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Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 1 – Module 1 The Number System - Integers (Approximately 5 days) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics Florida Math Standard Students should be able to: MFAS Tasks Suggested Instructional Resources MAFS.6.NS.3.5: 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 real-world contexts, explaining the meaning of 0 in each situation. Identify an integer and its opposite. Represent real-world quantities with positive and negative integers. Rainfall Change Relative Decimals Relative Fractions Relative Integers Go Math – Lessons 1.1 MAFS.6.NS.3.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7oC. Compare and order integers Graph integers on a number line Absolute Altitudes Positions of Numbers South Pole Submarines Visualizing Absolute Value Go Math – Lessons 1.2 MAFS.6.NS.3.7c: 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. Find absolute value of a rational number Interpret Absolute Altitudes Positions of Numbers South Pole Submarines Visualizing Absolute Value Go Math – Lessons 1.3 Module 1 - Key Vocabulary Absolute Value Integers Negative Numbers Positive Numbers Opposites Inequality Number Line Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 1 – Module 2 The Number System – Factors and Multiples (Approximately 4 days ) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics Florida Math Standard MAFS.6.NS.2.4: 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. Students should be able to: Find the greatest common factor of two whole numbers less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12. Represent real-world quantities with positive and negative integers. Module 2 - Key Vocabulary Greatest Common Factor Least Common Multiple MFAS Tasks Greatest Common Factor Least Common Multiple Using the Distributive Property Suggested Instructional Resources Go Math – Lessons 2.1 & 2.2 Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 1 - Module 3 The Number System – Rational Numbers (Approximately 5 days) Highlighted Math Practice MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. Click here for video examples from Inside Mathematics Florida Math Standard Students should be able to: MAFS.6.NS.3.6: MAFS.6.NS.3.6a: 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. MAFS.6.NS.3.6c: 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. MAFS.6.NS.3.7: Understand ordering and absolute value of rational numbers. MAFS.6.NS.3.7a: 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. MAFS.6.NS.3.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -30C > -70C to express the fact that -30C is warmer than 70C. MAFS.6.NS.3.7c: 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. MFAS Tasks Classify whole number, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between set of numbers Identify opposites and absolute values of rational numbers Compare and order set of rational numbers arising from mathematical and real –world context. Go Math – Lessons 3.1 & 3.2 Explaining Opposites Graphing on Cartesian Planes Graphing Points in the Plane Graphing Points on the Number Line Locating Quadrants Point Locations What is the Opposite Absolute Altitudes Positions of Numbers South Pole Submarines Visualizing Absolute Value Go Math – Lessons 3.3 Module 3 - Key Vocabulary Rational Numbers Venn Diagram Absolute Value Whole Number Integers Suggested Instructional Resources Irrational Number Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 2 – Module 4 Number Operation – Fraction (Approximately 8 days) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.4.1: Model with mathematics. Students should be able to: MFAS Tasks MAFS.6.NS.2.4 Find the greatest common factor of two whole numbers and the least common multiple of two whole numbers … Use the Distributive Property to express the sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers. Adding fraction and mixed number Subtraction fraction and mixed number Multiplying fractions with whole numbers MAFS.6.NS.1.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, … Multiply fractions Multiply mixed numbers Divide fractions Divide mixed numbers Solve problems involving multiplication and division of fractions Contextualizing Fraction Division Fraction Division Juicing Fractions Models of Fraction Division MAFS.K.12.MP.5.1: Use appropriately tools strategically. Greatest Common Factors Least Common Multiples Using the Identity Property Module 2 - Key Vocabulary Quotient Fraction Mixed number Reciprocal Numerator Denominator Suggested Instructional Resources Go Math – Lesson 4.1 Go Math – Lesson 4.2, 4.3, 4.4 Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 2 - Module 5 Number Operation- Decimal (Approximately 10 days ) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics MAFS.6.NS.2.2 Fluently divide mulitdigit numbers using the standard algorithm. Divide by whole number Interpret the remainder Long Division – 1 Long Division – 2 Long Division – 3 Go Math – Lessons 5.1 MAFS.6.NS.2.3: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation Add and subtract decimal multiply decimals divide decimals solve problems involving multiplication and division of fractions and decimals Adding Multidigit Decimals Dividing Multidigit Decimals Multiplying Multidigit Decimals Subtracting Multidigit Decimals Go Math – Lessons 5.2, 5.3, 5.4, 5.5 MAFS.K.12.MP.5.1: Look for and make use of structure. Click here for video examples from Inside Mathematics Students should be able to: Module 3 - Key Vocabulary Quotient Repeating decimal Terminating decimal MFAS Tasks Suggested Instructional Resources Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 3 - Module 6 Proportionality : Ratios and Rates (Approximately 6 days ) Highlighted Math Practice MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. MAFS.K.12.MP.4.1: Model with mathematics MAFS.K.12.MP.6.1: Attend to precision Florida Math Standard Students should be able to: Suggested Instructional Resources MAFS.6.RP.1.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. represent ratios with concrete models write ratios and find equivalent ratios Comparing Rectangles Comparing Time Interpreting Ratio Writing Ratios Go Math – Lessons 6.1 MAFS.6.RP.1.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. use rates and unit rates to compare quantities Book Rates Explaining Rates Identifying Unit Rates Writing Unit Rates Go Math – Lessons 6.2 MAFS.6.RP.1.3: 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 MAFS.6.RP.1.3a: 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. MAFS.6.RP.1.3b: Solve unit rate problems including those involving unit pricing and constant speed apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates Bargain Breakfast Comparing Rates Finding the Whole Homework Time Making Coffee Measurement Conversion Party Punch – Comparing Rates Sara’s Hike The Meaning of Pi Go Math- Lesson 6.1, 6.2, 6.3 Module 3 - Key Vocabulary Rate MFAS Tasks Unit rate Ratio Equivalent Ratio Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 3 - Module 7 Applying Ratios and Rates and Conversion in Measurement (Approximately 6 days ) Highlighted Math Practice MAFS.K.12.MP.4.1: Model with mathematics. MAFS.K.12.MP.7.1: Look for and make use of structure. Florida Math Standard MAFS.6.RP.1.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities Students should be able to: compare additive and multiplicative relationships represent mathematical and real-world problems involving ratios and rates using tables and graphs solve problems with proportions convert units within a measurement system MFAS Tasks Measurement Conversion Party Punch – Comparing Rates Sara’s Hike The Meaning of Pi Module 3 - Key Vocabulary Ratio Rate Proportion Scale Scale Drawing Units Suggested Instructional Resources Go Math – Lesson 7.1, 7.2, 7.3 Omit Go Math- Lesson 7.4 Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 3 - Module 8 Proportionality Ratios and Rates Percent (Approximately 7 days ) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.K.12.MP.4.1: Model with mathematics Florida Math Standard MAFS.6.RP.1.3 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. Students should be able to: represent percents with concrete models and fractions generate equivalent forms of fractions, decimals, and percents using real-world problems solve real-world problems involving percent MAFS.6.RP.1.3c 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. Module 3 - Key Vocabulary Percent Equivalent decimal Proportional reasoning MFAS Tasks Associative and Commutative Expressions Equal sides, Equivalent Expressions Generating Equivalent Expressions Suggested Instructional Resources Go Math – Lessons 8.1, 8.2, 8.3 Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 4 - Module 9 Equivalent Expressions: Numerical expression (Approximately 5 days ) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.6.EE.1.1: Write and evaluate numerical expressions involving wholenumber exponents. MAFS.K.12.MP.5.1: Use appropriately tools strategically. Students should be able to: generate equivalent numerical expressions using exponents generate equivalent numerical expressions using prime factorization simplify numerical expressions using the order of operations Module 3 - Key Vocabulary Exponent Order of Operation Base Power MFAS Tasks Cube House Evaluating Exponents Paul’s Pennies Suggested Instructional Resources Go Math – Lesson 9.1, 9.2, 9.3 Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 4 - Module 10 Equivalent Expression : Algebraic expression (Approximately 7 days ) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Florida Math Standard Students should be able to: MFAS Tasks Suggested Instructional Resources Parts of Expressions Substitute Resolution Writing Expressions Go Math – (Lesson 10.1) MAFS.6.EE.1.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). Equivalent Exponents Equivalent Expressions Identifying Equivalent Expressions MAFS.6.EE.2.6 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. Gavin’s Pocket Writing Real-World Expressions MAFS.6.EE.1.2a: Write expressions that record operations with numbers and with letters standing for numbers. MAFS.6.EE.1.2b: 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. determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations. MAFS.6.EE.1.2c: 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). evaluate algebraic expressions for the given value of a variable Parts of Expressions Substitute Resolution Writing Expressions Go Math – (Lesson 10.2) MAFS.6.EE.1.3: Apply the properties of operations to generate equivalent expressions. generate equivalent expressions using the properties of operations. Associative and Commutative Expression Equal Sides Equivalent Expressions Go Math- (Lesson 10.3) Module 4 - Key Vocabulary Base Exponent Numerical expression Operations Order of operation Algebraic expression Coefficient Constant Equivalent expressions Evaluating Simplify Like terms Term Variable Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 5 – Module 11 Equations and Inequalities: Equations and Relationships (Approximately 10 days ) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.K.12.MP.4.1: Model with mathematics. MAFS.K.12.MP.5.1: Use appropriately tools strategically. Florida Math Standard Students should be able to: MFAS Tasks MAFS.6.EE.2.5 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 inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. MAFS.6.EE.2.6 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. model and solve one-variable, one-step equations that represent problems Gavin’s Pocket Writing Real-World Expressions MAFS.6.EE.2.7 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 non-negative rational numbers. write corresponding real-world problems given one-variable, one-step equations Center Section Equally Driven Solar Solutions University Parking MAFS.6.EE.2.8 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 understand the relationship and plot the relationship with more than one inequality (example 3 < x > -2) solve two step equations and inequalities Acres and Altitudes Rational Number Lines Roadway Inequalities Transportation Number Lines write one-variable, one-step equations to represent constraints or conditions within problems write inequalities Finding Solutions of Equations Finding Solutions of Inequalities Solutions of Equations Solutions of Inequalities Suggested Instructional Resources Go Math – Lessons 11.1, 11.2, 11.3, 11.4 Module 3 - Key Vocabulary Algebraic expressions Solution Coeffient Term Properties of operation Variable Inequalities Evaluating Like terms Equivalent expression Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 5 - Module 12 Equation and Inequalties: Relationships in two variables (Approximately 10 days ) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.K.12.MP.4.1: Model with mathematics. Florida Math Standard Students should be able to: MAFS.6.NS.3.6b: 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 Identify and graph in all four quadrants Explaining Opposites Graphing on Cartesian Planes Graphing Points in the Plane Locating Quadrants Point Locations What is the Opposite? Bike Lot Coordinates Garden Area Garden Coordinates Analyzing the Relationship Bicycling Equations Grinding Equations Table to Equation MAFS.6.NS.3.6c: Find and position integers and other rational numbers on ... number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. MAFS.6.NS.3.8: 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. MFAS Tasks Describe the location of points. For example five units right and two units up. (also use north, south , east, west) MAFS.6.EE.3.9: 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 the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Suggested Instructional Resources Go Math – (Lessons 12.1) Module 3 - Key Vocabulary Axis Coordinate plane Dependent variables Independent variables Ordered Pair Quadrant x-axis y-axis y-coordinate x-coordinate Coordinate Origin Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 6 - Module 13 Geometry : Area and Polygons (Approximately 8 days ) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.1.1: Make sense of problems and persevere in solving them MAFS.6.G.1.1: Find the area of triangles, special quadrilaterals, and polygons. MAFS.K.12.MP.4.1: Model with mathematics. MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. Students should be able to: MAFS.6.EE.2.7: 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 non-negative rational numbers. model area formulas for parallelograms, trapezoids, and rhombuses by decomposing and rearranging parts of these shapes model area formulas for triangles by decomposing and rearranging parts of shapes write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles where dimensions are positive rational numbers write equations that represent problems related to the volume of right rectangular prisms where dimensions are positive rational numbers MFAS Tasks Area of Kite Area of Quadrilateral Area of Triangle Lost Key Swimming Pool Walkway Center Section Equally Driven Solar Solutions University Parking Suggested Instructional Resources Go Math – Lesson 13.1, 13.2, 13.3, 13.4 Module 3 - Key Vocabulary Parallelogram Rhombus Trapezoid Triangle Polygon Quadrilateral Rectangular prism Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 6 - Module 14 Geometry: Distance and Area in Coordinate Plane (Approximately 4 days ) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.6.NS.3.6b: 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. MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. Students should be able to: use absolute value to find distances between points in the coordinate plane solve problems that involve drawing polygons in the coordinate plane and finding the length of a side MAFS.6.NS.3.8: 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. MAFS.6.G.1.3: 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 same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. MFAS Tasks Explaining Opposites Graphing on Cartesian Planes Graphing Points in the Plane Locating Quadrants Point Locations What is the Opposite? Suggested Instructional Resources Go Math -Lessons 14.1, 14.2 Bike Lot Coordinates Garden Area Garden Coordinates solve problems that involve drawing polygons in the coordinate plane and finding the length of a side Fence Length Patio Area Polygon Coordinates Polygon Grid Module 3 - Key Vocabulary Area Axis Perimeter Polygon Reflection Vertex Vertices Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 6 - Module 15 Geometry: Surface Area and Volume (Approximately 10 days ) Highlighted Math Practice MAFS.K.12.MP.4.1: Model with mathematics MAFS.K.12.MP.6.1: Attend to precision Florida Math Standard Students should be able to: MAFS.6.G.1.2: 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 formulasV = 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. Find volume using the volume formula. Use nets to find surface area MAFS.6.G.1.4: 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 real-world and mathematical problems. MAFS.6.EE.2.7: 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 non-negative rational numbers. Solve equations of the form x + p = q and px = q MFAS Tasks Bricks Clay Blocks Moving Truck Prism Packing Pyramid Project Rust Protection Skateboard Ramp Windy Pyramid Center Section Equally Driven Solar Solutions University Parking Suggested Instructional Resources Go Math – Lesson 15.1, 15.2, 15.3 Module 3 - Key Vocabulary Net Base Height Rectangular prism Volume Pyramid Surface area Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 7- Module 16 Measurement and Data: Summarizing Data (Approximately 12 days ) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. MAFS.6.SP.1.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. MAFS.6.SP.1.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. MAFS.K.12.MP.4.1: Model with mathematics. MAFS.K.12.MP.5.1: Use appropriately tools strategically. Students should be able to: MAFS.6.SP.2.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MAFS.6.SP.2.5: Summarize numerical data sets in relation to their context, such as by: MAFS.6.SP.2.5c: 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. MAFS.6.SP.2.5d: 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. represent numeric data graphically, including dot plots, histograms, and box plots use graphical representations of numeric data to describe the center, spread, and shape of a data distribution summarize numeric data with numerical summaries, including the mean and median and the range and interquartile range (IQR) interpret numeric data summarized in dot plots, histograms, and box plots summarize categorical data with numerical and graphical summaries, including mode and relative frequency tables MFAS Tasks Questions About a Class TV Statistics Compare Measures of Center and Variability Explain Measures of Center Explain Measures of Variability Basketball Histogram Chores Data Shark Attack Data Analyzing Physical Activity Florida Lakes Quiz Mean and Deviation Select the Better Measure Suggested Instructional Resources Go Math – Lesson 16.1, 16.2, 16.3, 16.4, 16.5 Module 3 - Key Vocabulary Upper quartile Data Survey Box plot Histogram Interquartile range Lower quartile Mean absolute deviation Median Mode Measure of center Measure of spread Range Statistical questions Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 8 - Module 17 Number System – Integers Addition and Subtraction (Approximately 5 days ) Highlighted Math Practice MAFS.K.12.MP.5.1: Use appropriately tools strategically. Click here for video examples from Inside Mathematics MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics MAFS.K.12.MP.1.1: Make sense of problems and persevere in solving them. Click here for video examples from Inside Mathematics Florida Math Standard MAFS.7.NS.1.1: 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. MAFS.7.NS.1.1.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. MAFS.7.NS.1.1.d: Apply properties of operations as strategies to add and subtract rational numbers. Students should be able to: Students represent integer operations with concrete models and connect the actions with the models to standardized algorithms: add integers fluently subtract integers fluently solve multi-step problems involving addition and subtraction of integers MFAS Tasks MAFS.7.NS.1.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Adding Integers Exploring Additive Inverse Finding the Difference Rational Addition and Subtraction Rational Water Management Using Positive and Negative Numbers in Context Suggested Instructional Resources Go Math – Lesson 17.1, 17.2, 17.3, 17.4 Positive and Negative Fractions A Rational Number Expression Complex Fractions Monitoring Water Temperatures Trail Mix Munchies Module 3 - Key Vocabulary Difference Integers Negative numbers Opposites Absolute value Additive inverse Expressions model Positive number Sum Whole number Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 8 - Module 18 Number Systems: Multiply and Dividing Integers (Approximately 4 days ) Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.2.1: Reason abstractly and quantitatively.Click here for video examples from Inside Mathematics MAFS.7.NS.1.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAFS.7.NS.1.1.b: 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, then -( p _ q) = ___ (-p) q = ___p (-q) . Interpret quotients of rational numbers by describing real-world contexts. MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics MAFS.K.12.MP.7.1: Look for and make use of structure.Click here for video examples from Inside Mathematics Students should be able to: MFAS Tasks Students represent integer operations with concrete models and connect the actions with the models to standardized algorithms. multiply integers fluently divide integers fluently Adding Integers Exploring Additive Inverse Finding the Difference Rational Addition and Subtraction Rational Water Management Using Positive and Negative Numbers in Context use the order of operations to solve multistep problems involving integers Positive and Negative Fractions A Rational Number Expression Complex Fractions Monitoring Water Temperatures Trail Mix Munchies MAFS.7.NS.1.1.c: Apply properties of operations as strategies to multiply and divide rational numbers. MAFS.7.NS.1.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Applying Rational Number Properties Find Decimal Using Long Division Integer Division Negative Times Negative Explained Quotients of Integers Understanding Products Suggested Instructional Resources Go Math – Lessons 18.1, 18.2, 18.3 Module 3 - Key Vocabulary Divide Dividend Divisor Integers Opposites Positive number Product quotient Multiply Negative number Operation Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 8 - Module 19 Number System : Rational Numbers (Approximately 5 days ) Students should be able to: Highlighted Math Practice Florida Math Standard MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics MAFS.7.NS.1.1.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. MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. Click here for video examples from Inside Mathematics MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics MFAS Tasks Adding Integers Exploring Additive Inverse Finding the Difference Rational Addition and Subtraction Rational Water Management Applying Rational Number Properties Find Decimal Using Long Division Integer Division Negative Times Negative Explained MAFS.7.NS.1.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Positive and Negative Fractions A Rational Number Expression Complex Fractions MAFS.7.EE.1.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Equivalent Perimeters Equivalent Rational Expressions Factored Forms MAFS.7.EE.2.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies Alexa’s Account Discount and Tax Gas Station Equations Reeling in Expressions Using Estimation MAFS.7.NS.1.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAFS.7.NS.1.2.d: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Students represent and use rational numbers in a variety of forms: write rational numbers as decimals add, subtract, multiply, and divide rational numbers fluently Suggested Instructional Resources Go Math – Lessons 19.1 to 19.7 Module 3 - Key Vocabulary Rational number Repeating decimal Terminating decimal Integer Whole numbers Additive inverse Opposite Rational number Negative number Pattern Positive number Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. Unit 9 - Module 20 Rates and Proportionality (Approximately 7days ) Highlighted Math Practice MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics Florida Math Standard Students should be able to: MAFS.7.RP.1.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. MAFS.7.RP.1.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. MAFS.7.RP.1.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. MAFS.7.RP.1.2c: Represent proportional relationships by equations. MAFS.7.RP.1.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Students represent and solve proportional relationships: calculate unit rates from rates represent constant rates of change given a table, verbal description, equation, or graph determine constant of proportionality in real-world situations MAFS.7.RP.1.3: Use proportional relationships to solve multistep ratio and percent problems. MFAS Tasks Comparing Unit Rates Computing unit Rates Unit Rate Area Unit Rate Length Explain Equivalent Expressions Rectangle Expressions Estimating: Counting Trees Finding Fees Gasoline Prices Making Cookies Tiffany’s Cookies Suggested Instructional Resources Go Math – Lessons 20.1, 20.2, 20.3 Module 3 - Key Vocabulary Constant Conversion factor Equivalent ratio Percent Rate Constant of Proportion Proportional relationship Rate of change Unit rate Ratio Complex fraction Grade Six Advanced Mathematics Curriculum Map Course Number: 1205020 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module. proportionality Unit 9 - Module 21 Proportions and Percent (Approximately 5 days ) Highlighted Math Practice Florida Math Standard Students should be able to: MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics MAFS.7.RP.1.3: Recognize and represent proportional relationships between quantities. MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics MAFS.7.EE.1.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. MAFS.K.12.MP.5.1: Use appropriately tools strategically. Click here for video examples from Inside Mathematics Students represent and solve problems involving proportional relationships: solve problems involving percent increase, percent decrease, and percent of change solve markup and markdown problems use percents to find sales tax, tips, total cost, simple interest MAFS.7.EE.2.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. MFAS Tasks Estimating: Counting Trees Finding Fees Gasoline Prices Making Cookies Tiffany’s Cookies Explain Equivalent Expressions Rectangle Expressions Alex’s Account Discount and Tax Gas Station Equations Reeling in Expressions Using Estimation Suggested Instructional Resources Go Math – Lessons 6.1 Module 3 - Key Vocabulary Proportion Percent Principal Simple interest Rate Ratio Unit rate Percent of decrease Percent of increase