UNIT: EXPRESSIONS Suggested Pacing: 18 Days Standard: 6.EE.1, 2, 3 Write and evaluate numerical expressions involving whole-number exponents. Clarifying Objectives 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2Write, read, and evaluate expressions in which letters stand for numbers. First Nine Weeks a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient; view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3and A = 6 s2to find the volume and surface area of a cube with sides of length s = ½ Essential Questions What is the difference between expressions and equations? What is meant by an “algebraic expression”? How can algebraic expressions be used to represent real-life situations? How is a variable used in the real world? Why do we need an order of operations? Why is algebraic reasoning important? How do we use it every day? Essential Vocabulary Expression Exponent Power Evaluate Numerical Expression Exponent Evaluate Numerical term Algebraic term Order of Operations Variables Properties Inverse Coefficient Distribute Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp. 1 pg. 1-39 Expressions and Number Properties Internet Resources: Common Core Unit on Expressions https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit3 SE.pdf Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Supplemental Resources: Classroom Activities and Lessons: AIMS Education Foundation, Writing and Simplifying Expressions, Grade 6th Common Core Clinics, Ratios and Proportions and Expressional Reasoning 6.EE.3Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. What does it mean to be equivalent, mathematically speaking? Why do you think it is called the distributive property? Equivalent Expression Distributive property UNIT: OPERATIONS WITH DECIMALS Suggested Pacing: 11 Days Standard:6.NS.2, 3Compute fluently with multi-digit numbers and find common factors and multiples. Clarifying Objectives 6.NS.2Fluently divide multi-digit numbers using the standard algorithm. Essential Questions 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation First Nine Weeks What are the steps used for dividing multi-digit numbers? Can I set up a division algorithm? How do you determine the decimal location in a multiplication algorithm? How do you determine the decimal location in a division algorithm? How is decimal placement different for addition, subtraction, multiplication, and division algorithms? Essential Vocabulary Dividend Divisor Estimation Quotient Place value Decimal Place Value Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp 3pg 105-143. Internet Resources: Common Core Number System Fluency Unit https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit1 SE.pdf Online Decimal Math Games http://www.math-play.com/decimalmath-games.html Solving Problems with Decimals Interactive Website http://www.learnalberta.ca/content/m esg/html/math6web/index.html?page= lessons&lesson=m6lessonshell05.swf Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Supplemental Resources: Common Core Clinics, The Number System UNIT: OPERATIONS WITH FRACTIONS Suggested Pacing: 15 Standard:6.NS.1, 4 Apply and extend previous understands of multiplication and division to divide fractions by fractions. Clarifying Objectives 6.NS.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Essential Questions Why is it important to know the greatest common factor of two numbers? Why is it important to understand the least common multiple of two numbers? First Nine Weeks OPTIONAL: Unit 4: Fractions Adding & Subtracting 5.NF.A.1 =Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 6.NS.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. What are the steps for adding or subtracting fractions? How can a mixed number be changed into an improper fraction? What are the steps for dividing a fraction by fraction? How are multiplying fractions and dividing fractions connected? Why does a fraction get smaller if multiplied by another fraction? Why does it grow if multiplied by a whole number greater than 1? Essential Vocabulary Divisibility Prime Composite Prime Factorization Factor Multiples Greatest common factor (GCF) Least common multiple (LCM) Distributive property Numerator Denominator Mixed number Improper fraction Numerator Denominator Quotient Mixed number Improper fraction Reciprocal Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp. 2 pg. 43-101 Multiplying and Dividing Fractions Chp. 4 pg. 147-185 Fractions, Decimals, and Percents Internet Resources: Common Core Number System Fluency Unit: https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit1 SE.pdf Factors, Multiples and Prime Factorization Interactive Website: http://www.learnalberta.ca/content/m esg/html/math6web/index.html?page= lessons&lesson=m6lessonshell07.swf Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Supplemental Resources: Common Core Clinics, The Number System Classroom Activities and Lessons: AIMS Education Foundation, Fabulous Fractions Classroom Activities and Lessons: AIMS Education Foundation, Actions with Fractions UNIT: RATIOS AND PROPORTIONS Suggested Pacing: 22 Days Standard:6.RP.1, 2, 3 Understand ratio concepts and use ratio reasoning to solve problems. Clarifying Objectives What is the relationship between ratios and fractions?’ What is the meaning of ratio, how can it be expressed, and reduced? Essential Vocabulary Ratio Proportion Part to whole Part to part Equivalent Quantity Simplify Reduce Second Nine Weeks 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Essential Questions Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp 5 pg. 189-233 Ratios, Rates, and Data Analysis Internet Resources: Common Core Rate, Ratio and Proportional Reasoning Using Equivalent Fractions: https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit2 SE.pdf Introduction and Reinforcement Videos: http://studyjams.scholastic.com/studyj ams/services/searchresults?query=Ratios Lesson Plan for Ratios (Optimizing Security Cameras): http://map.mathshell.org/materials/les sons.php?taskid=482#task482 Lesson Plan for Ratios (Sharing Costs: Traveling to School): http://map.mathshell.org/materials/les sons.php?taskid=489#task489 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship.“This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is What is the unit rate of …? (cups of flour to sugar, gallons of gas to miles, miles traveled per hour, price per ounce) Unit Rate Ratio Relationship Rate Simplify Interactive Website on Ratios: http://www.learnalberta.ca/content/m esg/html/math6web/index.html?page= lessons&lesson=m6lessonshell03.swf ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Expectations for unit rates in this grade are limited to non-complex fractions. 6.RP.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. a. 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 b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. What are ratios and proportions and why do we use them? What are relationships among given ratios? What do ordered pairs represent on a coordinate plane? What is the best bargain/better buy? How long will it take to complete a job given a ration of previous job? (4 lawns are moved in 7 hours, how many lawns can be mowed in 35 hours?) What is the saying for conversions of the metric system and the standard measurement system? How would you solve conversions of centimeters to inches and kilometers to miles? What percentage of sixth grades are in _____ homeroom? What is the conversion process used to calculate 7/5 into a percent? Reduce Unit Rate Ratio Relationship Rate Simplify Reduce Table Tape Diagrams Double Line Diagrams Input/Output Table Constant Percent Interactive Website on Percents: http://www.learnalberta.ca/content/m esg/html/math6web/index.html?page= lessons&lesson=m6lessonshell04.swf Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Supplemental Resources: Common Core Clinics, Ratios and Proportions and Expressional Reasoning Classroom Activities and Lessons: AIMS Education Foundation, Proportional Reasoning, Grades 69 Classroom Activities and Lessons: AIMS Education Foundation, Through the Eyes of the Explorers, Grades 5-9 Classroom Activities and Lessons: AIMS Education Foundation, Fabulous Fractions, Grade 3-5 UNIT: INTEGERS Suggested Pacing: 22 Days Standard:6.NS.5, 6, 7, 8 Apply and extend previous understandings of numbers to the system of rational numbers. Clarifying Objectives Second Nine Weeks 6.NS.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., – (–3) = 3, and that 0 is its own opposite b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the Essential Questions What in the world are negative numbers and how do we use them? How can temperature be represented on a number line? How does paying bills and receiving checks utilize a number line? Can I find the opposite of any given number? What do opposite signs represent on a number? What are the quadrants of the coordinate plane system and how are ordered pairs signs related to the quadrants? What is the meaning to absolute value? Why are negative integers the opposite of positive integers? Where in the real world are negative integers and values used? What is the relationship between two ordered pairs differing only by signs? How do I recognize this as a Essential Vocabulary Integer Positive Negative Above/below zero Elevation Credit Debit Deposit Withdrawal Absolute Value Rational Number Coordinates x-axis y-axis Ordered pair Opposite Number Line Coordinate Plane Quadrants Reflection Location Vertical Horizontal Distance Absolute Value Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp. Internet Resources: Common Core Rational Explorations: Numbers and their Opposites Unit: https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit7 SE.pdf Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Supplemental Resources: Common Core Clinics, The Number System Classroom Activities and Lessons: Positive vs. Negative: Investigations with Integers, Grade 6-9 points are related by reflections across one or both axes. c. 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. 6.NS.7 Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line. F or 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. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3oC > –7oC to express the fact that –3oC is warmer than –7oC. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute 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. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 reflection? Inequality Greater Than Less Than Equal to Positive Negative dollars. 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. What is the distance between points Aand B? What are the signs for X and Y in each quadrant? Define and determine absolute value between two points. Graph coordinates for polygons and find missing vertices based on properties of triangles and quadrilaterals. Coordinates Coordinate Plane Quadrants (I,II,III,IV) Points Ordered pair x-axis y-axis UNIT: ALGEBRA Suggested Pacing: 29 Days Standard:6.EE.4, 5, 6, 7, 8, 9 Apply and extend previous understanding of arithmetic to algebraic expressions. Third Nine Weeks Clarifying Objectives 6.EE.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. 6.EE.5Understand 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. 6.EE.6 Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8Write 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. Essential Questions What does it mean for two expressions to be equivalent? How does the value of the variable change the value of the equation? How does using the inverse operations help me solve equations and inequalities? What is a variable in the real world? How is algebra used in the world we live in every day? What does it mean to be unequal? What is an inequality in terms of algebraic expressions? Essential Vocabulary Base Power Exponent Expression Equivalent Simplify Coefficient Equation Inequality Substitution Variable Expression Equation Substitution Variable Expression Equation Substitution Variable Expression Inverse operation Equation Substitution Variable Expression Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp. 7 pg. 275-323 Equations Chp. 8 pg. 327-361 Inequalities Internet Resources: Common Core One Step Equations and Inequalities Unit: https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit4 SE.pdf Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Introduction and Reinforcement Videos: http://studyjams.scholastic.com/studyj ams/services/searchresults?query=equations Supplemental Resources: Common Core Clinics, Ratios and Proportions and Expressional Reasoning Classroom Activities and Lessons: Solving Equations: A Conceptual Approach , Grade 6-9 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Why is it important to be able to apply the rules of algebra in the world around us? Can you create one scenario of everyday life that would naturally have an algebraic equation involved? Expression Equivalent Simplify Coefficient Variable Dependent variable Independent variable UNIT: GEOMETRY Suggested Pacing: 23 Days Standard:6.G.1, 2, 3, 4 Solve real-world and mathematical problems involving area, surface area, and volume Third Nine Weeks/Fourth Nine Weeks Clarifying Objectives 6.G.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.3Draw 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 realworld and mathematical problems. 6.G.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. Essential Questions What does area mean? Why are there different formulas to find the area of different polygons? Essential Vocabulary Area Triangles Quadrilaterals Formula Squared What does volume mean? How can the volume of a triangular prism be found by placing unit cubes inside it? Volume Length Width Height Base Side Cubed Formula Unit How can the use of a coordinate plane aid in find area, lengths, and widths of a polygon? How can this idea be applied to city grids? Coordinate Plane Polygon Length Formula How can a net make it easier to find surface area of a 3-demensional object? How can be nets be used to find surface area on irregular polygons? Nets 3D/Threedimensional Surface Area Formula Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp. 6 pg. 248-273 Circles and Area Internet Resources: Common Core Area and Volume Unit: https://www.georgiastandards.org/Co mmonCore/Common%20Core%20Framewo rks/CCGPS_Math_6_6thGrade_Unit5 SE.pdf Lesson Plan on Geometry (Laws of Arithmetic): http://map.mathshell.org/materials/les sons.php?taskid=484#task484 Lesson Plan on Geometry (Designing Candy Cartoons): http://map.mathshell.org/materials/les sons.php?taskid=488#task488 Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Supplemental Resources: Common Core Clinics, Geometry UNIT: DATA AND STATISTICS Suggested Pacing: 15 days Standard:6.SP.1, 2, 3, 4, 5Develop understanding of statistical variability Clarifying Objectives Fourth Nine Weeks 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 6.SP.2Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape. Essential Questions How are statistics used to collect, analyze, and draw conclusions in today’s society? Why are statistics important in the world? Essential Vocabulary Statistics Data Variability Resources/ References Textbooks: 6th Grade Big Ideas Math Book, Chp. 9 pg. 365-403 Tables, Graphs, and Functions Internet Resources: 6.SP.3Recognize 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. 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking What are the ways that data be represented visually? How can data vary? What real-world situations give us data? Why is it better to use different graphs and diagrams to understand data? What are the different ways in which we can summarize data sets? Data Center Spread Shape Value Variation Spread Standard deviation Numerical data Number line Histogram Box plot Numerical data Observational data Measurement Mean Median Mode Range Interquartile range Absolute deviation Practice Questions per Common Core Standard Objective: http://www.ixl.com/math/grade-6 Introduction and Reinforcement Videos: http://studyjams.scholastic.com/studyj ams/services/searchresults?query=number%20lines Box and Whisker Plot Maker: http://www.mathwarehouse.com/chart s/box-and-whisker-plot-maker.php Box and Whisker Plot PowerPoint Lesson: http://www.brainingcamp.com/conten t/box-and-whisker-plots/lesson.php Box Plot Activity Lesson: http://www.graniteschools.org/depart/ teachinglearning/curriculuminstructio n/math/secondarymathematics/PreAlg ebra%20Lessons/35NewPreAlgLessonHApr2BoxWhiske rPlot.pdf Histograms Lesson and Practice: http://www.gaston.k12.nc.us/schools/ cramerton/faculty/kllasky/Course%20 deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Variability Measure of center Distribution Outline%20and%20Syllabus/Textboo k/Ch%2003/Text%203.5.pdf Supplemental Resources: Common Core Clinics, Statistics and Graphs UNIT: Resources for End of Grade Testing Review Suggested Pacing: 10-20 days or until testing begins Standard:All Domain Ratios and Proportional Relationships The Number System Expressions and Equations Geometry Statistics and Probability Resources/ References
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