Campbellsport School District Understanding by Design (UbD) Template


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1 Campbellsport School District Understanding by Design (UbD) Template Class Curriculum/Content Area: Math Course Length: 1 year Course Title: 6 th Grade Math Date last reviewed: April 24, 2015 Prerequisites: 5 th Grade Math Board approval date: pending Desired Results: Course description and purpose: Course Description Mathematics at the Sixth grade level focuses on: Ratios and Proportional Relationships Understand Ratio Concepts; Use Ratio Reasoning The Number System Perform Fraction and Decimal Operations; Understand Rational Numbers Expressions and Equations Write, Interpret, and Use Expressions, Equations, and Inequalities Geometry Solve Problems Involving Area, Surface Area, and Volume Statistics and Probability Summarize and Describe Distributions; Understand Variability Purpose Understand and demonstrate basic math computational skills and apply understandings to higher level mathematical concepts and reasoning, as well as apply mathematical skills to realworld phenomenon. Enduring Understandings (EUs) The student will: 1. Write and evaluate mathematical expressions and equations in realworld situations. 2. Use formulas to solve problems involving area and perimeter of polygons and circumference and area of circles. 3. Describe mathematical relationships using expressions and visual representations. 4. Use order of operations to evaluate expressions. 5. Add, subtract, multiply, and divide multidigit numbers efficiently, including realworld problems. 6. Add, subtract, multiply, and divide fractions and decimals efficiently, including realworld problems. 7. Explain and justify procedures for adding, subtracting, multiplying, and dividing fractions and decimals. 8. Verify reasonableness of answers using various strategies, such as estimating. 9. Compare and order fractions, decimals, and percents. 10. Construct and analyze tables and graphs. 11. Determine measures of central tendency. (mean, median, mode) 12. Use reasoning to solve rate and ratio problems. 13. Write and solve onestep and twostep equations. 14. Write, solve, and graph onestep and twostep Essential Questions (EQs) 1. How do you write and solve mathematical expressions and equations? 2. What formulas are used to find the area and perimeter of polygons? 3. How do change mathematical sentences into expressions and visual representations? 4. What is the order of operations and how is it used to evaluate expressions? 5. What are the mathematical processes for adding, subtracting, multiplying, and dividing multidigit numbers, fractions and decimals? 6. Why is it important to verify the reasonableness of an answer? 7. How do you compare and order fractions, decimals, and percents? 8. Why is it important to construct and analyze tables and graphs? 9. How do you determine measures of central tendency? 10. How do you solve rate and ratio problems? 11. What is the process in writing and solving equations? 12. What is the process in writing, solving, and graphing inequalities? 13. How do you calculate dimensions for plane figures and prisms? 14. How do you use tables and graph to write and
2 inequalities. 15. Find dimensions of plane figures and prisms. 16. Construct and analyze tables, graphs, and equations to describe linear functions and other simple relations. 17. Write, interpret, understand, and explain concepts involving all rational numbers.(positive and negative) 18. Understand and use the coordinate plane to solve realworld and mathematical problems. solve linear functions? 15. What are the rules for adding, subtracting, multiplying, and dividing positive and negative numbers? 16. How can you use mathematical expressions and equations to represent realworld situations? 17. How do you use the coordinate plane to solve mathematical problems? Assessment Evidence Performance assessments: Other assessments: Formative assessments (classroom observations, quizzes, tests, projects) Numerical Expressions and Factors A. Whole Number Operations B. Powers and Exponents C. Order of Operations D. Prime Factorization E. Greatest Common Factor F. Least Common Multiple G. Adding and Subtracting Fractions 6.NS.2 Fluently divide multidigit numbers using the standard algorithm. 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.EE.1 Write and evaluate numerical expressions involving wholenumber exponents. 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 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. 1. I can divide multidigit numbers. 2. I can find the greatest common factor and least common multiple of two or more numbers. 3. I can read, write and evaluate numerical expressions. 4. I can use Order of operations to solve numerical expressions. Fractions and Decimals A. Multiplying Fractions B. Dividing Fractions C. Dividing Mixed Numbers D. Adding and Subtracting Decimals E. Multiplying Decimals
3 F. Dividing Decimals 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. 6.NS.3 Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. 1. I can add and subtract fractions, mixed numbers, and decimals. 2. I can multiply and divide fractions, mixed numbers, and decimals. Algebraic Expressions and Properties A. Algebraic Expressions B. Writing Expressions C. Properties of Addition and Multiplication D. The Distributive Property E. Factoring Expressions 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. 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. 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 wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 6.EE.3 Apply the properties of operations to general equivalent expressions. 6.EE.4 Identify when two expressions are equivalent 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. 1. I can read, write and evaluate numerical expressions as well as identify components of algebraic expressions. 2. I can identify equivalent expressions using basic math properties (identity, commutative, associative, distributive). 3. I can use variables and numbers to read and write algebraic expressions. 4. I can use Order of operations to simplify numerical expressions. Areas of Polygons A. Areas of Parallelograms
4 B. Areas of Triangles C. Areas of Trapezoids D. Areas of Composite Figures E. Polygons in the Coordinate Plane 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 6.G.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 length of the prism. Apply the formulas V =lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to fi nd 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. 1. I can calculate area of geometric figures using formulas for parallelograms, triangles, trapezoids, and composite figures. 2. I can graph ordered pairs in a coordinate plane to calculate area of geometric figures. Ratios and Rates A. Ratios B. Ratio Tables C. Rates D. Comparing and Ordering Ratios E. Percents F. Solving Percent Problems G. Converting Measures Standards (CCSS, Next Generation, ACT College and Career Readiness, etc.) 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 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. 6.RP.3 Use ratio and rate reasoning to solve realworld and mathematical problems. a. 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 tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. c. Find a percent of a quantity as a rate per 100; 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. 1. I can recognize and compare ratios and rates. 2. I can calculate unit rates. 3. I can solve realworld problems involving rates and ratios. 4. I can use ratios to convert measurements.
5 5. I can find percent of numbers. Integers and the Coordinate Plane A. Integers B. Comparing and Ordering Integers C. Fractions and Decimals on a Number Line D. Absolute Value E. The Coordinate Plane F. Reflecting Points in a Coordinate Plane 6.NS.5 Understand 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 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, 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 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. NS.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. b. Write, interpret, and explain statements of order for rational numbers in realworld contexts. c. 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 realworld situation. d. Distinguish comparisons of absolute value from statements about order. NS.8 Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distance between points with the same first coordinate or the same second coordinate. 1. I can describe quantities with positive and negative numbers. 2. I can compare and order integers and absolute value numbers with and w/o a number line. 3. I can graph ordered pairs in all four quadrants of a coordinate plane and find distances between two points. 4. I can understand integers to solve reallife applications. 5. I can reflect points in a coordinate plane. Equations and Inequalities A. Writing Equations in One Variable B. Solving Equations Using Addition and Multiplication C. Solving Equations Using Multiplication and Division D. Writing Equations in Two Variables E. Writing and Graphing Inequalities F. Solving Inequalities Using Addition and Subtraction
6 G. Solving Inequalities Using Multiplication and Division 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or 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.7 Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infi nitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.9 Use variables to represent two quantities in a realworld 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. 1. I can determine if a value is a solution. 2. I can write word sentences as equations and inequalities. 3. I can solve onestep equations and inequalities using addition, subtraction, multiplication, and division. 4. I can represent inequalities and recognize the many solutions. 5. I can write equations and inequalities to solve realworld problems. 6. I can identify independent and dependent variables. 7. I can use tables and graphs to analyze information. 8. I can use a number line to graph the solution set of inequalities. Surface Area and Volume A. ThreeDimensional Figures B. Surface Area of Prisms C. Surface Area of Pyramids D. Volumes of Rectangular Prisms 6.G.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 length of the prism. Apply the formulas V =lwh and V = bh to fi nd volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 6.G.4 Represent threedimensional 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. 1. I can find area of triangles, special quadrilaterals, and polygons 2. I can use nets made up of rectangles and triangles to find surface area. 3. I can find the volume of prisms and pyramids.
7 4. I can classify plane and solid figures. 5. I can draw threedimensional figures. 6. I can identify faces, edges, and vertices of prisms and pyramids. 7. I can use surface area and volume to solve realworld problems. Statistical Measures A. Introduction to Statistics B. Mean C. Measures of Center D. Measures of Variation E. Mean Absolute Deviation 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation 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 deviations from the overall pattern with reference to the context in which the data were gathered. 1. I can recognize statistical questions. 2. I can understand data to answer statistical questions. 3. I can use measures to summarize values in a data set. 4. I can use dot plots to display numerical data. 5. I can find the mean, median, mode, and range of a set of data. 6. I can compare the mean, median, and modes of a set of data. 7. I can understand mean absolute deviation. Data Displays (may not cover) A. Stem and Leaf Plots B. Histograms C. Shapes of Distributions D. Choosing Appropriate Measures E. Box and Whisker Plots 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
8 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: c. Giving quantitative measures of center (median and/or mean) and variability(interquartile range and/or mean absolute deviation), as well as describing anyoverall pattern and any striking 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. 1. I can display data on a number line, including line plots, stem and leaf plots, histograms, and box and whisker plots. 2. I can describe shapes of distributions. 3. I can choose appropriate measures of center and variation to represent data sets. Scope & Sequence Numerical Expressions and Factors 17 days Fractions and Decimals 24 days Algebraic Expressions and Properties 18 days Areas of Polygons 18 days Ratios and Rates 25 days Integers and the Coordinate Plane 20 days Equations and Inequalities 23 days Surface Area and Volume 15 days Statistical Measures 20 days ************************ 180 days Data Displays 15 days **may switch last 2 units around**
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