HWM 6 Accelerated Math Curriculum Overview 2018 Overview Standards for Mathematical Content Unit Focus Standards for Mathematical Practice Unit 1: Numerical Expressions and Factors (BI chapter 1) 6.NS.2 6.EE.1 6.NS.4 6.EE2b Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Compute fluently with multi-digit numbers and find common factors and multiples. MP.1 Make sense of problems and persevere in solving them. Apply and extend previous understandings of arithmetic to algebraic expressions. MP.2 Reason abstractly and quantitatively. Unit 2: Fractions and Decimals (BI chapter 2) Unit 3: Integers and the Coordinate Plane (BI chapter 6) 6.NS.1 6.NS.3 6.NS.5 6.NS.6a 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d 6.NS.8 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Compute fluently with multi-digit numbers and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools
Unit 4: Integers (BI chapter 11) Unit 5: Algebraic Expressions and Properties (BI chapter 3) 7.NS.1 7.NS.1a 7.NS.1b 7.NS.1.c 7.NS.1.d 7.NS.2a 7.NS.2b 7.NS.2c 7.NS.3 6.EE.2c 6.EE.2a 6.EE.3 6.EE.4 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of arithmetic to algebraic expressions. strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. Unit 6: Areas of Polygons (BI chapter 4) Unit 7 Ratios and Rates (BI chapter 5) 6.G.1 6.G.3 6.RP.1 6.RP.2 6.RP3 6.RP3a 6.RP3b 6.RP.3c 6.RP.3d Solve real-world and mathematical problems involving area, surface area, and volume Understand ratio concepts and use ratio reasoning to solve problems. MP.8 Look for and express regularity in repeated reasoning. Unit 8: Equations and Inequalities (BI chapter 7) 6.EE.5 6.EE.6 6.EE.7 6.EE.8 6.EE.9 Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables.
Unit 9: Surface Area and Volume (BI chapter 8) 6.G.2 6.G.4 Solve real-world and mathematical problems involving area, surface area, and volume Unit 10: Statistical Measures (BI chapter 9) 6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5a 6.SP.5c Develop understanding of statistical variability. Summarize and describe distributions. Unit 11: Data Displays (BI chapter 10) 6.SP.2 6.SP.4 6.SP.5c 6.SP5d Develop understanding of statistical variability. Summarize and describe distributions. Unit 12: Rational Numbers (BI chapter 12) Unit 13: Expressions and Equations (BI chapter 13) 7.NS.1a 7.NS.1b 7.NS.1.c 7.NS.1.d 7.NS.2a 7.NS.2b 7.NS.2c 7.NS.3 7.EE.1 7.EE.2 7.EE.4a Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Unit 14: Ratios and Proportions (BI chapter 14) Unit 15: Percents (BI chapter 15) 7.RP.2 7.RP.2a 7.RP.2b 7.RP.2c 7.RP.2d 7.RP.3 7.EE3 7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. Analyze proportional relationships and use them to solve real-world and mathematical problems Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Unit :1 Numerical Expressions and Factors Content Standards 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. Suggested Standards for Mathematical Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable Critical Knowledge & Skills Students are able to: Use models to multiply fractions Multiply fractions by fractions Write reciprocals of numbers Use models to divide fractions Divide fractions by fractions Use models to divide mixed numbers
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents 6.NS.4 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. 6.EE2b Write, read, and evaluate expressions in which letters stand for numbers. arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Solve real life problems involving division of fractions by fraction Students are able to: Write expressions as powers. Find values as powers. Evaluate numerical expressions with whole number exponents. Students are able to: Use divisibility rules to find prime factorization of numbers Use diagrams to identify common factors Find the greatest common factor Use diagrams to identify common multiples Find the least common multiple Use LCM to add and subtract fractions Use the distributive property to find products Use the distributive property to produce equivalent expressions Students are able to: 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 Unit 1: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test
District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy
Content Standards Suggested Standards for Mathematical Practice Unit 2: Fractions and Decimals Critical Knowledge & Skills 6.NS.1 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. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Student will be able to: Use models to multiply fractions Multiply fractions by fractions Write reciprocals of numbers Use models to divide fractions Divide fractions by fractions Use models to divide mixed numbers Solve real life problems involving division of fractions by fraction Student will be able to: Use models to add and subtract decimals. Add and subtract decimals. Use models to multiply decimals. Multiply decimals. Use models to divide decimals. Divide decimals. Unit 2: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework District/School Summative Assessment Plan Unit quizzes Unit test
Classwork Exit cards District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy
Content Standards Unit 3: Integers and the Coordinate Plane Suggested Standards for Critical Knowledge & Skills Mathematical Practice: 6.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, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation 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. 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 6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3o C > 7o C to express the fact that 3o C is warmer than 7o C. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. 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, credits/debits, positive/negative electric charge) ( Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. ( Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
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 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. 6.NS.8 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 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. Use absolute values to compare numbers in real life situations 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. Unit 3: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom
Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 4: Integers Critical Knowledge & Skills
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.1a Describe situations in which opposite quantities combine to make 0 7.NS.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.1.d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Students are able to: Add integers. Add rational numbers. Students are able to: Add integers. Add rational numbers. Students are able to: Interpret problems with the format of p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative and identify when this case exists in problems Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Students are able to: Subtract integers. Explain subtraction of rational numbers as adding the additive inverse, p - q = p + (-q) and identify when this case exists in a problem Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts Students are able to: Apply properties of operations as strategies to add and subtract rational numbers. Students are able to: Multiply Integers. Multiply rational numbers. Divide rational numbers. Interpret products and quotients of rational numbers by describing real-world contexts.
numbers. Interpret products of rational numbers by describing realworld contexts. 7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, New Jersey Student Learning Standards for Mathematics 50 then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real world contexts 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.1 Students are able to: Divide integers. Define a rational number as an integer divided by an integer and identify examples of this case Convert rational numbers to decimals. Students are able to: Apply properties of operations as strategies to multiply rational numbers. Apply properties of operations as strategies to divide rational numbers. Students are able to: Solve real-world and mathematical problems involving the four operations with rational numbers. Unit 4: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources
Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Unit 5: Algebraic Expressions and Properties
Content Standards 6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used 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). 6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers.numbers. 6.EE.3 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 6.EE.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). Suggested Standards for Mathematical Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Critical Knowledge & Skills Use order of operations to evaluate algebraic expressions Use variables to represent numbers in algebraic expressions write algebraic expressions Apply the properties of operations to generate equivalent expressions Use Distributive property to simplify 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)
Unit 5: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy
written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Content Standards 6.G.1 Find the 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. 6.G.4 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 realworld and mathematical problems. Suggested Standards for Mathematical Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. Unit 6: Areas of Polygons Critical Knowledge & Skills Find the area of right triangles, other triangles,parallelograms, trapezoids 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. Represent three-dimensional figures using nets made up of rectangles and triangles use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning. Unit 6: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills
Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards 6.RP3 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. 6.RP3a 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. 6.RP3b Solve unit rate problems including those involving unit pricing Suggested Standards for Mathematical Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically Unit 7: Ratios and Rates Critical Knowledge & Skills Use ratio and rate reasoning to solve real-world and mathematical problem Make tables of equivalent ratios relating quantities with whole-number measurements Find missing values in the tables Plot the pairs of values on the coordinate plane Use tables to compare ratios. Use ratio and rate reasoning to solve real-world and mathematical problem Make tables of equivalent ratios relating quantities with whole-number measurements Find missing values in the tables Plot the pairs of values on the coordinate plane Use tables to compare ratios.
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? 6.RP3c 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. 6.RP3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Solve unit rate problems including those involving unit pricing and constant speed Write percents as fractions with denominators of 100 Write fractions as percents Find percent of numbers Find the whole given the part and percent Use conversion factors (rates) to convert units of measurement Unit 7: 6th Grade Accelerated Math District/School Formative Assessment Plan: Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented
Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 8: Equations and Inequalities Critical Knowledge & Skills 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or MP.1 Make sense of problems and persevere in solving them. Use additions or subtractions to solve equations. Use substitution to determine whether a given number in a specified set makes an equation
inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.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 unknown number, or, depending on the purpose at hand, any number in a specified set 6.EE.7 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. 6.EE.8 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. 6.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 dependent variable, in terms of the other quantity, thought of as MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. true. Write word sentences as inequalities. Use number line to graph the solution set of inequalities. Use substitution to determine whether a given number in a specified set makes an inequality true. 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. 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. 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. Identify independent and dependent variables. write equations in two variables. use tables and graphs to analyze the relationship between two variables.
the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Unit 8: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Scientific calculator activities Khan academy Geogebra
Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 9 Surface Area and Volume Critical Knowledge & Skills 6.G.2 MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable 6.G.4 arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use 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. Represent three-dimensional figures using nets made up of rectangles and triangles. use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
of structure. MP.8 Look for and express regularity in repeated reasoning. Unit 9: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills
Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 10: Statistical Measures Critical Knowledge & Skills 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers 6.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. 6.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 MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 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. 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
describes how its values vary with a single number 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5a Reporting the number of observations. 6.SP.5c 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 were gathered. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. number. Find, compare and interpret the mean of data sets. Display numerical data in plots on a dot plots. Display numerical data in plots in a histograms. Display numerical data in plots in a box plots. Reporting the number of observations. Give quantitative measures of center (median and/or mean) as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Give quantitative measure 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 were gathered. Unit 10: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom Accommodations and Modifications ELL, Special Education, Gifted and Talented
Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 11 Data Displays Critical Knowledge & Skills 6.SP.2 MP.1 Make sense of problems and persevere in solving them. 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.
6.SP.4 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. 6.SP.5c MP.5 Use appropriate tools strategically MP.6 Attend to precision. MP.7 Look for and make use of structure. 6.SP5d MP.8 Look for and express regularity in repeated reasoning. Display numerical data in plots on a dot plots. Display numerical data in plots in a histograms. Display numerical data in plots in a box plots. Give quantitative measures of center (median and/or mean) as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (DOK 2) Give quantitative measure 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 were gathered. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Unit 11: 6th Grade Accelerated Math District/School Formative Assessment Plan Teacher check in Student questioning Homework Classwork Exit cards District/School Summative Assessment Plan Unit quizzes Unit test District/School Primary and Supplementary Resources Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool, Big Idea s Laurie s Notes, Khan academy, Buzzmath, Google Classroom
Accommodations and Modifications ELL, Special Education, Gifted and Talented Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth 21st Century Skills Technology and Interdisciplinary skills Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate. Students listen to and evaluate others reasoning and offer improvements and corrections, with supporting arguments. They listen to others feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities. Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others reasoning. Students identify and ask significant questions about mathematics and engage in analyzing each other s answers Scientific calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy Content Standards Suggested Standards for Mathematical Practice Unit 12: Rational Numbers Critical Knowledge & Skills
7.NS.1a Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments & critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically MP.6 Attend to precision. Student will be able to: Add integers. Add rational numbers. Student will be able to: Interpret problems with the format of p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative and identify when this case exists in problems Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. MP.7 Look for and make use of structure. 7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in MP.8 Look for and express regularity in repeated reasoning. Subtract integers. Explain subtraction of rational numbers as adding the additive inverse, p - q = p + (-q) and identify when this case exists in a problem Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts