1. 1 REQUIREMENT INFORMATIONASSESSMENT INFORMATION TD3 Textbook Resource Glencoe Math: Course 1 Note: The Standards in each unit are not required to be taught in order. Every attempt should be made to teach material in the quarter to which it has been assigned. NWEA/MAP Assessment AZMerit Assessment AZMerit is a computer-based test which provides engaging questions and measures critical thinking skills for college and career readiness. For schools that are not yet ready, a paper-based version is available. AZMerit is aligned to Arizona’s state learning standards which detail what students should be able to do at each grade level. The test is designed to measure student learning and progress towards readiness for college and career. HOW TO READ THE CURRICULUM MAP Standards are grouped into units in each quarter. Example : Quarter 1: Unit 1 Knowledge for each standard appears directly adjacent to the strand and standard identification. When part of a standard is crossed out, that part of the standard will be addressed in a later unit. “Big Ideas” are what the students will understand by the end of the unit. “Essential Questions” stimulate ongoing thinking of “Big Ideas.” Key terms come from the Standards as well as additional academic words to support instruction. Standards are labeled by grade level (6), domain (RP), cluster (A), and standard (3). Example: 6.RP.A.3 The Big Ideas, Essential Questions, and Key Terms are student friendly language.(They are also highlighted in Blue) 3/1/2016Tempe Elementary School District #3 6th GRADE - MATH 6 th GRADE NWEA/MAP INFORMATION Spring National Norm (2011) 240

2. Overview of Math Domains for 6 th Grade Ratios and Proportional Relationships (RP)  Understand ratio concepts and use ratio reasoning to solve problems. The Number System (NS)  Apply and extend previous understandings of multiplication and division to divide fractions by fractions.  Compute fluently with multi‐digit numbers and find common factors and multiples.  Apply and extend previous understandings of numbers to the system of rational numbers. Expressions and Equations (EE)  Apply and extend previous understandings of arithmetic to algebraic expressions.  Reason about and solve one‐variable equations and inequalities.  Represent and analyze quantitative relationships between dependent and independent variables. Geometry (G)  Solve real‐world and mathematical problems involving area, surface area, and volume. Statistics and Probability (SP)  Develop understanding of statistical variability.  Summarize and describe distributions. 2Tempe Elementary School District #3 6th GRADE - MATH 3/1/2016

3. Standards for Mathematical Practices (MP) Standards Students are expected to: Explanations and Examples 6.MP.1. Make sense of problems and persevere in solving them. In Grade 6, students solve problems involving ratios and rates and discuss how they solved them. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?” 6.MP.2. Reason abstractly and quantitatively. In Grade 6, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations. 6.MP.3. Construct viable arguments and critique the reasoning of others. In Grade 6, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?” “Does that always work?” They explain their thinking to others and respond to others’ thinking. 6.MP.4. Model with mathematics. In Grade 6, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students begin to explore covariance and represent two quantities simultaneously. Students use number lines to compare numbers and represent inequalities. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences about and make comparisons between data sets. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context. 3Tempe Elementary School District #3 6th GRADE - MATH 3/1/2016

4. Standards for Mathematical Practices (MP), continued Standards Students are expected to: Explanations and Examples 6.MP.5. Use appropriate tools strategically. Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 6 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. Additionally, students might use physical objects or applets to construct nets and calculate the surface area of three‐ dimensional figures. 6.MP.6. Attend to precision. In Grade 6, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to rates, ratios, geometric figures, data displays, and components of expressions, equations or inequalities. 6.MP.7. Look for and make use of structure. Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables recognizing both the additive and multiplicative properties. Students apply properties to generate equivalent expressions (i.e. 6 + 2x = 2 (3 + x ) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality; c=6 by division property of equality). Students compose and decompose two‐ and three‐ dimensional figures to solve real world problems involving area and volume. 6.MP.8. Look for and express regularity in repeated reasoning. In Grade 6, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d = ad/bc and construct other examples and models that confirm their generalization. Students connect place value and their prior work with operations to understand algorithms to fluently divide multi‐ digit numbers and perform all operations with multi‐ digit decimals. Students informally begin to make connections between covariance, rates, and representations showing the relationships between quantities. 4Tempe Elementary School District #3 6th GRADE - MATH 3/1/2016

5. 6 th Grade Key Terms ALL CAPS Term = second and final year of appearance 5 absolute value absolute value symbol (| |) additive identity property algebra tiles algebraic expression associative property average axis (x,y) bar notation symbol box plot cluster commutative property composite constant coordinate (x,y) coordinate plane dependent variable distribution distributive property dot plot double number line diagram evaluate exponent frequency table gap greatest common factor histogram independent variable inequality infinite integer interquartile range interval kite least common multiple mean mean absolute deviation median mode multiplication symbol () multiplicative identity property multiplicative inverse property negative (-) net numerical expression ordered pair origin outlier peak per percent (%) positive (+) quadrant range rate ratio ratio table rational number reciprocal reflection right rectangular prism simplest form skew spread statistical question statistics substitution surface area unit rate variability variable volume Tempe Elementary School District #3 6th GRADE - MATH 3/1/2016

6. Tempe Elementary School District #36 7 The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 4 The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 5 Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. 3/1/2016 6th GRADE - MATH

7. Quarter 1 Unit 1 Suggested Number of Days: 8 Days Big Ideas/Enduring Understandings: Understanding place value helps to justify the steps of standard algorithms. Fractions, decimals, and percents express the same quantity in a form that is appropriate to the context. Essential Questions: Why is understanding place value important for standard algorithms? What determines when to use fractions, decimals, or percents? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster NS.B: Compute fluently with multi-digit numbers and find common factors and multiples. NS.C: Apply and extend previous understanding of numbers to the system of rational numbers. Key Terms AZCCRSKnowledgeSkills multiplication symbol (  ) percent (%) rational number bar notation symbol 6.NS.B.2 Also in Q2-Unit 5 Division standard algorithmFluently DIVIDE multi-digit numbers using the standard algorithm. 6.NS.B.3 Also in Q2-Unit 5 Standard algorithm for decimal addition, subtraction, multiplication, division Fluently ADD, SUBTRACT, MULTIPLY, AND DIVIDE multi-digit decimals using the standard algorithm for each operation. Note: Fluency expected by the end of Unit 5. AZ.6.NS.C.9 Positive rational numbersC ONVERT between expressions for positive rational numbers, including fractions, decimals, and percents. Resources: http://bit.ly/24QIDSI 7 6th GRADE - MATH Tempe Elementary School District #33/1/2016

8. Quarter 1 Unit 2 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: Ratios and rates are multiplicative comparisons of two quantities or measurements. Solving real-world problems using visual models helps strengthen understanding of ratio and rate reasoning. Understanding unit rates helps solve real-world mathematical problems when comparing a quantity related to a unit of one. Essential Questions: What are ratios and rates? How can ratio and rate reasoning be understood? What is the purpose of unit rates? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster RP.A: Understand ratio concepts and use ratio reasoning to solve problems. Key Terms AZCCRSKnowledgeSkills ratio rate unit rate per double number line diagram 6.RP.A.1 RatioUnderstand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Note: 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.” 6.RP.A.2 Unit rateUnderstand 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. 8 6th GRADE - MATH Tempe Elementary School District #33/1/2016

9. Note: For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Note: Expectations for unit rates in this grade are limited to non- complex fractions. 6.RP.A.3 Also in Q1-Unit 3 Ratio and rate reasoning Equivalent ratios Unit rate Percent Measurement conversion U SE 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.S OLVE unit rate problems including those involving unit pricing and constant speed. Note: 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. Resources: http://bit.ly/1X8hd8a 9 6th GRADE - MATH Tempe Elementary School District #33/1/2016

10. Quarter 1 Unit 3 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: Proportional relationships are recognized or represented through tables, graphs, equations, diagrams and verbal descriptions. The whole and the proportional relationship are essential for solving a ratio and percent problem. Essential Questions: How are proportional relationships recognized or represented? What are essential components of a ratio and percent problem? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster RP.A: Understand ratio concepts and use ratio reasoning to solve problems. Key Terms AZCCRSKnowledgeSkills ratio table ordered pair coordinate plane coordinate (x, y) axis (x, y) origin quadrant 6.RP.A.3 Also in Q1-Unit 2 Ratio and rate reasoning Equivalent ratios Unit rate Percent U SE 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. M AKE 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. U SE tables to compare ratios. b.S OLVE unit rate problems including those involving unit pricing and constant speed. Note: 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.F IND 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. 10 6th GRADE - MATH Tempe Elementary School District #33/1/2016

11. Measurement conversiond.U SE ratio reasoning to CONVERT measurement units; MANIPULATE and TRANSFORM units appropriately when multiplying or dividing quantities. Resources: http://bit.ly/1Op1D6D 11 6th GRADE - MATH Tempe Elementary School District #33/1/2016

12. Quarter 1 Unit 4 Suggested Number of Days: 10 Days Big Ideas/Enduring Understandings: Dividing a fraction by a fraction involves determining how much of the divisor makes up the dividend. Essential Questions: What is involved in dividing a fraction by a fraction? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster NS.A: Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Key Terms AZCCRSKnowledgeSkills reciprocal simplest form 6.NS.A.1 Quotients of fractionsInterpret 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. Note: For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Note: Through use of conceptual understanding, i.e. visual models, the standard algorithm of (a/b) ÷ (c/d) = ad/bc will be developed by the end of the unit. Resources: http://bit.ly/27kQv12 12 6th GRADE - MATH Tempe Elementary School District #33/1/2016

13. Quarter 2 Unit 5 Suggested Number of Days: 14 Days Big Ideas/Enduring Understandings: Expressions can be recorded, interpreted, and evaluated based on operational relationships between the quantities. Symbols represent quantities and operations that determine how to evaluate expressions. Essential Questions: How can expressions be recorded, interpreted, and evaluated? How are symbols used to evaluate expressions? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster EE.A: Apply and extend previous understandings of arithmetic to algebraic expressions. EE.B: Reason about and solve one-variable equations and inequalities. NS.B: Compute fluently with multi-digit numbers and find common factors and multiples. Key Terms AZCCRSKnowledgeSkills variable constant numerical expression algebraic expression evaluate algebra tiles exponent coefficient volume greatest common factor least common multiple distributive property 6.EE.B.6 VariablesU SE variables to REPRESENT numbers and WRITE expressions when solving a real-world or mathematical problem; UNDERSTAND that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.A.1 Numerical expressions Exponents W RITE and EVALUATE numerical expressions involving whole- number exponents. 6.EE.A.2 Also in Q4-Unit 13, Q4-Unit 14 Expressions Numbers and variables W RITE, READ, and EVALUATE expressions in which letters stand for numbers. a.W RITE expressions that record operations with numbers and with letters standing for numbers. 13 6th GRADE - MATH Tempe Elementary School District #33/1/2016

14. Parts of expressions Note: 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. Note: 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 real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Note: For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. 6.NS.B.4 Greatest common factor Least common multiple Distributive property Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Note: For example, express 36 + 8 as 4 (9 + 2). 6.NS.B.2 Also in Q1-Unit 1 Division standard algorithmFluently divide multi-digit numbers using the standard algorithm. 14 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

15. 6.NS.B.3 Also in Q1-Unit 1 Standard algorithm for decimal addition, subtraction, multiplication, division Fluently ADD, SUBTRACT, MULTIPLY, and DIVIDE multi-digit decimals using the standard algorithm for each operation. Resources: http://bit.ly/24QIVcl 15 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

16. Quarter 2 Unit 6 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: Properties of operations support strategies used in evaluating expressions and solving equations. Real-world situations can be solved by creating, interpreting, and evaluating expressions and equations. Essential Questions: Why are properties of operations important? How can mathematical real-world situations be solved? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster EE.A: Apply and extend previous understanding of arithmetic to algebraic expressions. EE.B: Reason about and solve one-variable equations and inequalities. Key Terms AZCCRSKnowledgeSkills associative property commutative property additive identity property multiplicative identity property multiplicative inverse property substitution 6.EE.A.3 Equivalent expressionsApply the properties of operations to generate equivalent expressions. Note: 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. 6.EE.A.4 Equivalent expressionsIdentify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). Note: For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. 16 6th GRADE - MATH Tempe Elementary School District #33/1/2016

17. 6.EE.B.5 Also in Q3-Unit 10 Equations Substitution U NDERSTAND 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? U SE substitution to DETERMINE whether a given number in a specified set makes an equation or inequality true. 6.EE.B.7 Real-world problems with equations Nonnegative rational numbers S OLVE 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. Resources: http://bit.ly/1rKNBSN 17 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

18. Quarter 2 Unit 7 Suggested Number of Days: 13 Days Big Ideas/Enduring Understandings: Real-world examples help strengthen understanding of both the magnitude and direction of integers. Opposite quantities have a sum of zero. Essential Questions: How can integers be understood? What is the relationship of opposite quantities? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster NS.C: Apply and extend previous understanding of numbers to the system of rational numbers. Key Terms AZCCRSKnowledgeSkills integer positive (+) negative (-) absolute value absolute value symbol (| |) 6.NS.C.5 Positive and negative numbersU NDERSTAND that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); USE positive and negative numbers to REPRESENT quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.C.6 Also in Q3-Unit 8 Rational numbers Number line Opposite signs U NDERSTAND a rational number as a point on the number line. E XTEND 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.R ECOGNIZE 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. 18 6th GRADE - MATH Tempe Elementary School District #33/1/2016

19. 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. 6.NS.C.7 Also in Q3-Unit 10 Rational numbers Statements of order Absolute value Number line U NDERSTAND 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. Note: For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b.W RITE, INTERPRET, and EXPLAIN statements of order for rational numbers in real-world contexts. Note: For example, write –3° C > –7° C to express the fact that –3° C is warmer than –7° C. c.U NDERSTAND 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. Note: For example, for an account balance of –30 dollars, write |– 30| = 30 to describe the size of the debt in dollars. 19 6th GRADE - MATH Tempe Elementary School District #33/1/2016

20. Comparisons of absolute value and order d.Distinguish comparisons of absolute value from statements about order. Note: For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Resources: http://bit.ly/1s82DSD 20 6th GRADE - MATH Tempe Elementary School District #33/1/2016

21. Quarter 3 Unit 8 Suggested Number of Days: 10 Days Big Ideas/Enduring Understandings: Plotting ordered pairs shows the relationship of location and distance from the origin on a coordinate plane. Essential Questions: What does plotting ordered pairs show? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster NS.C: Apply and extend previous understanding of numbers to the system of rational numbers. G.A: Solve real-world and mathematical problems involving area, surface area, and volume. Key Terms AZCCRSKnowledgeSkills Reflection 6.NS.C.6 Also in Q2-Unit 7 Rational numbers Number line Opposite signs Ordered pairs Vertical number line Horizontal number line Coordinate plane 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 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. 21 6th GRADE - MATH Tempe Elementary School District #33/1/2016

22. 6.G.A.3 Polygons Coordinate plane Real-world problems with polygons 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.NS.C.8 Real-world problems with distances 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. Resources: http://bit.ly/1Op2cNG 22 6th GRADE - MATH Tempe Elementary School District #33/1/2016

23. Quarter 3 Unit 9 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: The relationship between variables in an equation can be represented in a table, verbal description, and on a graph. Essential Questions: How can the relationship between variables in an equation be represented? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster EE.C: Represent and analyze quantitative relationships between dependent and independent variables. Key Terms AZCCRSKnowledgeSkills dependent variable independent variable 6.EE.C.9 Real-world problems with variables Relationship between variables 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. Note: 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. Resources: http://bit.ly/1s82Yob 23 6th GRADE - MATH Tempe Elementary School District #33/1/2016

24. Quarter 3 Unit 10 Suggested Number of Days: 13 Days Big Ideas/Enduring Understandings: An inequality shows a relationship between two expressions. Substitution can help in solving equations and inequalities by inserting values to evaluate. Essential Questions: What does an inequality show? How can substitution help in solving equations and inequalities? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster EE.B: Reason about and solve one-variable equations and inequalities. NS.C: Apply and extend previous understandings of numbers to the system of rational numbers. Key Terms AZCCRSKnowledgeSkills inequality Infinite 6.EE.B.5 Also in Q2-Unit 6 Equations and inequalities Substitution U NDERSTAND 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? U SE substitution to DETERMINE whether a given number in a specified set makes an equation or inequality true. 6.EE.B.8 Real-world problems with constraints or conditions W RITE an inequality of the form x > c or x c or x < c have infinitely many solutions; REPRESENT solutions of such inequalities on number line diagrams. 6.NS.C.7 Also in Q2-Unit 7 Rational numbers Inequality U NDERSTAND ordering and absolute value of rational numbers. a.I NTERPRET statements of inequality as statements about the relative position of two numbers on a number line diagram. 24 6th GRADE - MATH Tempe Elementary School District #33/1/2016

25. Statements of order Absolute value Number line Comparisons of absolute value and order Note: For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b.Write, interpret, and explain statements of order for rational numbers in real-world contexts. Note: For example, write –3° C > –7° C to express the fact that –3° C is warmer than –7° C. 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 real-world situation. Note: For example, for an account balance of –30 dollars, write |– 30| = 30 to describe the size of the debt in dollars. d.Distinguish comparisons of absolute value from statements about order. Note: For example, recognize that an account balance less than – 30 dollars represents a debt greater than 30 dollars. Resources: http://bit.ly/1TTazjE 25 6th GRADE - MATH Tempe Elementary School District #33/1/2016

26. Quarter 3 Unit 11 Suggested Number of Days: 9 Days Big Ideas/Enduring Understandings: The mean, median, and mode are measures that describe the center of data. Keeping data in a real-world context when answering a statistical question can help gain an understanding of the relationship of the information. Essential Questions: How are the mean, median, and mode helpful in understanding data in real-world situations? Why is it important to keep data related to a real-world context when answering a statistical question? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster SP.A: Develop understanding of statistical variability. Key Terms AZCCRSKnowledgeSkills statistics statistical question variability distribution interval spread mean average median mode range outlier cluster peak gap skew dot plot box plot histogram 6.SP.A.1 Statistical questionRecognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Note: 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.A.2 Data Distribution 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. 26 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

27. 6.SP.A.3 Measure of center Measure of variation R ECOGNIZE 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. Resources: http://bit.ly/1OsmII1 27 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

28. Quarter 4 Unit 12 Suggested Number of Days: 13 Days Big Ideas/Enduring Understandings: Numerical data can be represented on a number line, dot plot, histogram, and box plot. The measurement of center is selected based on the reason why data was gathered. Essential Questions: How can numerical data be represented? How does the context in which data was gathered impact which measurement of center is selected? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster SP.B: Summarize and describe distributions. Key Terms AZCCRSKnowledgeSkills frequency table interquartile range mean absolute deviation 6.SP.B.4 Numerical dataDisplay numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.B.5 Numerical data sets Attribute Measures of center Variability 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. 28 6th GRADE - MATH Tempe Elementary School District #33/1/2016

29. Measures of center Variability d.R ELATING the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered. Resources: http://bit.ly/1TLycaZ 29 6th GRADE - MATH Tempe Elementary School District #33/1/2016

30. Quarter 4 Unit 13 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: Polygons are composed and decomposed into known shapes to find area. Essential Questions: How are polygons composed and decomposed to find area? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster G.A: Solve real-world and mathematical problems involving area, surface area, and volume. EE.A: Apply and extend previous understandings of arithmetic to algebraic expressions. Key Terms AZCCRSKnowledgeSkills kite composite 6.G.A.1 Area of polygonsFind 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.EE.A.2 Also in Q2-Unit 5, Q4-Unit 14 Expressions Numbers and variables Parts of expressions 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. Note: 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. 30 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

31. Note: 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 real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Note: For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Resources: http://bit.ly/1Wvl2Gc 31 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

32. Quarter 4 Unit 14 Suggested Number of Days: 15 Days Big Ideas/Enduring Understandings: Three-dimensional figures can be represented using two-dimensional nets. Surface area is the sum of the areas of the two-dimensional surfaces that make up a three-dimensional figure. Essential Questions: How can three-dimensional figures be represented? What is the relationship between area and surface area? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster G.A: Solve real-world and mathematical problems involving area, surface area, and volume. EE.A: Apply and extend previous understandings of arithmetic to algebraic expressions. Key Terms AZCCRSKnowledgeSkills right rectangular prism net surface area 6.G.A.2 Volume Real-world problems Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l  w  h and V = b  h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real- world and mathematical problems. 6.G.A.4 Nets Surface area Real-world 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. 6.EE.A.2 Also in Q2-Unit 5, Q4-Unit 13 Expressions Numbers and variables 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. For example, 32 6th GRADE - MATH Tempe Elementary School District #3 3/1/2016

33. Parts of expressions 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. Note: 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 real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Note: For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Resources: http://bit.ly/24XskXM 33 6th GRADE - MATH Tempe Elementary School District #33/1/2016