.5.4) Number theory: Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses(NO.2.6.4) Number theory: Apply rules (conventions) for order of operations to whole numbers with and without parentheses(NO.2.7.3) Number theory: Apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets or exponents(NO.2.8.4) Number theory: Apply rules (conventions) for order of operations to rational numbers(M.13.6.4) Attributes and Tools: Establish and apply formulas to find area and perimeter of triangles, rectangles, and parallelograms(M.13.7.4) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materialsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Arkansas Frameworks(A.5.7.3) Expressions, Equations and Inequalities: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like terms(NO.2.8.4) Number theory: Apply rules (conventions) for order of operations to rational numbers(NO.2.7.3) Number theory: Apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets or exponents(NO.2.6.4) Number theory: Apply rules (conventions) for order of operations to whole numbers with and without parentheses(NO.2.5.4) Number theory: Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses(NO.2.5.3) Number theory: Identify the distributive property by using physical models to solve computation and real world problems(NO.2.6.2) Number theory: Apply the distributive property of multiplication over addition to simplify computations with whole numbers(NO.2.7.1) Number theory: Apply the distributive property of multiplication over addition or subtraction to simplify computations with integers, fractions and decimals(A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomialsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic expressions. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Arkansas Frameworks(A.5.7.3) Expressions, Equations and Inequalities: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like termsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Sixth Grade Math

Common Core State Standard

CC.6.EE.6 Reason about and solve one-variable equations and inequalities. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Arkansas Frameworks(A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology(A.5.7.1) Expressions, Equations and Inequalities: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology(A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials(NO.2.7.2) Number theory: Apply the addition, subtraction, multiplication and division properties of equality to one-step equations with integers, fractions, and decimalsQtr. WEEK Qtr. WEEK

1 1 2 3 4 5 6 7 8 9 10 11 2 1 2 3 4 5 6 7 8 9 10 113 1 2 3 4 5 6 7 8 9 10 11 4 1 2 3 4 5 6 7 8 9 10 11

Common Core State Standard

CC.6.EE.7 Reason about and solve one-variable equations and inequalities. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Arkansas Frameworks(A.5.7.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using positive rational numbers(A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology(A.5.7.1) Expressions, Equations and Inequalities: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology(A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials(A.5.5.1) Expressions, Equations and Inequalities: Model and solve simple equations by informal methods using manipulatives and appropriate technology(A.5.7.2) Expressions, Equations and Inequalities: Solve simple linear equations using integers and graph on a coordinate plane(A.5.8.2) Expressions, Equations and Inequalities: Solve and graph linear equations (in the form y=mx+b)Qtr. WEEK Qtr. WEEK

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Sixth Grade Math

Common Core State Standard

CC.6.EE.8 Reason about and solve one-variable equations and inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Arkansas Frameworks(A.5.7.1) Expressions, Equations and Inequalities: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology(A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology(A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials(SEI.2.AI.4) Solve and graph simple absolute value equations and inequalitiesQtr. WEEK Qtr. WEEK

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Common Core State Standard

CC.6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. 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 dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Arkansas Frameworks(A.7.8.1) Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost)(A.4.8.4) Patterns, Relations and Functions: Use tables, graphs, and equations to identify independent/dependent variables (input/output)(A.7.7.1) Analyze Change: Use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of change(LF.2.AC.2) Create, given a situation, a graph that models the relationship between the independent and dependent variables(LF.2.AC.3) Determine the independent and dependent variables, domain and range of a relation from an algebraic expression, graph, set of ordered pairs, or table of dataQtr. WEEK Qtr. WEEK

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Sixth Grade Math

Common Core State Standard

CC.6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Arkansas Frameworks(M.13.6.4) Attributes and Tools: Establish and apply formulas to find area and perimeter of triangles, rectangles, and parallelograms(M.13.5.4) Attributes and Tools: Develop and use strategies to solve real world problems involving perimeter and area of rectangle(M.13.7.3) Attributes and Tools: Develop and use strategies to solve problems involving area of a trapezoid and circumference and area of a circle(M.13.8.5) Applications: Estimate and compute the area of irregular two-dimensional shapes(M.13.7.7) Applications: Estimate and compute the area of more complex or irregular two-dimensional shapes by dividing them into more basic shapesQtr. WEEK Qtr. WEEK

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Common Core State Standard

CC.6.G.2 Solve real-world and mathematical problems involving area, surface area, and volume. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Arkansas Frameworks(M.13.7.4) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials(G.8.6.1) Characteristics of Geometric Shapes: Identify three-dimensional geometric figures using models (rectangular prisms, cylinders, cones, pyramids and spheres)Qtr. WEEK Qtr. WEEK

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Sixth Grade Math

Common Core State Standard

CC.6.G.3 Solve real-world and mathematical problems involving area, surface area, and volume. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the 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.

Arkansas Frameworks(G.10.7.2) Coordinate Geometry: Plot points that form the vertices of a geometric figure and draw, identify and classify the figure.(G.10.6.2) Coordinate Geometry: Plot points that form the vertices of a geometric figure and draw, identify and classify the figure.(G.10.8.1) Coordinate Geometry: Use coordinate geometry to explore the links between geometric and algebraic representations of problems (lengths of segments/distance between points, slope/perpendicular-parallel lines)(G.8.6.1) Characteristics of Geometric Shapes: Identify three-dimensional geometric figures using models (rectangular prisms, cylinders, cones, pyramids and spheres)Qtr. WEEK Qtr. WEEK

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Common Core State Standard

CC.6.G.4 Solve real-world and mathematical problems involving area, surface area, and volume. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Arkansas Frameworks(G.11.6.1) Spatial Visualization and Models: Identify two-dimensional patterns (nets) for three-dimensional solids, such as prisms, pyramids, cylinders, and cones(G.11.7.1) Spatial Visualization and Models: Build three-dimensional solids from two-dimensional patterns (nets)(M.13.8.2) Applications: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology(M.13.7.4) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials(G.11.5.1) Spatial Visualization and Models: Using grid paper, draw and identify two-dimensional patterns (nets) for cubes(G.8.6.1) Characteristics of Geometric Shapes: Identify three-dimensional geometric figures using models (rectangular prisms, cylinders, cones, pyramids and spheres)Qtr. WEEK Qtr. WEEK

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Sixth Grade Math

Common Core State Standard

CC.6.SP.1 Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

Arkansas Frameworks(DAP.14.6.1) Collect, organize and display data: Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population(DAP.14.7.1) Collect, organize and display data: Identify different ways of selecting samples and compose appropriate questions(DAP.14.5.1) Collect, organize and display data: Develop appropriate questions for surveysQtr. WEEK Qtr. WEEK

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Common Core State Standard

CC.6.SP.2 Develop understanding of statistical variability. 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.

Arkansas Frameworks(DAP.15.6.2) Data Analysis: Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range)(DAP.15.5.2) Data Analysis: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data(DAP.15.7.2) Data Analysis: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)(DAP.15.8.2) Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread(DAP.15.8.3) Data Analysis: Given at least one of the measures of central tendency create a data set(DAP.15.8.4) Data Analysis: Describe how the inclusion of outliers affects those measures(DAP.14.5.3) Collect, organize and display data: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs(DAP.14.6.3) Collect, organize and display data: Construct and interpret graphs, using correct scale, including line graphs and double-bar graphs(DAP.14.7.3) Collect, organize and display data: Construct and interpret circle graphs, box-and-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology(DAP.14.8.3) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, double-bar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs(DAP.15.5.1) Data Analysis: Interpret graphs such as line graphs, double bar graphs, and circle graphs(DAP.15.6.1) Data Analysis: Interpret graphs such as double line graphs and circle graphs(DAP.15.7.1) Data Analysis: Analyze data displays, including ways that they can be misleading(DAP.14.5.1) Collect, organize and display data: Develop appropriate questions for surveysQtr. WEEK Qtr. WEEK

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Sixth Grade Math

Common Core State Standard

CC.6.SP.3 Develop understanding of statistical variability. 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.

Arkansas Frameworks(DAP.15.5.2) Data Analysis: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data(DAP.15.6.2) Data Analysis: Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range)(DAP.15.7.2) Data Analysis: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)(DAP.15.8.2) Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread(DAP.15.8.3) Data Analysis: Given at least one of the measures of central tendency create a data set(DAP.15.8.4) Data Analysis: Describe how the inclusion of outliers affects those measuresQtr. WEEK Qtr. WEEK

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Common Core State Standard

CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Arkansas Frameworks(DAP.14.5.3) Collect, organize and display data: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs(DAP.14.6.3) Collect, organize and display data: Construct and interpret graphs, using correct scale, including line graphs and double-bar graphs(DAP.14.7.3) Collect, organize and display data: Construct and interpret circle graphs, box-and-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology(DAP.14.7.2) Collect, organize and display data: Explain which types of display are appropriate for various data sets (line graph for change over time, circle graph for part-to-whole comparison, scatter plot for trends)Qtr. WEEK Qtr. WEEK

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Sixth Grade Math

Common Core State Standard

CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by: -- a. Reporting the number of observations. -- b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. -- c. Giving quantitative measures 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.

Arkansas Frameworks(DAP.14.5.3) Collect, organize and display data: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs(DAP.14.5.1) Collect, organize and display data: Develop appropriate questions for surveys(DAP.15.6.2) Data Analysis: Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range)(DAP.15.8.2) Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread(DAP.15.8.3) Data Analysis: Given at least one of the measures of central tendency create a data set(DAP.15.8.4) Data Analysis: Describe how the inclusion of outliers affects those measures(DAP.14.6.3) Collect, organize and display data: Construct and interpret graphs, using correct scale, including line graphs and double-bar graphs(DAP.14.6.1) Collect, organize and display data: Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population(DAP.14.7.1) Collect, organize and display data: Identify different ways of selecting samples and compose appropriate questions(DAP.16.8.1) Inferences and Predictions: Use observations about differences between sets of data to make conjectures about the populations from which the data was taken(DAP.16.6.1) Inferences and Predictions: Use observations about difference(DAP.16.5.1) Inferences and Predictions: Make predictions and justify conclusions based on data s in data to make justifiable inferences(DAP.15.8.1) Data Analysis: Compare and contrast the reliability of data sets with different size populations(DAP.14.8.1) Collect, organize and display data: Design and conduct investigations which include:-- adequate number of trials,-- unbiased sampling,-- accurate measurement,-- record-keeping(DAP.14.8.2) Collect, organize and display data: Explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit)(DAP.14.6.2) Collect, organize and display data: Collect data and select appropriate graphical representations to display the data including Venn diagrams(DAP.14.5.2) Collect, organize and display data: Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots(DAP.14.7.3) Collect, organize and display data: Construct and interpret circle graphs, box-and-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology(DAP.14.8.3) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, double-bar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs(DAP.15.6.1) Data Analysis: Interpret graphs such as double line graphs and circle graphs(DAP.15.7.1) Data Analysis: Analyze data displays, including ways that they can be misleading(DAP.15.5.2) Data Analysis: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of dataQtr. WEEK Qtr. WEEK

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