Valley Central School District 944 State Route 17K Montgomery, NY 12549 Telephone Number: (845)457-2400 ext. 18121 Fax Number: (845)457-4254 Grade 6 Math Curriculum Board of Education Approved May 21, 2018
Unit Title: The Number System (Operations Including Dividing by a Fraction) (25 days) Focus Standards: 6.NS.A.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.B.2 Fluently divide multi-digit numbers using a standard algorithm 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation. 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100. 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 other than 1. Find the least common multiple of two whole numbers less than or equal to 12. Foundational Standards: Understanding of place value of whole numbers and decimals Division concept: Division as an unknown factor problem Dividing whole numbers Multiplying/ dividing by powers of ten Use equivalent fractions to add and subtract Multiplying and dividing with unit fractions and whole numbers Adding/ subtracting decimals Adding/ subtracting mixed numbers and fractions Progressions in Future Courses: Identifying proportional ratios Scale drawings Factoring and expanding linear expressions Add, subtract, multiply, and divide rational numbers Converting rational numbers to decimals Use properties to generate equivalent expressions Solve problems using numerical and algebraic expressions and equations Area and circumference of circles Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning. Key Concepts:
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 Topic A: Divisibility Students will be able to determine divisibility of a number using established rules. Notes with Examples (shared drive) Divisibility Duck (foldable) Worksheets (e.g. 4-1 Reteach, 4-1 Practice A-C, 4-1 Problem Solving) Topic B: Greatest Common Factor & Least Common Multiple Students will be able to find the greatest common factor of two whole numbers less than or equal to 100. GCF and LCM Notes with examples (shared drive) Distributive Property Notes with Examples (shared drive) Coach Book Lesson 12 - Extending Factors and Multiples to GCF and LCM (page 74) GCF Worksheets (e.g. 4-3 Reteach, 4-3 Practice A-C, 4-3 Problem Solving) LCM Worksheets (e.g. 5-1 Reteach, 5-1 Practice A-B, 5-1 Problem Solving) Topic B: Interpreting and Computing Quotients of Fractions Students will be able to apply and extend previous understandings of multiplication and division to divide fractions by fractions. Dividing Fractions by Fractions Using Models Notes with Examples (shared drive) Divide Fractions Using Algorithm Notes with Examples (shared drive) Dividing Fractions by Whole Number Using Models Notes with Examples (shared drive) Coach Book Lesson 7 - Interpreting and Computing Quotients of Fractions (page 46) Coach Book Lesson 8 - Problem Solving: Dividing with Fractions (page 52) Worksheets (e.g. 5-9 Reteach, 5-9 Practice A-C, 5-9 Problem Solving) Topic C: Dividing Whole Numbers Students will be able to fluently divide multi-digit numbers using a standard algorithm. Notes with Examples (teacher created) Coach Book Lesson 9 - Dividing Whole Numbers (page 56) Worksheets (e.g. Spectrum Math Lesson 2.5 and Lesson 2.6)
Topic D: Adding and Subtracting Decimals Students will be able to fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation. Notes with Examples (shared drive) Coach Book Lesson 10 - Adding and Subtracting Decimals (page 62) Worksheets (e.g. 3-3 Reteach, 3-3 Practice A-C, 3-3 Problem Solving) Topic E: Multiply and Divide Decimals Students will be able to fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation. Multiplying Decimals Notes with Examples (shared drive) Dividing Decimals Notes with Examples (shared drive) Coach Book Lesson 11 - Multiply and Divide Decimals (page 68) Worksheets (e.g. 3-5 Reteach, 3-5 Practice A-C, 3-5 Problem Solving) Evidence of Learning/Assessments: Lesson Exit Tickets (teacher created) Divisibility Quiz (shared drive) GCF/ LCM Quiz (shared drive) Dividing Fractions Quiz (shared drive) Dividing Whole Numbers Quiz (shared drive) Basic Operations of Decimals (shared drive) Coach Book Review (page 114-116 #1-28, #46) The Number System Unit 1 Test (shared drive)
Unit Title: Ratios and Proportional Relationships (35 days) Focus Standards: 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to zero, and use rate language in the context of a ratio relationship. 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems 6.RP.A.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use the tables to compare ratios. 6.RP.A.3b Solve unit rate problems. 6.RP.A.3c Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent. 6.RP.A.3d Use ratio reasoning to convert measurements units; manipulate and transform units appropriately when multiplying or dividing quantities. Key Concepts: Foundational Standards: Understand the place value system Perform operations with multidigit whole numbers and with decimals to hundredths Apply and extend previous understandings of multiplication and division to multiply and divide fractions Dividing whole numbers Convert like measurement units within a given measurement system Graph points on the coordinate to solve real-world and mathematical problems Progressions in Future Courses: Analyze proportional relationships and use them to solve real-world and mathematical problems Use random sampling to draw inferences about a population Draw informal comparative inferences about two populations Investigate chance processes and develop, use, and evaluate probability models Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Understand ratio concepts Understand unit rate concept Calculate percents Convert measurements Use ratio reasoning to solve problems (including rates, percents, conversions) Topic A: Ratios Students will be able to understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Coach Book Lesson 1 - Understanding Ratio (page 6) Worksheets (e.g. Exploring Ratio p75, Presentation Problems Day 1-3) Topic B: Unit Rates Students will be able to understand the concept of a unit rate a/b and use ratio and rate reasoning to solve real-world and mathematical problems Coach Book Lesson 2 - Understanding Unit Rates (page 10) Coach Book Lesson 4 - Problem Solving: Unit Rates (page 22) Worksheets (e.g. e.g. 7-1 Reteach, 7-1 Practice A-c, 7-1 Problem Solving, 3-6 Challenge, Rates and Ratios (Carson-Dellosa), 8-1 Study Guide (Glencoe)) Topic C: Equivalent Ratios Students will be able to 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. Coach Book Lesson 3 - Using Tables of Equivalent Ratios (page 16) Worksheets (e.g. 7-2 Reteach, 7-2 Practice A-C, 7-2 Problem Solving) Topic D: Percents
Students will be able to find a percent of a quantity as a rate per 100, solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent. Coach Book Lesson 5 - Using Percent (page 28) Worksheets (e.g. 7-7 Reteach, 7-7 Practice A-C, 7-7 Problem Solving, The Meaning of Percent, 7-8 Reteach, 7-8 Practice A-C, 7-8 Problem Solving,7-9 Reteach, 7-9 Practice A-C, 7-9 Problem Solving, Blizzard Math, Discount Sale Price, Discounts and Tips Worksheet) Topic E: Ratios to convert Measurement Units Students will be able to use ratio reasoning to convert measurements units. Coach Book Lesson 6 - Using Ratios to Convert Measurement Units (page 34) Worksheets (Module 1 Lesson 21 Problem Set with Conversion Chart) Evidence of Learning/Assessments: Lesson Exit Tickets Ratio Quiz (shared drive) Percents Quiz (shared drive) Measurement Conversions Quiz (NYS Module 1: Lesson 21 Problem Set) Coach Book Review (page 40-42 #1-40) Ratios and Proportions Unit 2 Test (shared drive) (Coach Assessments Book- Domain Assessment: Ratios)
Unit Title: 2AD - Ratios and Proportional Relationships Focus Standards: 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 1/4 miles per hour, equivalently 2 miles per hour. 7.RP.A.2 Recognize and represent proportional relationships between quantities. a. 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. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost is proportional to the number of items purchased at a constant price, the relationship between the total cost and the number of items can be expressed as = Foundational Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to zero, and use rate language in the context of a ratio relationship. Use ratio and rate reasoning to solve real-world and mathematical problems Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use the tables to compare ratios. Solve unit rate problems. Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent. Use ratio reasoning to convert measurements units; manipulate and transform units appropriately when multiplying or dividing Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
. d. Explain what a point (, ) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1, ), where is the unit rate. quantities. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Key Concepts: Computing Unit Rate Identifying Proportional Relationships Representing Proportional Relationships Ratio and Percent Topic A: Unit Rate Students will be able to compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units 7th Grade Coach Book Lesson 1 - Computing Unit Rate (page 6) Topic B: Proportional Relationships Students will be able to decide whether two quantities are in a proportional relationship and identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Students will be able to represent proportional relationships by equations and explain what a point (, ) on the graph of a proportional relationship means in terms of the situation Coach Book Lesson 2 - Identifying Proportional Relationships (page 10)
Coach Book Lesson 3 - Representing Proportional Relationships (page 14) Topic C: Ratios and Percents Students will be able to use proportional relationships to solve multistep ratio and percent problems Coach Book Lesson 4 - Word Problems with Ratios and Percents (page 18) Evidence of Learning/Assessments: Lesson Exit Tickets Coach Book Review (page 24) Ratios and Proportions Unit 2 Test (shared drive)
Unit Title: The Number System (Rational Numbers) (25 days) Focus Standards: 6.NS.C.5 Understanding that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.C.6 Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates. 6.NS.C.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. 6.NS.C.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. 6.NS.C.6c Find and position integers and other rational numbers on a horizontal or vertical number line. Find and position pairs of integers and other rational numbers on a coordinate plane. Foundational Standards: Graph points on the coordinate plane so solve real-world and mathematical problems Progressions in Future Courses: 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 Algebraic Expressions and Equations Draw, construct, and describe geometrical figures and describe the relationships between them Solve real-life and mathematical problems involving angle measure, area, surface area, and volume Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
6.NS.C.7 Understand ordering and absolute value of rational numbers. 6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 6.NS.C.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. 6.NS.C.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. 6.NS.C.7d Distinguish comparisons of absolute value from statements about order. 6.NS.C.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. Key Concepts: Integer concepts (values, real-world contexts, opposites) Signs of numbers in ordered pairs and relationship to location on number line and in quadrants Locating and plotting integers and other rational numbers on number lines and coordinate planes Topic A: Positive and Negative Integers on a Number Line
Students will be able to locate and plot positive and negative integers on a number line. Students will recognize the relationship between integers and real-world contexts. Coach Book Lesson 13- Locating Positive and Negative Integers on a Number Line (page 82) Worksheets (e.g. 11-1 Reteach, 11-1 Practice A-C, 11-1 Problem Solving, 11-1 Challenge) Topic B: Absolute Value Students will be able to understand the absolute value of a rational number as its distance from 0 on the number line. Students will interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. Students will distinguish comparisons of absolute value from statements about order. Coach Book Lesson 14 - Understanding Absolute Value (page 86) Worksheets (e.g. CommonCoreSheets: Understanding Absolute Value, Examining Absolute Value, Comparing Absolute Value) Topic C: Rational Numbers on a Number Line Students will find and position integers and other rational numbers on a horizontal or vertical number line diagram. Coach Book Lesson 15- Locating Rational Numbers on a Number Line (page 92) Worksheets (CommonCoreSheets: Negative Number Location on Number Line, Identifying Fraction Location Positive & Negative, Finding Decimals on a Number Line) (Continued on next page) Topic D: Ordering Rational Numbers
Students will be able to order and find absolute value of rational numbers. Students will be able to interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Students will write, interpret, and explain statements of order for rational numbers in real-world contexts. Coach Book Lesson 16- Ordering Rational Numbers (page 98) Worksheets (11-2 Reteach, 11-2 Practice A-C, 11-2 Problem Solving, CommonCoreSheets: Comparing Negative Numbers, ) Topic E: Ordered Pairs and Reflections Students will find and position pairs of integers and other rational numbers on a coordinate plane. Students will be able to understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Students will recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Students will use coordinates and absolute value to find distances between points that have one common coordinate. Students will solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Plotting Ordered Pairs Notes with examples (shared drive) Reflections on the Coordinate Plane Notes with examples (shared drive) Coach Book Lesson 17-Plotting Ordered Pairs on the Coordinate Plane (page 104) Coach Book Lesson 18- Problem Solving: Using the Coordinate Plane (page 110) Worksheets (11-3 Practice A-C, 11-3 Problem Solving, CommonCoreSheets: Finding Quadrant based on Coordinates, Graphitis, Reflections Worksheet w/ graph paper) Evidence of Learning/Assessments Lesson Exit Tickets Integers and Absolute Value Quiz (shared drive) Rational Numbers Quiz (shared drive) Labeling Graph Quiz (shared drive) Coach Book Review (page 114-116 #29-45, #47-49) Rational Numbers Unit 3 Test (shared drive)
Unit Title: 3 AD - The Number System (Integers and Rational Numbers) Focus Standards: 7.NS.A.1.A Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 7.NS.A.1.B 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.A.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.A.1.D Apply properties of operations as strategies to add and subtract rational numbers. Foundational Standards: Understanding that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line. Find and position pairs of integers and other rational numbers on a coordinate plane. Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning. Key Concepts: Adding and Subtracting Rational Numbers Topic A: Adding and Subtracting Rational Numbers
Apply properties of operations as strategies to add and subtract rational numbers. Coach Book Lesson 5- Adding and Subtracting Rational Numbers (page 30) Coach Book Lesson 6 - Applying Properties of Operations to Add and Subtract Rational Numbers (page 36) Evidence of Learning/Assessments Lesson Exit Tickets Adding and Subtracting Rational Numbers Quiz (shared drive) Rational Numbers Unit 3 Test (shared drive)
Unit Title: Expressions, Equations, and Inequalities (45 days) Focus Standards: 6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.A2b Identify parts of an expression using mathematical terms (term, coefficient, sum, difference, product, factor and quotient); view one or more parts of an expression as a single entity. 6.EE.A.2c Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order. (Order of Operations) 6.EE.A.3 Apply the properties of operations to generate equivalent expressions. 6.EE.A.4 Identify when two expressions are equivalent. 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a Foundational Standards: Evaluating numerical expressions Writing and interpreting numerical expressions Multiplying fractions Interpreting fractions as division Dividing with unit fractions and whole numbers Analyze numerical patterns and relationships Apply and extend previous understandings of multiplication and division to multiply and divide fractions Progressions in Future Courses: Factoring and expanding linear expressions Writing equivalent expressions using properties of operations Adding and subtracting algebraic expressions Angle pairs Representing and analyze proportional relationships and use them to solve real-world and mathematical problems Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
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. 6.EE.B.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. Word problems with equations and inequalities Solve real-life and mathematical problems involving angle measure, area, surface area, and volume 6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x p = q; px = q; and = q for cases in which p, q and x are all nonnegative rational numbers, p 0 and where x represents the unknown quantity. 6.EE.B.8 Write an inequality of the form x > c, x c, x c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line. 6.EE.C.9 Use variables to represent two quantities in a realworld problem that change in relationship to one another. Given a verbal context and an equation, identify 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. Key Concepts: Read, write, and evaluate expressions including exponents and/or variables using order of operations Use mathematical terms to identify parts of expressions and equations Determine equivalence between two expressions Use substitution to solve an equation or inequality; determine if it makes statement true Use variables to write equations or inequalities when solving a real-world or mathematical problem. Topic A: Numerical Expressions Students will evaluate exponents and write equivalent expressions. Students will be able to write and evaluate numerical expressions involving whole-number exponents using order of operations. Writing and Evaluating Numerical Expressions Notes with examples (shared drive) Coach Book Lesson 19 - Writing and Evaluating Numerical Expressions (page 120) Worksheets (1-3 Practice, 1-4 Reteach, 1-4 Practice, Order of Operations (boxes) Topic B: Algebraic Expressions Students will identify parts of an expression using mathematical terms. Students will write expressions that record operations with numbers and with letters standing for numbers. Students will be able to evaluate expressions at specific values of their variables. Students will apply the properties of operations to generate equivalent expressions. Students will identify when two expressions are equivalent. Reading and Writing Algebraic Expressions Notes with examples (shared drive) Coach Book Lesson 20 - Reading and Writing Algebraic Expressions (page 124) Evaluating Algebraic Expressions Notes with examples (shared drive) Coach Book Lesson 21 - Evaluating Algebraic Expressions (page 130) Generating and Identifying Equivalent Expressions Notes with examples (shared drive) Coach Book Lesson 22 - Generating and Identifying Equivalent Expressions (page 136) Worksheets (2-1 Practice A-C, 2-1 Problem Solving, 2-2 Practice A-C, 2-2 Problem Solving) (Continued on next page) Topic C: Writing and Solving Equations Students will be able to 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.
Students will understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Solving One-Step Equations Notes with examples (shared drive) Coach Book Lesson 23- Writing and Solving Equations (page 140) Worksheets (2-5 Practice B, 2-6 Practice B, 2-7 Practice B, 2-8 Practice B) Topic D: Writing and Solving Inequalities Students will be able to 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. Students will understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Students will be able to recognize that inequalities of the form x > c or x < c have infinitely many solutions. Writing and Solving Inequalities Notes with examples (shared drive) Equations cs. Inequalities Worksheet (shared drive) Coach Book Lesson 24 - Writing and Solving Inequalities (page 146) Worksheets (Number Lines, Inequalities Practice, Matching Inequalities to a Number Line, Writing Inequalities from a Number Line, Expressing Inequalities from a Number Line, 12 Inequalities Packet) Topic E: Dependent and Independent Variables Students will be able to analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Dependent and Independent Variables Notes with examples (shared drive) Coach Book Lesson 25 - Dependent and Independent Variables (page 152) Coach Book Lesson 26 - Problem Solving: Using Equations (page 158) Worksheets (Independent and Dependent Variables Worksheet, Partner Practice, Chapter Questions Packet) (example in shared drive) Evidence of Learning/Assessments: Lesson Exit Tickets Order of Operations Writing Prompt Numerical Expressions Quiz (shared drive) Algebraic Expressions Quiz (shared drive) Inequalities Quiz (shared drive)
Solving One-Step Equations Quiz (shared drive) Coach Book Review (page 162-164 #1-43) Expressions, Equations, and Inequalities Unit 4 Test (shared drive)
Unit Title: Expressions, Equations, and Inequalities (45 days) Focus Standards: 6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.A2b Identify parts of an expression using mathematical terms (term, coefficient, sum, difference, product, factor and quotient); view one or more parts of an expression as a single entity. 6.EE.A.2c Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order. (Order of Operations) 6.EE.A.3 Apply the properties of operations to generate equivalent expressions. 6.EE.A.4 Identify when two expressions are equivalent. 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a Foundational Standards: Evaluating numerical expressions Writing and interpreting numerical expressions Multiplying fractions Interpreting fractions as division Dividing with unit fractions and whole numbers Analyze numerical patterns and relationships Apply and extend previous understandings of multiplication and division to multiply and divide fractions Progressions in Future Courses: Factoring and expanding linear expressions Writing equivalent expressions using properties of operations Adding and subtracting algebraic expressions Angle pairs Representing and analyze proportional relationships and use them to solve real-world and mathematical problems Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
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. 6.EE.B.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. Word problems with equations and inequalities Solve real-life and mathematical problems involving angle measure, area, surface area, and volume 6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x p = q; px = q; and = q for cases in which p, q and x are all nonnegative rational numbers, p 0 and where x represents the unknown quantity. 6.EE.B.8 Write an inequality of the form x > c, x c, x c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line. 6.EE.C.9 Use variables to represent two quantities in a realworld problem that change in relationship to one another. Given a verbal context and an equation, identify 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. Key Concepts: Read, write, and evaluate expressions including exponents and/or variables using order of operations Use mathematical terms to identify parts of expressions and equations Determine equivalence between two expressions Use substitution to solve an equation or inequality; determine if it makes statement true Use variables to write equations or inequalities when solving a real-world or mathematical problem. Topic A: Numerical Expressions Students will evaluate exponents and write equivalent expressions. Students will be able to write and evaluate numerical expressions involving whole-number exponents using order of operations. Writing and Evaluating Numerical Expressions Notes with examples (shared drive) Coach Book Lesson 19 - Writing and Evaluating Numerical Expressions (page 120) Worksheets (1-3 Practice, 1-4 Reteach, 1-4 Practice, Order of Operations (boxes) Topic B: Algebraic Expressions Students will identify parts of an expression using mathematical terms. Students will write expressions that record operations with numbers and with letters standing for numbers. Students will be able to evaluate expressions at specific values of their variables. Students will apply the properties of operations to generate equivalent expressions. Students will identify when two expressions are equivalent. Reading and Writing Algebraic Expressions Notes with examples (shared drive) Coach Book Lesson 20 - Reading and Writing Algebraic Expressions (page 124) Evaluating Algebraic Expressions Notes with examples (shared drive) Coach Book Lesson 21 - Evaluating Algebraic Expressions (page 130) Generating and Identifying Equivalent Expressions Notes with examples (shared drive) Coach Book Lesson 22 - Generating and Identifying Equivalent Expressions (page 136) Worksheets (2-1 Practice A-C, 2-1 Problem Solving, 2-2 Practice A-C, 2-2 Problem Solving) (Continued on next page) Topic C: Writing and Solving Equations Students will be able to 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.
Students will understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Solving One-Step Equations Notes with examples (shared drive) Coach Book Lesson 23- Writing and Solving Equations (page 140) Worksheets (2-5 Practice B, 2-6 Practice B, 2-7 Practice B, 2-8 Practice B) Topic D: Writing and Solving Inequalities Students will be able to 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. Students will understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Students will be able to recognize that inequalities of the form x > c or x < c have infinitely many solutions. Writing and Solving Inequalities Notes with examples (shared drive) Equations cs. Inequalities Worksheet (shared drive) Coach Book Lesson 24 - Writing and Solving Inequalities (page 146) Worksheets (Number Lines, Inequalities Practice, Matching Inequalities to a Number Line, Writing Inequalities from a Number Line, Expressing Inequalities from a Number Line, 12 Inequalities Packet) Topic E: Dependent and Independent Variables Students will be able to analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Dependent and Independent Variables Notes with examples (shared drive) Coach Book Lesson 25 - Dependent and Independent Variables (page 152) Coach Book Lesson 26 - Problem Solving: Using Equations (page 158) Worksheets (Independent and Dependent Variables Worksheet, Partner Practice, Chapter Questions Packet) (example in shared drive) Evidence of Learning/Assessments: Lesson Exit Tickets Order of Operations Writing Prompt Numerical Expressions Quiz (shared drive) Algebraic Expressions Quiz (shared drive) Inequalities Quiz (shared drive)
Solving One-Step Equations Quiz (shared drive) Coach Book Review (page 162-164 #1-43) Expressions, Equations, and Inequalities Unit 4 Test (shared drive)
Unit Title: Geometry (20 Days) Focus Standards: 6.G.A.1 Find area of triangles, trapezoids, parallelograms, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals; apply these techniques in the context of solving real-world and mathematical problems. 6.G.A.2 Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.A.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 the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.A. 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. *6.G.A.5 (New) Use area and volume models to explain perfect squares and perfect cubes. Foundational Standards: Perform operations with multidigit whole numbers and with decimals to hundredths. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties. Progressions in Future Courses: Draw, construct, and describe geometrical figures and describe the relationships between them.. Area and Circumference of Circles Volume of Three-Dimensional Figures Area and Surface Area of Three- Dimensional Figures Determining square and cubic roots. Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning. Key Concepts:
Find area of triangles, trapezoids, parallelograms, and other polygons Find volumes of right rectangular prisms (including fractional edge length) Draw polygons in the coordinate plane given coordinates for the vertices Use coordinates to find the length of a side (points have same first coordinate or the same second coordinate) Use area and volume to solve real-life mathematical what problems. Topic A: Area of Triangles, Quadrilaterals, and Composite Polygons Students will be able to understand the concept of area and determine the area of a quadrilateral by counting the whole and partial squares inside the figure. Students will determine the area of triangles and quadrilateral by using a formula. Students will determine the area of composite polygons by decomposing into triangles and quadrilaterals. Students will use area model to explain perfect squares. *Based on Learning Standards for Mathematics Revised 2017 (Learning Activities to be added.) Area Notes with examples (shared drive) Coach Book Lesson 27 - Finding Area of Triangles and Quadrilaterals (page 168) Worksheets (10-1 Practice B, Practice p150, 10-2 Practice B, Practice p146, 10-3 Practice B, Practice p154) Topic B: Volume of Rectangular Prisms Students will understand the concept of volume and find the volume of a rectangular prism by counting cubic units and by using a formula Students extend their comprehension of volume by finding a missing dimension when the volume is given and by solving real-world and mathematical problems that involve volume. Students will use area model to explain perfect cubes. *Based on Learning Standards for Mathematics Revised 2017 (Learning Activities to be added.) Volume Notes with examples (shared drive) Perfect Squares and Perfect Cubes Notes (shared drive) Coach Book Lesson 28 - Finding the Volume of Rectangular Prisms (page 176) Worksheets (10-5 Practice (Glencoe), Practice p162, Box it Up) Topic C: Drawing Polygons on the Coordinate Plane Students will plot ordered pairs on a coordinate plane and connect the points to form polygons with horizontal and vertical line segments. They will apply absolute value to the difference to the x- or y- coordinates of two points in a horizontal or vertical line segment in order to determine the distance between the points. Drawing Polygons on Coordinate Plane Notes with examples (shared drive) Coach Book Lesson 29 - Drawing Polygons on the Coordinate Plane (page 182) Worksheets (if needed to reinforce)
Topic D: Three-Dimensional Figures and Nets Students will use the attributes of a solid figure to create a net and will use the shapes of the net to identify the three-dimensional object that it represents. Foldables with Organizer Coach Book Lesson 30 - Representing Three-Dimensional Figures Using Nets (page 186) Worksheets (10-6 Practice B, 10-6 Challenge) (shared drive) Topic E: Surface Area Students will draw nets of three-dimensional figures, apply the formulas for the area of triangles and rectangles to determine the surface area of solid figures, and use nets to solve real-world and mathematical problems involving surface area. Coach Book Lesson 31 - Using Nets to Find Surface Area (page 190) Worksheets (10-9 Practice A, 10-6 Practice (Glencoe), Practice p166) (shared drive) Evidence of Learning/Assessments: Lesson Exit Tickets Area Quiz (shared drive) Volume Quiz (shared drive) Coach Book Review (page 194-196 #1-24) Geometry Unit 5 Test (shared drive)
Unit Title: 5 AD - Geometry Focus Standards: 7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle 7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step Foundational Standards: Find area of triangles, trapezoids, parallelograms, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals; apply these techniques in the context of solving real-world and mathematical problems. Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 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. Use area and volume models to explain perfect squares and perfect cubes. Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
problem to write and solve simple equations for an unknown angle in a figure. 7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Key Concepts: Scale Drawings Geometric Shapes Examining Cross Sections Area and Circumference of Circles Angle Pairs Area and Surface Area (Problem Solving) Topic A: Scale Drawings Students will solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Scale Drawings with examples (shared drive) Coach Book Lesson 18 - Scale Drawings (page 104) Topic B: Geometric Shapes Students will draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Drawing Shapes with examples (shared drive) Coach Book Lesson 19 - Drawing Geometric Shapes (page 110) Worksheets (10-5 Practice (Glencoe), Practice p162, Box it Up) Topic C: Cross Sections of Three-Dimensional Figures
Students will describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Coach Book Lesson 20 - Examining Cross Sections of Three-Dimensional Figures (page 114) Worksheets (if needed to reinforce) Topic D: Area and Circumference of Circles Students will know the formulas for the area and circumference of a circle and use them to solve problems. Coach Book Lesson 21 - Area and Circumference of Circles (page 118) Worksheets (shared drive) Topic E: Angle Pairs Students will use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Coach Book Lesson 22 - Angle Pairs (page 124) Worksheets (shared drive) Evidence of Learning/Assessments: Lesson Exit Tickets Quizzes (shared drive) Coach Book Review (page 138) Geometry Unit 5 Test (shared drive)
Unit Title: Statistics and Probability (25 Days) Focus Standards: 6.SP.A.1 1a. Recognizing that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers. 1b. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. 1c. Develop the concept of sampling when collecting data (qualitative or quantitative) from a population and decide the best method to collect data for a particular question. 6.SP.A.2 Understand that a set of quantitative data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.A.3 Recognize that a measure of center for a quantitative 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 6.SP.B.4 Display quantitative data in plots on a number line, including dot plots, and histograms. 6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: 6.SP.B.5a Reporting the number of observations. 6.SP.B.5b Describing the nature of the attribute Foundational Standards: Represent and interpret data Line Plots Progressions in Future Courses: Understanding sampling Use random sampling to draw inferences about a population Draw informal comparative inferences about two populations Using Mean Absolute Deviation Standards for Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.