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- 1. 6th Grade Math Curriculum Map 6th Grade Math Curriculum Map IntroductionThis document contains all mandated 2010 Arizona Mathematical Standards for 6th grade mathematics. The standards have been organized intounits and clusters. The units represent the major domain under which the identified standards fall. The cluster represents the collection of similarconcepts within the larger domain. Within these units and clusters the performance objectives have been sequenced to represent a logical progressionof the content knowledge. It is expected that all teachers follow the sequence of units and clusters as described in the following document. OrganizationApproximate TimeApproximate times are based on a 60-minute instructional session for grades 6-8. All units and clusters must be taught prior to the 2013 AIMSassessment.Essential QuestionsEssential Questions are to be posed to the students at the beginning of the cluster and revisited throughout the cluster. They are designed to facilitateconceptual development of the content and can be used as a tool for making connections, higher order thinking and inquiry. The students should beable to answer these on their own by the end of the cluster.Big IdeasBig Ideas are the essential understandings that are critical for students’ learning. These are the enduring understandings we want students to carrywith them from grade level to grade level. Answering the Essential Questions is indicative of a student mastering the Big Idea, however they are notalways synonymous. Thus, in cases that the answer to the Essential Question does not include all components of the Big Idea, the Big Idea (for teacheruse) has been provided in italics.Common MisconceptionsThese are common misunderstandings students bring to the learning process. Being aware of such misconceptions allows us to plan for them duringinstruction.Content Standards and Mathematical PracticesThis document has been organized by content standards and mathematical practices. The content standards are those that represent knowledgespecific to the mathematical standard (The five domains). The mathematical practices describe varieties of expertise that mathematics educators atall levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance inmathematics education. The content standards and mathematical standards have been paired to represent possible combinations of content standardswith mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, thepairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to adeeper level of understanding and/or should be connected to the other standards in the cluster.9/10/2012 1 Isaac Elementary School District
- 2. 6th Grade Math Curriculum MapCommon Core/Cross CurricularThe standards in the Common Core/Cross Curricular column represent possible reading, writing, math and language standards that can be reinforcedor taught through the mathematical content standards with which they are paired.PriorityWith input from grade level teachers, standards have been prioritized in two ways. The content standards have been prioritized using a three-pointscale. Essential standards represent those that are heavily weighted on state/national exams, foundational, and/or applicable in multiple contexts.Important standards are those that are applicable in many contexts and less heavily weighted on state/national exams. Useful standards are thosewith the least weight on state/national exams and are likely only useful in a specific context. This is denoted in the priority column with the codes E(essential), I (important) and U (useful). This label applies to the content standards only. The skill/process standards that are a priority for thisgrade level are highlighted in blue and are expected to be mastered at this grade level.Key VocabularyThe key vocabulary that should be taught for each of the performance objectives is listed under key vocabulary. These vocabulary words are codedas tier one (1), tier two (2) or tier three (3). Tier one words are those that are very common and should not be explicitly taught. Tier two words arehigh utility words that can be used across content areas or contexts. Tier three words are content specific words.ResourcesThe two types of resources listed are the Web Resources resources and the Core Resources. All are suggestions that teachers may use to supportinstruction. They are aligned to the standards listed in the same row. The web resources are useful Internet links that can be used for the teacher’sedification prior to instruction or as a tool during instruction. The core resources are suggested pages from the adopted texts.Unit/Cluster ProjectThe Unit/Cluster Projects are possible projects that teachers can use to support students in making connections, critical thinking, higher order thinking,and/or spiraling curriculum. Unit projects support standards from all clusters within a unit while cluster project support the standards in a particularcluster. While it is not required that a teacher do a project with every unit or cluster these resources will support project-based instruction andpractice should the teacher choose to implement them.AssessmentThe assessment section of the map has been left blank for teachers to plan the dates that they will give a formative assessment for the cluster. It isexpected that each cluster be assessed using a common formative assessment.OtherStandards may appear more than once. Each time they should be taught within the context of the cluster and/or revisited to a deeper level ofknowledge. Underlined segments of a standard indicate an additional piece of the standard that was likely not covered in previous clusters.[Brackets] will occasionally appear though out the document and indicate clarification of the standard. Bracketed information is not a part of thestandard itself.9/10/2012 2 Isaac Elementary School District
- 3. 6th Grade Math Curriculum Map Unit: Ratios and Proportional Relationships Cluster: Ratios and Rates Approximate Time: 1 week Essential Questions Big Ideas How are parts of a number represented? The same number can be written as a rate and a How are ratios and rates related? ratio. Why is it important to know the equivalent form of numbers? Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.RP.1. Understand the concept of 6.MP.2 6-8.RST.4 Ratio Comparing Ratios and MC: 6-1 a ratio and use ratio language to 6.MP.6 6-8.WHST.2d Rate Rates Worksheet describe a ratio relationship Unit rate between two quantities. Equivalent Ratios Worksheet Introduction 6.RP.2. Understand the concept of 6.MP.2 6-8.RST.4 Ratio Example Problems for MC: 6-1 a unit rate a/b associated with a 6.MP.6 Rate Solving Unit Rates ratio a:b with b 0, and use rate Unite rate language in the context of a ratio Ratio and Rate Venn relationship. Diagram 6.RP.3. Use ratio and rate 6.MP.1 6.EE.9 Double number line Types of Ratios MC: 6-2 reasoning to solve real-world and 6.MP.2 6-8.RST.7 Diagrams mathematical problems, e.g., by 6.MP.4 ET06-S6C2-03 Equations reasoning about tables of 6.MP.5 SC06-S2C2-03 Equivalent ratios equivalent ratios, tape diagrams, 6.MP.7 Rate double number line diagrams, or Ratio equations. Tape diagrams Unit Project: Assessment:9/10/2012 3 Isaac Elementary School District
- 4. 6th Grade Math Curriculum Map Unit: The Number System Cluster: Fractions, Decimals, and Percents Approximate Time: 5 weeks Essential Questions Big Ideas How are parts of a number represented? The same number can be written as a fraction, How are fractions, decimals, and percents related? decimal, and percent. Why is it important to know equivalent forms of numbers? Why is it important to know the percent of a number? How a number is represented depends on the given What are the strategies we use to multiply and divide fractions? situation and/or need.9/10/2012 4 Isaac Elementary School District
- 5. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.NS.1. Interpret and compute 6.MP.1 6-8.RST.7 Compute Dividing Fractions MC: 5-7, 5-8, 5-9, quotients of fractions, and solve 6.MP.2 Equations Student Copy 5-10 word problems involving division 6.MP.3 Fractions of fractions by fractions, e.g., by 6.MP.4 Improper fraction Dividing Fractions CM: Bits & Pieces II using visual fraction models and 6.MP.7 Product Teacher Copy Investigation 3 & 4 equations to represent the 6.MP.8 Interpret problem. Mixed number Fractions in Division Quotient Word Problems Reciprocal Simplest form Math Is Fun-Dividing Fractions 6.NS.4. Find the greatest common 6.MP.7 6-8.RST.4 Composite numbers LCM and GCF MC: 1-2, 4-1, 4-5 factor of two whole numbers less Multiple than or equal to 100 and the Distributive property Prime factorization CM: Prime Time least common multiple of two Factor Investigation 1, 3-5 whole numbers less than or equal GCF Factor Game to 12. Use the distributive LCM property to express a sum of two Prime factorization whole numbers 1–100 with a Prime numbers common factor as a multiple of a Sum sum of two whole numbers with no Whole number common factor. 6.NS.9. Convert between 6.MP.2 Annex Changing fractions, MC: 4-7, 4-8, 7-1, expressions for positive rational 6.MP.8 Convert percents, and decimals 7-3 numbers, including fractions, Decimal decimals, and percents Equivalent PowerPoints Fraction CM: Bits & Pieces 1 Percent Converting Game 3.4, 4.4 Rational number Introduction *S1C1PO 4. Compare and order Ascending order MC: 3-2, 4-6 integers; and positive fractions, Compare decimals, and percents. Descending order CM: Bits & Pieces 1 Fractions 3.5, Investigation 2 Integers Least common denominator Percents Unit Project: Assessment:9/10/2012 5 Isaac Elementary School District
- 6. 6th Grade Math Curriculum Map Unit: The Number System Cluster: Decimal Operations Approximate Time: 2 weeks Essential Questions Big Ideas What are the strategies we use to add, subtract, multiply, and divide Decimal placement affects the value of the solution. decimals? Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.NS.2. Fluently divide multi-digit 6.MP.2 6-8.RST.3 Algorithm Math Live MC: 5th Grade: 4-4 numbers using the standard 6.MP.7 Dividend algorithm. 6.MP.8 Divisor Quotient 6.NS.3. Fluently add, subtract, 6.MP.2 6-8.RST.3 Addend Math Live MC: 3-4, 3-5, 3-6, multiply, and divide multi-digit 6.MP.7 Algorithm 3-7, 3-8, 3-9 decimals using the standard 6.MP.8 Difference Fluency with Decimals algorithm for each operation. Dividend CM: Bits & Pieces III Divisor 1.2, 2.3, 3.3 Factor Minuend Product Quotient Subtrahend Sum Unit Project: Assessment:9/10/2012 6 Isaac Elementary School District
- 7. 6th Grade Math Curriculum Map Unit: The Number System Cluster: Absolute Value and Integers Approximate Time: 2 weeks Essential Questions Big Ideas What is absolute value? Integers are used in a wide array of contexts. How do you order integers? How do you model integers?9/10/2012 7 Isaac Elementary School District
- 8. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.NS.5. Understand that positive 6.MP.1 6-8.RST.4 Integers Introduction MC: 2-9 and negative numbers are used 6.MP.2 6-8.WHST.2d MC: 7th Grade: 2-1 together to describe quantities 6.MP.4 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.6. Understand a rational 6.MP.2 6-8.RST.7 Coordinate axes Whole Numbers and MC: 2-9 number as a point on the number 6.MP.4 SS06-S1C1-03 Line diagrams Integers MC: 7th Grade: 2-1 line. Extend number line diagrams Rational numbers and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.7. Understand ordering and 6.MP.1 6-8.WHST.1c Absolute value Absolute Value War MC: 11-1 absolute value of rational 6.MP.2 6-8.WHST.2a Ascending order LA: 2-4 numbers. 6.MP.4 Descending order Absolute Value 6. Greater than Worksheet 7. a. Interpret statements of Inequality inequality as statements about the Integers Khan Academy relative position of two numbers on Less than a number line diagram. For Line diagram AAAMath example, interpret –3 > –7 as a Rational numbers statement that –3 is located to the Number Balls right of –7 on a number line oriented from left to right. Coolmath b. Write, interpret, and explain Eduplace statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as9/10/2012 8 Isaac Elementary School District
- 9. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 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. d. 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 dollars. *S1C2PO1. Apply and interpret the Integers Addition MC: 11-2, 11-3 concepts of addition and subtraction Zero pairs with integers using models. Subtraction Gizmo with Number Lines Gizmo with Chips Unit Project: Assessment:9/10/2012 9 Isaac Elementary School District
- 10. 6th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Expressions and Order of Operations Approximate Time: 2 weeks Essential Questions Big Ideas What is an algorithm? Algorithms are useful strategies for computing. What argument can you provide to explain your solution? The order of operations will affect solutions.9/10/2012 10 Isaac Elementary School District
- 11. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.EE.1. Write and evaluate numerical expressions 6.MP.2 6-8.RST.4 Base Order of MC: 1-3, involving whole-number exponents. Exponents Operations 1-4 Order of operations Parentheses Order of Powers Operations Whole number Examples Evaluate Expressions Order of Operations Lessons/Practice 6.EE.2. Write, read, and evaluate expressions in 6.MP.1 6-8.RST.4 Coefficient Translate to MC: 1-5 which letters stand for numbers. 6.MP.2 6-8.WHST.2d Exponent Algabraic 6.MP.3 Expressions Expressions a. Write expressions that record operations with 6.MP.4 Factor numbers and with letters standing for numbers. 6.MP.6 Order of operations For example, express the calculation “Subtract y Parenthesis Gizmos to from 5” as 5 – y. Product Translate Quotient Algebraicl b. Identify parts of an expression using Substitution Expressions mathematical terms (sum, term, product, factor, Sum quotient, coefficient); view one or more parts of Term an expression as a single entity. For example, Variable Worksheet 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 Translate to Algebraic c. Evaluate expressions at specific values of their Equations variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving Substitution 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=s3 and A=6 s2 to find the volume and surface area of a cube with sides of length s=1/2. *S1C1PO 6. Express the inverse relationships Cube root Perfect Squares MC: 7th between exponents and roots for perfect squares Cubed Grade: 1- and cubes. Exponents 3 Inverse Perfect Cubes9/10/2012 11 Isaac Elementary School District
- 12. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core Perfect Squares Radical sign Square root Squared Unit Project: Assessment:9/10/2012 12 Isaac Elementary School District
- 13. 6th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Properties Approximate Time: 1 week Essential Questions Big Ideas What are the math properties and why do we use them? Distributive Property a(b + c) = a(b) + a(c) a(b) + a(c) = a(b + c) Commutative Property a+b=b+a a*b=b*a Associative Property a + (b + c) = (a + b) + c a * (b * c) = (a * b) * c Identity Property a+0=a a*1=a9/10/2012 13 Isaac Elementary School District
- 14. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.EE.3. Apply the properties of 6.MP.2 6-8.RST.4 Associative property Basic Number MC: 12-1, 12-2 operations to generate equivalent 6.MP.3 Identity property Properties expressions. 6.MP.4 Distributive property MC: 7th Grade: 1- 6.MP.6 Commutative More Basic Number 8 6.MP.7 property Properties Equivalent expressions Distributive Property 6.EE.4. Identify when two 6.MP.2 6-8.RST.5 Combine like terms Combining Like Terms MC: 12-2 expressions are equivalent 6.MP.3 Equivalent 6.MP.4 expressions Combining Like Terms 6.MP.6 Game 6.MP.7 Equivalent Expressions Worksheet Unit Project: Assessment:9/10/2012 14 Isaac Elementary School District
- 15. 6th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Solving Equations Approximate Time: 3 weeks Essential Questions Big Ideas What does a variable represent? Variables represent numbers. How do you solve/interpret equations? Algebra is used to solve real world situations. What are the multiple ways you can represent the process and solution? Estimates can be used to verify the reasonableness of a result.9/10/2012 15 Isaac Elementary School District
- 16. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.EE.5. Understand solving an 6.MP.1 6-8.RST.7 Equation MC: 12-3, 12-4, equation or inequality as a 6.MP.2 Inequality 12-5 process of answering a question: 6.MP.4 Inverse operations which values from a specified set, 6.MP.7 Inverse properties MC: 7th Grade: 5- if any, make the equation or Substitution 6 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 6.MP.2 6-8.RST.4 Expression Expressions and MC: 12-3, 12-4, numbers and write expressions 6.MP.4 Variable 12-5 when solving a real-world or 6.MP.7 Equations mathematical problem; MC: 7th Grade: 3- understand that a variable can Writing Expressions 1, 5-6 represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7. Solve real-world and 6.MP.1 6-8.RST.7 Equation One-step Equations MC: 12-3, 12-4, mathematical problems by writing 6.MP.2 Rational numbers 12-5 and solving equations of the form x 6.MP.3 Equation Game + p = q and px = q for cases in 6.MP.4 MC: 7th Grade: 3- which p, q and x are all nonnegative 6.MP.7 Solving One-step 1, 5-6 rational numbers Equation Video *S3C3PO 2. Create and solve two- Coefficient Two-step Equations MC: 7th Grade: 3- step equations that can be solved Equation 5 using inverse properties with Inverse properties Equation Game fractions and decimals. Term Two-step equations Multi-step equation Variable Video Unit Project: Assessment:9/10/2012 16 Isaac Elementary School District
- 17. 6th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Inequalities Approximate Time: 2 weeks Essential Questions Big Ideas What is an inequality? When ≤ or ≥ are used, the circle on the graph is filled in to show that the number is included in the solution. What symbol represents greater/less than and greater/less than or equal to? What symbol represents the phrase not equal to?9/10/2012 17 Isaac Elementary School District
- 18. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.EE.8. Write an inequality of the 6.MP.1 6-8.RST.7 Inequality Solving Inequalities Video MC: 7th Grade: form x > c or x < c to represent 6.MP.2 Infinite pg. 740 a constraint or condition in a 6.MP.3 Number line Solving Linear Inequalities: real-world or mathematical 6.MP.4 diagrams Addition/Subtraction MC: 8th Grade: 8- problem. Recognize that 6.MP.7 Solution 6, 8-7, 8-8 inequalities of the form x > c or Online Quiz: Solving x < c have infinitely many Linear Inequalities: solutions; represent solutions of Addition/Subtraction such inequalities on number line diagrams. Solving Linear Inequalities: Multiplication/Division Online Quiz: Solving Linear Inequalities: Multiplication/Division Real Life Problems Worksheet Graphing Inequalities Foldable-Student Copy Solving Inequalities Foldable-Teacher Copy 6.EE.9. Use variables to 6.MP.1 6.RP.3 Dependent variable Graphing From Function MC: 1-6, 6-6 represent two quantities in a 6.MP.2 6-8. RST.7 Equation Tables real-world problem that change 6.MP.3 ET06-S1C2-01 Function in relationship to one another; 6.MP.4 ET06-S1C2-02 Input (x) Function Machine write an equation to express one 6.MP.7 ET06-S1C2-03 Output (y) quantity, thought of as the 6.MP.8 ET06-S6C2-03 In/out table Stop That Creature dependent variable, in terms of SC06-S2C2-03 Independent variable 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. Unit Project: Assessment:9/10/2012 18 Isaac Elementary School District
- 19. 6th Grade Math Curriculum Map Unit: Geometry Cluster: Coordinate Plane Approximate Time: 2 weeks Essential Questions Big Ideas How do you use a coordinate plane? Ordered pairs show an exact location on a coordinate plane. How do you find a missing coordinate? What are the features of a coordinate plane? How do values on a coordinate plane relate to integers?9/10/2012 19 Isaac Elementary School District
- 20. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.NS.8. Solve real-world and 6.MP.1 6.G.3 Coordinate plane The Math Worksheet MC: 4-9, 11-7 mathematical problems by 6.MP.2 6-8.RST.7 Ordered pairs Site graphing points in all four 6.MP.4 Quadrant quadrants of the coordinate 6.MP.5 Origin Coordinate Plane plane. Include use of coordinates 6.MP.7 X-axis and absolute value to find Y-axis Coordinate Plane distances between points with the Game same first coordinate or the same second coordinate. Khan Academy Coordinate Plane Template Distance Between Points Worksheet 6.G.3. Draw polygons in the 6.MP.1 6.NS.8 Coordinate plane Galileo coordinate plane given 6.MP.2 6-8.RST.7 Ordered pair Study Island coordinates for the vertices; use 6.MP.4 Origin coordinates to find the length of a 6.MP.5 Polygon side joining points with the same 6.MP.7 Parallelogram first coordinate or the same Quadrilateral second coordinate. Apply these Vertex (vertices) techniques in the context of solving real-world and mathematical problems. *S4C2PO1. Identify a simple Coordinate plane Introduction MC: 11-8 translation or reflection and model Origin its effect on a 2-dimensional figure Quadrants on a coordinate plane using all four Reflection quadrants. Translation X-axis Y-axis *S4C2PO2. Draw a reflection of a Coordinate plane MC: 11-9 polygon in the coordinate plane Horizontal line using a horizontal or vertical line of Origin reflection. Reflection X-axis Y-axis Unit Project: Assessment:9/10/2012 20 Isaac Elementary School District
- 21. 6th Grade Math Curriculum Map Unit: Geometry Cluster: Area, Volume, and Surface Area Approximate Time: 4 weeks Essential Questions Big Ideas What real world use is there for knowing area, volume, and surface area? Measures of length are expressed in linear units, measures of area are expressed in square units, and measures of volume are expressed in cubic units.9/10/2012 21 Isaac Elementary School District
- 22. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 6.G.1. Find the area of right 6.MP.1 6-8.RST.7 Area Decomposing Polygons MC: 1-9, 10-4 triangles, other triangles, special 6.MP.2 6-8.WHST.2b,d Length to find Area quadrilaterals, and polygons by 6.MP.3 ET06-S1C2-02 Polygons MC: 7th Grade: 3- composing into rectangles or 6.MP.4 Quadrilaterals 6, 11-2, 11-6 decomposing into triangles and other 6.MP.5 Right triangles shapes; apply these techniques in the 6.MP.6 Width CM: Covering and context of solving real-world and 6.MP.7 Surrounding mathematical problems. 6.MP.8 6.G.2. Find the volume of a right 6.MP.1 6-8.RST.4 Area of the base MC: 10-6 rectangular prism with fractional 6.MP.2 ET06-S1C2-02 Edge edge lengths by packing it with unit 6.MP.3 Face cubes of the appropriate unit 6.MP.4 Height fraction edge lengths, and show 6.MP.5 Rectangular prism that the volume is the same as 6.MP.6 Vertex would be found by multiplying the 6.MP.7 Volume edge lengths of the prism. Apply 6.MP.8 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.4. Represent three-dimensional 6.MP.1 6-8.RST.7 Edge Surface Area and Nets MC: 10-7, LA20 figures using nets made up of 6.MP.2 6-8.WHST.2b Face Foldable rectangles and triangles, and use the 6.MP.3 ET06-S1C2-02 Nets MC: 7th Grade: 12- nets to find the surface area of these 6.MP.4 ET06-S1C2-03 Surface area Surface Area and Nets 4 figures. Apply these techniques in the 6.MP.5 Three-dimensional Foldable-Teacher Copy context of solving real-world and 6.MP.6 Vertex mathematical problems. 6.MP.7 Surface Area and Nets 6.MP.8 Cut Outs PowerPoint *S4C4PO 5. Solve problems Area MC: 10-1 involving area and perimeter of Irregular polygon regular and irregular polygons Perimeter CM: Covering and Regular polygon Surrounding *S4C1PO1. Define (pi) as the Circle MC: 10-2 ratio between the circumference and Circumference diameter of a circle and explain the Diameter CM: Covering and relationship among the diameter, Pi Surrounding radius, and circumference. Radius9/10/2012 22 Isaac Elementary School District
- 23. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S4C1PO 2. Solve problems using Complementary MC: LA 10 properties of supplementary, angles complementary, and vertical angles. Supplementary MC: 7th Grade: angles 10-1, 10-2 Vertical angles Unit Project: Assessment:9/10/2012 23 Isaac Elementary School District
- 24. 6th Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Graphing and Measures of Central Tendency Approximate Time: 4 weeks Essential Questions Big Ideas How can you collect, organize, and display data? Charts, tables, and graphs help us make valid inferences, decisions, and arguments. How does the type of data influence the choice of graph? Appropriate graphs need to be used in specific How do you use modes of central tendency? situations. How do we determine which information is relevant or missing?9/10/2012 24 Isaac Elementary School District
- 25. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Resources Practices Curricular Vocabulary Web Resources Core 6.SP.1. Recognize a statistical question as one 6.MP.1 Galileo that anticipates variability in the data related to 6.MP.3 the question and accounts for it in the answers. 6.MP.6 Study Island 6.SP.2. Understand that a set of data collected to 6.MP.2 6-8.RST.4 Maximum Teacher Tube MC: 2-6, 2-7 answer a statistical question has a distribution 6.MP.4 Mean Lesson that can be described by its center, spread, and 6.MP.5 Median MC: 7th Grade: overall shape. 6.MP.6 Minimum Jeopardy Game 8-1, 8-2 6.MP.7 Mode Outliers CM: Data About Range Us 6.SP.3. Recognize that a measure of center for a 6.MP.2 6-8.RST.4 Absolute Galileo numerical data set summarizes all of its values with 6.MP.4 deviation a single number, while a measure of variation 6.MP.5 Standard Study Island describes how its values vary with a single number. 6.MP.6 deviation 6.MP.7 6.SP.4. Display numerical data in plots on a 6.MP.2 6-8.RST.7 Box and whiskers Box Plots MC: 2-5, LA25 number line, including dot plots, histograms, and 6.MP.4 ET06-S6C2-03 Dot plot box plots. 6.MP.5 SC06-S1C4-01 Histogram Histograms MC: 8th Grade: 6.MP.6 SC06-S1C4-02 Interquartile 8-1, 8-4 6.MP.7 SS06-S1C1-02 Line plot Box Plots SS06-S1C2-02 Lower quartile Foldable-Student MC: 8th Grade: SS06-S1C4-01 Maximum Copy 11-6 Minimum Box Plots Stem and leaf Foldable-Teacher CM: plot Copy Data About Us Upper quartile Investigation 2 6.SP.5. Summarize numerical data sets in relation 6.MP.2 6-8.WHST.2a-f Absolute Grab a Handful to their context, 6.MP.3 ET06-S6C2-03 deviation Box Plot Activity a. Reporting the number of observations. 6.MP.4 Box and whiskers 6.MP.5 Dot plot Minute to Win It b. Describing the nature of the attribute under 6.MP.6 Histogram Box Plots investigation, including how it was measured and 6.MP.7 Interquartile Recording Sheet its units of measurement Line plot Lower quartile Minute to Win It c. Giving quantitative measures of center (median Maximum Games and/or mean) and variability (interquartile range Mean and/or mean absolute deviation), as well as Median Box and Whiskers describing any overall pattern and any striking Minimum Task Analysis deviations from the overall pattern with reference Mode to the context in which the data were gathered. Outliers d. Relating the choice of measures of center and Range9/10/2012 25 Isaac Elementary School District
- 26. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Resources Practices Curricular Vocabulary Web Resources Core variability to the shape of the data distribution Standard and the context in which the data were gathered. deviation Stem and leaf plot Upper quartile *S2C1P2. Formulate and answer questions by Histograms Histograms MC: 2-4 interpreting, analyzing, and drawing inferences Stem-and-leaf Stem-and-Leaf Plot from displays of data, including histograms and plots stem-and-leaf plots. Unit Project: Assessment:9/10/2012 26 Isaac Elementary School District
- 27. 6th Grade Math Curriculum Map Unit: Probability Cluster: Theoritical and Experimental Probability Approximate Time: 1 week Essential Questions Big Ideas How are theoretical probability and experimental probability different? Probability is a form of estimation. What is a sample space and how is it used? Using a systematic approach can confirm solutions. What is a conjecture? Why do we replicate an experiment? What are the multiple ways you can represent a sample space?9/10/2012 27 Isaac Elementary School District
- 28. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S2C2PO1. Use data collected Certain Expressing MC: 7-4 from multiple trials of a single event Experimental probability Likelihood to form a conjecture about the Conjecture CM: How likely is theoretical probability. Favorable outcomes it? Possible outcomes Impossible Probability Random Theoretical probability Tree diagram *S2C2PO 2. Use theoretical Certain Theoretical MC: 7-4 probability to Experimental Probability predict experimental Conjecture CM: How likely is outcomes, Favorable outcomes it? compare the outcome of the Possible outcomes experiment to the Impossible prediction, and Probability replicate the experiment and Random compare results Theoretical Tree diagram *S2C2PO3. Determine all possible Possible outcomes Sample Space MC: 7-5 outcomes (sample space) of a given Probability situation using a systematic Sample space CM: How likely is approach. Tree diagram it? *S2C3PO 1. Build and explore tree Certain MC: 7-5 diagrams where items repeat. Conjecture Favorable outcomes CM: How likely is Possible outcomes it? Impossible Probability Random Repeat Sample space Tree diagram Unit Project: Assessment:9/10/2012 28 Isaac Elementary School District
- 29. 6th Grade Math Curriculum Map Unit: Measurement Cluster: U.S. Customary and Metric System Approximate Time: 2 weeks Essential Questions Big Ideas What are the units in the U.S. customary system? There are appropriate units of measure for different situations. What are the units in the metric system? How do you convert between units?9/10/2012 29 Isaac Elementary School District
- 30. 6th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S4C4PO 1. Determine the Clock CM: Chapter 8 appropriate unit of measure for a Protractor given context and the appropriate Ruler tool to measure to the needed Scale precision (including length, capacity, angles, time, and mass). *S4C4PO 2. Solve problems Capacity CM: Chapter 8 involving conversion within the U.S. Centi Customary and within the metric Cup system Customary Feet Fluid ounce Gallon Gram Inch Kilo Length Liter Mass Meter Metric Mile Milli Ounce Pint Pound Quart Ton Weight Yard *S4C4PO 3. Estimate the measure Scale CM: 7th Grade: 6-8 of objects using a scale drawing or Scale drawing map. Scale factor Scale model Unit Project: Assessment:9/10/2012 30 Isaac Elementary School District

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