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Curriculum DocumentOriginal Development: Spring 2013

Unit: UNIT 1: USING EXPRESSIONS AND EQUATIONS

Subject/Course: MATH

Grade Level: 6TH GRADE

School Year: 2013-14

This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)

Big Ideas: Why is this learning important? What generalization or principle do you want to know/do? The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.

Reading, writing and evaluating expressions in algebraic form will help to solve many real-world problems.

Common Core Standards / State StandardsContent Standard:including CODE + (Rigor)

DOMAIN: Expressions and EquationsCLUSTER: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard Code:

6.EE.1. Write and evaluate numerical expressions involving whole-number exponents. (Evaluate, DOK 2)

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. For example, express the calculation “Subtract y from 5” as 5 – y. (Remember, DOK 1)

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. (Remember, DOK 1)

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). 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. (Evaluate, DOK 1)

6.EE.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression

o 3 (2 + x) to produce the equivalent expression 6 + 3x;o apply the distributive property to the expression 24x + 18y to

produce the equivalent expression 6 (4x + 3y);o apply properties of operations to y + y + y to produce the

equivalent expression 3y. (Apply, DOK 1) 6.EE.4. Identify when two expressions are equivalent (i.e., when the two

document.docx Page 1

expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. (Remember, DOK 1)

DOMAIN: Expressions and EquationsCLUSTER: Reason about and solve one-variable equations and inequalities.Standard Code:

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. (Understand, DOK 2)

6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. (Understand, DOK 2)

6.EE.7. Solve 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. (Apply, DOK 2)

6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (Remember, DOK 3)

Reading StandardWriting StandardMath Practiceincluding CODE

College and Career Readiness Anchor Standards for ReadingKey Ideas and Details1. Read closely to determine what the text says explicitly and to make logical

inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

College and Career Readiness Anchor Standards for WritingProduction and Distribution of Writing5. Develop and strengthen writing as needed by planning, revising, editing,

rewriting, or trying a new approach.

Mathematical Practices (bold are to be emphasized in the unit)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.

TechnologyStandard:including CODE

ET06-S1C2-01: Recognize and explain relevant interdependent elements of a digital model or simulation. (6.EE.4)ET06-S1C2-02: Explore and experiment with system variables using models or simulations. (6.EE.2)ET06-S1C2-03: Compare and contrast two systems using a digital model or simulation. (6.EE.3)ET06-S1C4-02: Use digital collaborative tools to analyze information to produce original works and express ideas. (6.EE.2a, 6.EE.2b)


ET06-S4C2-01: Plan and manage research using credible digital resources to develop solutions to answer a question. (6.EE.2)

ELP Standard:including CODE

Completed by SEI/ELP teachers (later)

Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Exponential notation, sum, term, product, factor, quotient, coefficient, distributive property, exponents, inverse operation, equation, inequality, variablesDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Students will: Expressions mathematical terms

o sumo termo producto factoro quotiento coefficient

Order of Operations properties of operations equivalent expressions problems equations variablesProcedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Students will: WRITE(expressions and equations) READ(expressions) EVALUATE (expressions) IDENTIFY (mathematical terms) PERFORM (Order of Operations) APPLY (properties of operations) GENERATE equivalent expressions SOLVE (equations) SOLVE (real-world and mathematical problems)

Prerequisites: Use Hess’s Cognitive Rigor Matrix to “map” pre-requisite conceptual & procedure knowledge

Domain: Operation and Algebraic ThinkingCluster: Write and Interpret numerical expressionsStandard Code: 5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these

symbols.5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions

without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

AssessmentsProvide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor) 2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)

6.EE.2cWhat is the value of 2x3 + 4x2 3x2 6x when x = 3? document.docx Page 3

Show all work. Answer: ____________________Rationale: Substituting x = 3 into the expression yields 2(33) + 4(32) 3(32) 6(3), which simplifies to 45.6.EE.2a, 6.EE.2bRepresent the following expression algebraically: A number, x, decreased by the sum of 2x and 5 A (2x + 5) – x B x – (2x + 5) C x – 2x + 5 D (x + 2x) – 5 Rationale: Option B is correct and is consistent with the relationship between the minuend (x) and subtrahend (2x + 5). The expression in Option A confuses the minuend and subtrahend, identifying the minuend incorrectly as (2x + 5). The expression in Option C is incorrect and does not take into account the expression the sum of 2x and 5 as a single entity (2x + 5), joined through subtraction. The expression ignores the subtraction of each term in the subtrahend, not just the term 2x. The expression in Option D incorrectly identifies the sum of x and 2x as an expression.6.EE.2a, 6.EE.2c, 6.EE.3, 6.EE.7The figure below is a square with dimensions given. Part A: What is the perimeter of the square in terms of x? Perimeter = ________ Part B: If the length of each side of the square is doubled, what would be the perimeter of this new square, in terms of x? Perimeter = ________ Part C: If x = 5, what would be the ratio of the area of the original square to the area of the new square? Answer: ____________________Rationale: Part A: Since the length of each side of the square is 2x – 1, the perimeter of the square is the sum of the lengths of the sides of the square, or 4 times the length of each side. So the perimeter of the square would be 4(2x – 1) = 8x – 4. Part B: If the length of each side of the square is doubled, the length of each side of the new square would be 2(2x – 1), or 4x – 2 inches. The perimeter would be 4 times the length of each side, so the perimeter of the new square would be 4(4x – 2) = 16x – 8. Part C: If x = 5, the length of each side of the original square would be 9 inches. The area of the square is equal to 9 × 9, or 81 square inches. The length of each side of the new square is 18 inches, so the area of the new square is 324 square inches. The ratio of the area of the original square to the area of the new square is 81:324 or . This could also be represented in simplified form as 1:4, 1 to 4, or . 324 81 41


This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)

UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.EE.1 – SE Holt McDougal: 10–12, 14, 21, 39, 41, 45, 69, 286, 313, 618, EP26.EE.2 – SE Holt McDougal: 50–53, 54–57, 58–61, 64, 79, 93, 139, 159, 286, 456, 659, 709, EP46.EE.2a – SE Holt McDougal: 54–57, 58–61, 64, 69, 93, 139, 203, 456, EP46.EE.2b – SE Holt McDougal: 50–53, 54–57 Curriculum Companion: CC6, CC7, CC8, CC96.EE.2c – SE Holt McDougal: 18–21, 534–537, 540–543, 545–547,552–555, 566–569, 570–573, 576–5796.EE.3 – SE Holt McDougal: 22–23, 25, 28, 44, 62–63, 92, 119 Curriculum Companion: CC6, CC7, CC8, CC96.EE.4 – SE Holt McDougal: 66–69, 84, 89, 91, EP5 Curriculum Companion: CC6, CC7, CC8, CC96.EE.5 – SE Holt McDougal: 66–69, 84, 93, EP56.EE.6 – SE Holt McDougal: 71, 73, 76, 78, 82–83, 84, 90, 91, 93, 137–136, 240–241, 242, 634–6356.EE.7 – SE Holt McDougal: 71–73, 77–80, 84, 90, 91, 95, 107, 111–113, 123–125, 135, 136–138, 140, 146, 147, 168, 238–240, 256, 264–267, 268, 273–275, 317, 345, 362, 441, 452, 591, 632–634, 636, 642,643, 683, 695, 701, 705, EP5, EP10, EP11, EP246.EE.8 – SE Holt McDougal: 718–721, EP28 Curriculum Companion: CC38, CC39, CC40, CC41Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:“Teaching the Common Core Math Standards with Hands-On Activities” (Jossey-Bass Teacher Gr 6-8) pp 29-50.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutions

ONLINE RESOURCES:http://www.tempeschools.org/webpages/commoncore/http://www.internet4classrooms.com/common_core/write_evaluate_numerical_expressions_involving_whole_number_expressions_equations_sixth_6th_grade_math_mathematics.htmTeacher Instructional Strategies: Research-based strategies that “fit.”GroupingQuestioningNon-Linguistic Representations (Graphic Organizers/Visual Aids)High ExpectationsTechnology/MediaAssessments (ongoing)TAP RUBRIC

Learning objectives and state content standards are explicitly communicated. Learning objectives are: a) consistently connected to what students have previously learned, b) know

from life experiences, and c) integrated with other disciplines. State standards are displayed and referenced throughout the lesson. Content is personally meaningful and relevant to students. Lessons with beginning, middle, end and time for reflection. Pacing is brisk and provides many opportunities for individual students who progress at different learning

rates. Activities and Materials Questions are consistently sequenced with attention to the instructional goals. Variety & frequency in Questions/Questioning Wait time Academic Feedback is consistent, focused, frequent and high quality. Grouping Students to facilitate student understanding and learning efficiency, accountability and meets

the goals of the lesson. Teacher knowledge of students


http://www.internet4classrooms.com/common_core/write_evaluate_numerical_expressions_involving_whole_number_expressions_equations_sixth_6th_grade_math_mathematics.htm



http://www.tempeschools.org/webpages/commoncore/

Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S1C2-01: Recognize and explain relevant interdependent elements of a digital model or simulation. (6.EE.4)Math Examples:

Students use interactive learning tool (Balance Pans - Expressions Tool) to learn about equivalent expressions. Everything Balances Out in the End

ET06-S1C2-02: Explore and experiment with system variables using models or simulations. (6.EE.2)Math Examples:

Students play a game and discuss understanding of algebraic expressions. Algebraic Expressions Millionaire

ET06-S1C2-03: Compare and contrast two systems using a digital model or simulation. (6.EE.3)Math

Ker-Splash introduces students to algebra as they try to rack up points by combining like terms. Ker-Splash

Students use algebraic methods to solve a problem in a game format.Algebraic Reasoning Game

ET06-S1C4-02: Use digital collaborative tools to analyze information to produce original works and express ideas. (6.EE.2a, 6.EE.2b)Math Examples:Expressions and Equations

Using Word, Google Drive, or other program have students work in pairs. Each group will create a table consisting of at least two columns (algebraic expressions and

narratives). Each student will write 2 to 3 algebraic expressions, then exchange them with their partner. Students will then write brief narratives that can be matched with the expressions. Mixing up the expressions and narratives students will share their work with other groups to match

each algebraic expression with appropriate narrative. Extend by having students identify the parts of each expression.

ET06-S4C2-01: Plan and manage research using credible digital resources to develop solutions to answer a question. (6.EE.2)Math/Science Examples:

Students are assigned 2 states. They will conduct a comparative research on climate index VS greenhouse gas inventory that spans

20-30 years (e.g. 1990-2005) using NASA or Department of Energy website. They will use a spreadsheet to input and graph the result. They will use this data to determine the

relationship between the 2 variables investigated as well as the rate of change in each of these variables.

Based on this rate, they will predict their assigned states’ climate index VS greenhouse gas inventory in the span of 50 years.

Integration of ELP Strategies: (Language, Grammar, etc)Completed by SEI/ELP teachers (later)

Exemplary Learning Activities (Optional): List one exemplary strategy per box.

Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.


http://www.mathplayground.com/algebraic_reasoning.html

http://216.255.77.73/Ker-Splash

http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html

http://illuminations.nctm.org/LessonDetail.aspx?ID=L641



Unit: UNIT 2: OPERATING WITH POSITIVE RATIONAL NUMBERS






Dividing fractions by fractions and computing fluently with multi digit decimals will help to solve common real-world problems.


DOMAIN: The Number SystemCLUSTER: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.Standard Code:

6.NS.1. Interpret 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. 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? (Create, DOK 1)

DOMAIN: The Number SystemCLUSTER: Compute fluently with multi-digit numbers and find common factors and multiples.Standard Code:

6.NS.2. Fluently divide multi-digit numbers using the standard algorithm. 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals

using the standard algorithm for each operation. 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 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2). (Understand, DOK 1)

DOMAIN: GEOMETRYCLUSTER: Solve real-world and mathematical problems involving area, surface area, and volume.Standard Code:


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 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. (Understand, DOK 1)


College and Career Readiness Anchor Standards for ReadingKey Ideas and Details1. Read closely to determine what the text says explicitly and to make logical inferences

from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

Craft and Structure5. Analyze the structure of texts, including how specific sentences, paragraphs, and

larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

College and Career Readiness Anchor Standards for WritingProduction and Distribution of Writing2. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or

trying a new approach.



ET06-S1C2-01: Recognize and explain relevant interdependent elements of a digital model or simulation. (6.NS.1)ET06-S1C2-02: Explore and experiment with system variables using models or simulations. (6.G.2)



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Quotients, add, subtract, multiply, divide, place value, multi-digit, decimals, common factor, greatest common factor, least common multiple, whole numbers, distributive property, volumeDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Students will: division of fractions multi-digit decimals problems

o models o equations

standard algorithmProcedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Students will:document.docx Page 9

INTERPRET (quotients of fractions) COMPUTE (quotients of fractions) SOLVE (word problems involving division of fractions by fractions) REPRESENT (problems using models and equations) USE a standard algorithm to:

o ADD (multi-digit decimals)o SUBTRACT (multi-digit decimals)o MULTIPLY (multi-digit decimals)o DIVIDE (multi-digit decimals)


Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.Standard Code:5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems

involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Assessments

Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor) 2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)

6.NS.1If one lap of an elliptical track is 1/12mile, how many laps will equal 3/4mile? (3/4 ÷ 1/12 = 9)

If 1/8 teaspoon of baking soda is needed for each pan of biscuits, how manypans of biscuits can be made with ½ teaspoon of baking soda? (1/2 ÷ 1/8 = 4)

Orman has 2/3 cup of cocoa and plans to make chocolate cookies. If each batchof cookies uses 1/6 cup of cocoa, how many batches can he make? (2/3 ÷ 1/6 =4)

Ask students to create a division problem for the following information.Suppose that ¼ cup of sugar is needed and ¾ cup is available.6.NS.3Lela bought a DVD for $22.74 with tax. She gave the sales person $30.00. How much money did she get back? (Show your work)Lela bought a DVD for $22.74 with tax. She gave the sales person $30.00. How much money did she get back?


UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.NS.1 – SE Holt McDougal: 258–259, 260–263, 264–267, 268, 269, 274,275, 279, 555, 625, EP11 Curriculum Companion: CC10, CC116.NS.2 – SE Holt McDougal: SB5 Curriculum Companion:CC2, CC3, CC4, CC56.NS.3 – SE Holt McDougal: 110–113, 114, 115, 122–125, 126–128,129–132, 133–135, 139, 140, 141, 142,145–147, 150–151, 178, 221, 227, 263, 339, 367, 461, 499, EP6–EP76.NS.4 – SE Holt McDougal: 23–25, 28, 39, 41, 44, 61, 165–168, 172,178, 209, 211, 213, 218–221, 241, 242, 267,272, 275, 345, 359, 487, 725, EP3, EP8, EP10 Curriculum Companion: CC6, CC7, CC8, CC9document.docx Page 10

6.G.2 – SE Holt McDougal: SE: 566–569, 580, 581, 586, 587, EP22 Curriculum Companion: CC30, CC31Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:Teaching the Common Core Math Standards with Hands-On Activities (Jossey-Bass Teacher Gr 6-8) pp 9-18 and 57-59.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutions

ONLINE RESOURCES:http://www.tempeschools.org/webpages/commoncore/Teacher Instructional Strategies: Research-based strategies that “fit.”GroupingQuestioningNon-Linguistic Representations (Graphic Organizers/Visual Aids)High ExpectationsTechnology/MediaAssessments (ongoing)TAP RUBRIC





Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S1C2-01: Recognize and explain relevant interdependent elements of a digital model or simulation. (6.NS.1)Math Examples:

Solve word problems involving division of fractions by fractions using picture models. Division of Fractions using Models

ET06-S1C2-02: Explore and experiment with system variables using models or simulations. (6.G.2)Math Examples:

Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids. Find the Volume of a Rectangular PrismLinking Length, Perimeter, Area and Volume UnitPaper Pool: Analyzing Numeric and Geometric Patterns Unit




http://illuminations.nctm.org/LessonDetail.aspx?ID=U125


http://learnzillion.com/lessons/1062-find-the-volume-of-a-rectangular-prism-by-filling-it-with-unit-cubes

http://learnzillion.com/lessons/1382-solve-word-problems-involving-division-of-fractions-by-fractions-using-picture-models





Unit: UNIT 3: UNDERSTANDING POSTIVE AND NEGATIVE NUMBERS






Recognize and understand relationships of rational numbers on number lines and coordinate planes.Using quadrants of a coordinate plane to solve real-world problems.Common Core Standards / State StandardsContent Standard:including CODE + (Rigor)

DOMAIN: The Number SystemCLUSTER: Apply and extend previous understandings of numbers to the system of rational numbers.Standard Code:

6.NS.5. Understand 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. (Understand, DOK 1)

6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. (Remember,DOK 1)

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. (Understand, DOK 1)

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. (Remember, DOK 1)

6.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. 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. (Remember, DOK 2)

b. Write, interpret, and explain statements of order for rational document.docx Page 13

numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC. (Remember, DOK 3)

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. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. (Understand, DOK 3)

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. (Analysis, DOK 3)

6.NS.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. (Apply, DOK 3)




Craft and Structure4. Interpret words and phrases as they are used in a text, including determining

technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

5. Analyze structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

Range of Reading and Level of Text Complexity10. Read and comprehend complex literary and informational texts independently

and proficiently.

College and Career Readiness Anchor Standards for WritingText Types and Purposes2. Write informative/explanatory texts to examine and convey complex ideas and

information clearly and accurately through the effective selection, organization, and analysis of content.

Production and Distribution of Writing4. Produce clear and coherent writing in which the development, organization,

and style are appropriate to task, purpose, and audience. 5. Develop and strengthen writing as needed by planning, revising


Technology ET06-S1C3-01: Identify patterns and trends to draw conclusions and forecast document.docx Page 14

Standard:including CODE

possibilities. (6.NS.6)



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Positive number, negative number, opposite (direction), rational numbers, coordinate axes, plane, coordinate plane, quadrants, ordered pairs, reflections, integers, ordering, absolute value, zero pairDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Student will: rational numberso integerso oppositeso absolute value

absolute value as magnitudeo order for rational numbers in real-world contexts

number line diagrams o relative position of two numbers on a number line diagramo distance from 0 on the number line

coordinate planeo quadrantso ordered pairs/coordinateso reflections

Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Student will: UNDERSTAND o (rational numbers as points on numbers lines)o (ordered pairs as locations in coordinate plane)o (absolute value as distance on number line)

REPRESENT (points on number lines and coordinate plane) RECOGNIZE (opposites) FIND/POSITION (points on number lines and coordinate planes) ORDER (rational numbers) WRITE and EXPLAIN (statements of order/real world context) INTERPRET (relative position on number line)


Domain: GeometryCluster: Graph points on the coordinate plane to solve real-world and mathematical problems.Standard Code:5.G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection

of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

AssessmentsProvide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor) 2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)document.docx Page 15

6.NS.6 Which is the opposite from the point on the line?

6.NS.8: What are the coordinates of point V?

6.NS.8: What is the distance between (-1, -3) and (4, -3)?


UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.NS.5 – SE Holt McDougal: 594–597, 601, 613, 6436.NS.6 – SE Holt McDougal: 594–596, 601, 604–606, 607 Curriculum Companion: CC32, CC33, CC34, CC356.NS.6a – SE Holt McDougal: 594–597, 601, 612, 640, EP236.NS.6b – SE Holt McDougal: 604–607, 608–611, 612, 622, 641, EP236.NS.6c – SE Holt McDougal: 281, 312–313, 321, 328, 335, 403, 423, 594–596, 603, 605–607, 618, 638, 641, 643,647, 695, EP23 Curriculum Companion: CC32, CC33, CC34, CC356.NS.7 – SE Holt McDougal: 193, 595–596, 598–601, 603, 640, 6436.NS.7a – SE Holt McDougal: 598, 6006.NS.7b – SE Holt McDougal: 599–6016.NS.7c – SE Holt McDougal: 594–595 Curriculum Companion: CC12, CC13, CC14, CC156.NS.7d – SE Holt McDougal: 595–596 Curriculum Companion: CC12, CC13, CC14, CC156.NS.8 – SE Holt McDougal: 606–607, 610–611, 612, 638, 641, 643, 647 Curriculum Companion: CC32, CC33, CC34, CC35Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:Teaching the Common Core Math Standards with Hands-On Activities (Jossey-Bass Teacher Gr 6-8) pp 19-28.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutionsdocument.docx Page 16






Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S1C3-01: Identify patterns and trends to draw conclusions and forecast possibilities. (6.NS.6)Math Examples:

Students explore patterns and trends as they apply to the Stock MarketNew York Stock MarketWhat is the Stock Market

Students use Census data to explore population trends and analyze trends over time. Accessing and Investigating Population Data

Use statistics about endangered species to learn more about the extent of this global concern. Tracking the Wild OnesWhy Do Civilizations Fall

Students investigate home sales in an assigned zip code, enter data in a spreadsheet and forecast home sales for the future. Home Sales Forecast:

Students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. Expressions and Equations

Interactive activities and models provide students an opportunity to identify and plot patterns and trends on a coordinate grid system. Reflect points over the X and Y axes Translate Shapes Across the X and Y axes

Integration of ELP Strategies: (Language, Grammar, etc)Completed by SEI/ELP teachers (later)Exemplary Learning Activities (Optional): List one exemplary strategy per box.


http://learnzillion.com/lessons/493-translate-shapes-across-the-x-and-y-axes

http://learnzillion.com/lessons/492-reflect-points-over-the-x-and-y-axes


http://www.econedlink.org/lessons/docs_lessons/121_nn121_charts1.pdf

http://www.learner.org/interactives/collapse/

http://www.educationworld.com/a_lesson/03/lp310-02.shtml


http://www.themint.org/kids/what-is-the-stock-market.html

http://www.nyse.com/





Unit: UNIT 4: APPLICATION OF GEOMETRY






Using shapes to compose and decompose other shapes to solve real-world problems.


DOMAIN: GEOMETRYCLUSTER: Solve real-world and mathematical problems involving area, surface area, and volume.Standard Code:

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 real-world and mathematical problems. (Apply, DOK 3)

6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. (Apply, DOK 3)

6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. (Apply, DOK 3)



inferences from; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.



5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

College and Career Readiness Anchor Standards for WritingText Types and Purposes3. Write narratives to develop real or imagined experiences or events using effective

technique, well-chosen details, and well-structured event sequences.document.docx Page 19

Production and Distribution of Writing4. Produce clear and coherent writing in which the development, organization, and

style are appropriate to task, purpose, and audience.



ET06-S1C2-01: Recognize and explain relevant interdependent elements of a digital model or simulation. (6.G.1)ET06-S1C2-PO 3: Compare and contrast two systems using a digital model or simulation. (6.G.3)



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Area, triangles, quadrilaterals, polygons, coordinate plane, vertices, three-dimensional, surface areaDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Student will: Area of Polygons

o Triangleso Special quadrilaterals

Problemso With and without context

Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Student will: FIND/DETERMINE area of polygons

o COMPOSE (into rectangles)o DECOMPOSE (into triangles and other shapes)

SOLVE/APPLY (problems with and without context)Prerequisites: Use Hess’s Cognitive Rigor Matrix to “map” pre-requisite conceptual & procedure knowledge

Domain: GeometryCluster: Classify two-dimensional figures into categories based on their properties.Standard Code:5.G.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all

subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

5.G.4: Classify two-dimensional figures in a hierarchy based on properties. Assessments


6.G.1: The hexagon is made up of congruent triangles. What is the area of the hexagon?


What is the area of the parallelogram?

What is the area of the triangle shown below?



UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.G.1 – SE Holt McDougal: 534–537, 540–543, 545–547, 556, 584–585, 587, EP216.G.3 – SE Holt McDougal: Curriculum Companion: CC32, CC33, CC34, CC356.G.4 – SE Holt McDougal: 574–575, 576–579, EP22Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:Teaching the Common Core Math Standards with Hands-On Activities (Jossey-Bass Teacher Gr 6-8) pp 54-56 and 60-64.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutions






Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S1C2-01: Recognize and explain relevant interdependent elements of a digital model or simulation. (6.G.1)Math Examples:

Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids. Area of a Trapezoid

ET06-S1C2-PO 3: Compare and contrast two systems using a digital model or simulation. (6.G.3)Math Examples:

Students manipulate the legs of a triangle to build similar triangles by combining sides and angles. Geometry


Exemplary Learning Activities (Optional): List one exemplary strategy per box.document.docx Page 22

http://nlvm.usu.edu/en/nav/frames_asid_165_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html

http://learnzillion.com/lessons/1060-find-the-area-of-a-trapezoid-by-composing-a-parallelogram





Unit: UNIT 5: RATIOS AND RATES






Using ratios and rates to understanding and solving real-world problems.Understanding ratios as a relationship between quantities.Using rates and ratios to understand measurements.Common Core Standards / State StandardsContent Standard:including CODE + (Rigor)

DOMAIN: RATIOS AND PROPORTIONAL RELATIONSHIPSCLUSTER: Understand ratio concepts and use ratio reasoning to solve problems.Standard Code:

6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” (Understand, DOK 2)

6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ¹ 0, and use rate language in the context of a ratio relationship. 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.” (Expectations for unit rates in this grade are limited to non-complex fractions.) (Understand, DOK 2)

6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (Analysis, DOK 3)

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. (Analysis, DOK 2)

b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (Apply, DOK 2)

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.


(Apply, DOK 2)d. Use ratio reasoning to convert measurement units; manipulate

and transform units appropriately when multiplying or dividing quantities. (Apply, DOK 2)




3. Analyze how and why individuals, events, and ideas develop and interact over the course of a text.



5. Analyze the structure of texts, including how specific sentences, paragraphs and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

Range of Reading and Level of Text Complexity10. Read and comprehend complex literary and informational texts independently and proficiently.

College and Career Readiness Anchor Standards for WritingText Types and Purposes3. Write narratives to develop real or imagined experiences or events using

effective technique, well-chosen details, and well-structured event sequences.Production and Distribution of Writing4. Produce clear and coherent writing in which the development, organization,

and style are appropriate to task, purpose, and audience.



ET06-S1C1-01: Analyze information to generate new ideas and products. (6.RP.2)ET06-S1C2-02: Explore and experiment with system variables using models or simulations. (6.RP.1) (6.RP.3)ET06.S1C1-03: Compare and contrast two systems using a digital model or simulation. (6.RP.2)ET06-S4C2-01: Plan and manage research using credible digital resources to develop solutions to answer a question. (6.RP.3b)



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Ratio, unit rate (cost per item, distance per time), equivalent ratios, tape diagram, percent, double number line document.docx Page 25

diagramDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Student will: ratios and rates

o tables of equivalent ratioso missing values in tableso tape diagramso double number line diagramso equations

pairs of values on a coordinate plane unit rate

o unit pricingo constant speed

percent o a quantity as a rate per 100o finding the whole, given a part and the percent

measurement unitsProcedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Student will: UNDERSTAND (ratios/the concept of a unit rate) DESCRIBE (ratio relationship) USE (ratio and rate reasoning/language) SOLVE (with and without context) MAKE (tables of equivalent ratios) FIND (missing values in tables) PLOT (pairs of values on the coordinate plane) SOLVE (unit rate problems) FIND (percent of a quantity as a rate per 100) SOLVE (problems finding the whole, given a part and the percent) CONVERT (measurement units)


Domain: Number and Operations – FractionsCluster: Use equivalent fractions as a strategy to add and subtract fractions.Standard Code:5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems

involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Assessments


6.RP.1Write an equivalent ratio to the following:45 Answer: 4:56.RP.1document.docx Page 26

Two-ninths of the candy was chocolate. Which answer expresses the fraction below as a ratio?a. 2 to 2b. 2 to 9c. 9 to 2d. 9 to 9

6.RP.3A credit card company charges 11% interest on charges not paid at the end of the month. Based on the table below, how much interest would there be on $110?

Answer: $12.106.RP.3The ratio of cats to dogs is 15:10. Which ratio is the same as 15:10?

a. 3:2b. 10:5c. 18:13d. 10:15

Answer: 3:2


UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.RP.1 – SE Holt McDougal: 342–345, 350, 355, 391, 394, 397, 400, 475,510, 649, EP146.RP.2 – SE Holt McDougal: 343–345, 368, 394, 397, 401, EP146.RP.3 – SE Holt McDougal: 343–345, 347–349, 368, 394, 397, EP146.RP.3a – SE Holt McDougal: 346–349, 368, 394, 397, 707–708, 712, 717,EP14, EP27 Curriculum Companion: CC20, CC216.RP.3b – SE Holt McDougal: 343–345, 368, 394, 397, 401, EP146.RP.3c – SE Holt McDougal: 370, 371–374, 375–378, 379, 380–383,384–387, 390, 391, 396, 397, 401, 413, 456,EP15 Curriculum Companion:CC22, CC23, CC24, CC25, CC26, CC27,CC28, CC296.RP.3d – SE Holt McDougal: 184–185, 488–491, 492–495, 496, 498, 500,501, 505, 519, 523–524, 721, EP19Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:Teaching the Common Core Math Standards with Hands-On Activities (Jossey-Bass Teacher Gr 6-8) pp 2-6.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutions

ONLINE RESOURCES:http://www.tempeschools.org/webpages/commoncore/Teacher Instructional Strategies: Research-based strategies that “fit.”GroupingQuestioningNon-Linguistic Representations (Graphic Organizers/Visual Aids)High ExpectationsTechnology/Mediadocument.docx Page 27


Assessments (ongoing)TAP RUBRIC





Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S1C1-01: Analyze information to generate new ideas and products. (6.RP.2)Math Examples:

Using the front and back bike gear combinations, determine how many gear ratios on consecutive pedals are possible in completing different bike routes. Use this ratio to design a family bike race relay where the members in each team use 3-4 different types of bike to complete a route or two.

ET06-S1C2-02: Explore and experiment with system variables using models or simulations. (6.RP.1) (6.RP.3)Math Examples:

Students play a game and discuss understanding of algebraic expressions. Algebraic Expressions Millionaire

Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids. Find the Volume of a Rectangular PrismLinking Length, Perimeter, Area and Volume UnitPaper Pool: Analyzing Numeric and Geometric Patterns Unit

ET06.S1C1-03: Compare and contrast two systems using a digital model or simulation. (6.RP.2)Math Examples:

Ker-Splash introduces students to algebra as they try to rack up points by combining like terms. Ker-Splash

Students use algebraic methods to solve a problem in a game format.Algebraic Reasoning Game

Students manipulate the legs of a triangle to build similar triangles by combining sides and angles. Geometry

ET06-S4C2-01: Plan and manage research using credible digital resources to develop solutions to answer a question. (6.RP.3b)Math/Science Examples:

Students are assigned 2 states. They will conduct a comparative research on climate index VS greenhouse gas inventory that spans

20-30 years (e.g. 1990-2005) using NASA or Department of Energy website. They will use a spreadsheet to input and graph the result. They will use this data to determine the

relationship between the 2 variables investigated as well as the rate of change in each of these variables.

Based on this rate, they will predict their assigned states’ climate index VS greenhouse gas inventory in the span of 50 years.


http://nlvm.usu.edu/en/nav/frames_asid_165_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html

http://www.mathplayground.com/algebraic_reasoning.html

http://216.255.77.73/Ker-Splash



http://learnzillion.com/lessons/1062-find-the-volume-of-a-rectangular-prism-by-filling-it-with-unit-cubes

http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html






Unit: UNIT 6: ALGEBRAIC REASONING






Using expressions containing unknown variables and numbers to analyze real-world problems.Understand the relationship between dependent and independent variables.


DOMAIN: EXPRESSIONS AND EQUATIONSCLUSTER: Reason about and solve one-variable equations and inequalities.Standard Code:

6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. (Understand, DOK 3)

6.EE.7. Solve 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 (Apply, DOK 3)

DOMAIN: EXPRESSIONS AND EQUATIONSCLUSTER: Represent and analyze quantitative relationships between dependent and independent variables.Standard Code:

6.EE.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (Analysis, DOK 3)





technical connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

Integration of Knowledge and Ideas8. Delineate and evaluate the argument and specific claims in a text, including

the validity of the reasoning as well as the relevance and sufficiency of the document.docx Page 30

evidence.Range of Reading and Level of Text Complexity10. Read and comprehend complex literary and informational texts independently

and proficiently.

College and Career Readiness Anchor Standards for WritingText Types and Purposes3. Write narratives to develop real or imagined experiences or events using

effective technique, well-chosen details, and well-structured event sequences.Production and Distribution of Writing4. Produce clear and coherent writing in which the development, organization,

and style are appropriate to task, purpose, and audience.



ET06-S1C3-01: Identify patterns and trends to draw conclusions and forecast possibilities. (6.EE.9)



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?exponential notation, sum, term, product, factor, quotient, coefficient, distributive property, exponents, inverse operation, equation, inequality, variables, dependent variable, independent variable, constant, evaluate, algebraic expressionDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Student will: Variable Two quantities that change in relationship to one another

o Dependent variableo Independent variable

Expression Equation Graph Table

Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Student will: USE (variables) REPRESENT (dependent and independent variables) WRITE (expressions and equations) ANALYZE (relationships) USE (graphs and tables)document.docx Page 31

RELATE (to the equation) REPRESENT (numbers) SOLVE (problems by writing and solving equations of the form x + p = q and px = q (p,q and x 0)


Domain: Measurement and DataCluster: Convert like measurement units within a given measurement system.Standard Code:5.MD.1: Convert among different-sized standard measurement units within a given measurement system (e.g.,

convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

AssessmentsProvide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor) 2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)

6.EE.9For 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.



UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.EE.6 – SE Holt McDougal: 71, 73, 76, 78, 82–83, 84, 90, 91, 93, 137–136, 240–241, 242, 634–6356.EE.7 – SE Holt McDougal: 71–73, 77–80, 84, 90, 91, 95, 107, 111–113, 123–125, 135, 136–138, 140, 146, 147, 168, 238–240, 256, 264–267, 268, 273–275, 317, 345, 362, 441, 452, 591, 632–634, 636, 642, 643, 683, 695, 701, 705, EP5, EP10, EP11, EP246.EE.9 – SE Holt McDougal: 720–721, 723–725, 726, 732, 733, 737, EP28 Curriculum Companion: CC36Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:Teaching the Common Core Math Standards with Hands-On Activities (Jossey-Bass Teacher Gr 6-8) pp 42-45 and 51-53.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutions






Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S1C3-01: Identify patterns and trends to draw conclusions and forecast possibilities. (6.EE.9)Math Examples:

Students explore patterns and trends as they apply to the Stock MarketNew York Stock MarketWhat is the Stock Market

Students use Census data to explore population trends and analyze trends over time. Accessing and Investigating Population Data

Use statistics about endangered species to learn more about the extent of this global concern. Tracking the Wild OnesWhy Do Civilizations Fall


http://www.learner.org/interactives/collapse/

http://www.educationworld.com/a_lesson/03/lp310-02.shtml


http://www.themint.org/kids/what-is-the-stock-market.html

http://www.nyse.com/


Students investigate home sales in an assigned zip code, enter data in a spreadsheet and forecast home sales for the future. Home Sales Forecast:

Students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. Expressions and Equations

Interactive activities and models provide students an opportunity to identify and plot patterns and trends on a coordinate grid system. Reflect points over the X and Y axes





http://learnzillion.com/lessons/492-reflect-points-over-the-x-and-y-axes


http://www.econedlink.org/lessons/docs_lessons/121_nn121_charts1.pdf


Unit: UNIT 7: STATISTICS AND DISTRIBUTION






Describe and understand numerical data in the context in which obtained.Demonstrate understanding of quantitative measure of center (mean and median).Describe variability using range and deviation.Identify the correct presentation of data (numberline, plots, histogram, box plots)Applications of knowledge to real-world problem solving.Common Core Standards / State Standards


Content Standard:including CODE + (Rigor)

DOMAIN: STATISTICS AND PROBABILITYCLUSTER: Develop understanding of statistical variability.Standard Code:

6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. (Understand, DOK 2)

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. (Understand, DOK 2)

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. (Understand, DOK 2)

DOMAIN: STATISTICS AND PROBABILITYCLUSTER: Summarize and describe distributions.Standard Code:

6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Apply, DOK 1)

6.SP.5. Summarize numerical data sets in relation to their context, such as by:

o Reporting the number of observations. (Analysis, DOK 2)o Describing the nature of the attribute under investigation,

including how it was measured and its units of measurement. (Analysis, DOK 2)

o 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. (Analysis, DOK 3)

o 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. (Analysis, DOK 3)







5. Analyze the structure of the texts, including how specific sentences, paragraphs, and larger portions of the text (eg., a section, chapter, scene or stanza) relate to each other and the whole.

Integration of Knowledge and Ideas8. Delineate and evaluate the argument and specific claims in a text, including the

validity of the reasoning as well as the relevance and sufficiency of the evidence.9. Analyze how two or more texts address similar themes or topics in order to build

knowledge or to compare the approaches the authors take.Range of Reading and Level of Text Complexity10. Read and comprehend complex literary and informational texts independently and

proficiently.

College and Career Readiness Anchor Standards for WritingText Types and Purposes3. Write narratives to develop real or imagined experiences or events using effective

technique, well-chosen details, and well-structured event sequences.Production and Distribution of Writing4. Produce clear and coherent writing in which the development, organization, and

style are appropriate to task, purpose, and audience.



ET06-S2C1-01: Communicate digitally with others by selecting and using a variety of appropriate communication tools. (6.SP.1)ET06-S3C2-04: Use appropriate digital tools to synthesize research information to develop new ideas and/or create new understanding. (6.SP.4)ET06-S3C2- 05: Follow copyright laws when using text, images, videos and/or other sources and obtain permission to use the work of others and cite resources appropriately. (6.SP.4)ET06-S5C1-06: Exhibit legal and ethical behavior when using technology and discuss consequences of misuse. (6.SP.4)




Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Statistics, distribution, collect, analyze, interpret, data, center, spread, shape, mean, median, mode, range, valuesDeclarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?Student will: Measure of center

o Mediano Mean

Measure of variationo Rangeo Interquartile rangeo Mean absolute deviation

Numerical data setso Observationso Attributeso Overall pattern

Deviations fromo Choice of measures of center and variabilityo Shape of the data distribution

Center Spread Variability

Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?Student will: RECOGNIZE (measure of center and measure of variation) SUMMARIZE (numerical data sets) REPORT (observations) DESCRIBE (attribute) GIVE/FIND (measure of center and measure of variation) DESCRIBE (overall pattern) RELATE (choice of measure to shape of the data) RECOGNIZE (a statistical question) UNDERSTAND (data distribution is described by its center, spread, and overall shape) Display (numerical data)


Domain: Measurement and DataCluster: Represent and interpret data.Standard Code:5.MD.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use

operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Assessments


6.SP.3Consider the data shown in the dot plot of the six trait scores for organization for a group of students.

o How many students are represented in the data set? o What are the mean, median, and mode of the data set? What do these values mean? How do they compare? o What is the range of the data? What does this value mean?


6.SP.5Nineteen students completed a writing sample that was scored using the six traits rubric. The scores for the trait of organization were 0, 1,

2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6. Create a data display. What are some observations that can be made from the data display?

• Grade 6 students were collecting data for a math class project. They decided they would survey the other two grade 6 classes to determine how many DVDs each student owns. A total of 48 students were surveyed. The data are shown in the table below in no specific order. Create a data display. What are some observations that can be made from the data display?

A histogram using 5 bins (0-9, 10-19, …30-39) to organize the data is displayed below.

• Ms. Wheeler asked each student in her class to write their age in months on a sticky note. The 28 students in the class brought their sticky note to the front of the room and posted them in order on the white board. The data set is listed below in order from least to greatest. Create a data display. What are some observations that can be made from the data display?

Five number summary Minimum – 130 months Quartile 1 (Q1) – (132 + 133) ÷ 2 = 132.5 months Median (Q2) – 139 months Quartile 3 (Q3) – (142 + 143) ÷ 2 = 142.5 months Maximum – 150 months (Continued on next page)

This box plot shows that • ¼ of the students in the class are from 130 to 132.5 months old • ¼ of the students in the class are from 142.5 months to 150 months old • ½ of the class are from 132.5 to 142.5 months old • the median class age is 139 months.




UNIT Resources & InstructionPrimary text connections: List chapters, pages, etc.6.SP.1 – SE Holt McDougal: Curriculum Companion: CC12, CC13, CC14, CC156.SP.2 – SE Holt McDougal: 287, 288–291, 296, 301, 304–307, 308–309, 323–324, 328, 329, 332–334, 335, 336–337 Curriculum Companion: CC12, CC13, CC14, CC15, CC16, CC17, CC18, CC196.SP.3 – SE Holt McDougal: 288–291, 332, 335, 337 Curriculum Companion: CC12, CC13, CC14, CC15, CC16, CC17, CC18, CC196.SP.4 – SE Holt McDougal: 304–307 Curriculum Companion:CC12, CC13, CC14, CC15, CC16, CC17, CC18, CC196.SP.5 – SE Holt McDougal: 304–307, 308–309, 310, EP13 Curriculum Companion: CC16, CC17, CC18, CC196.SP.5a – SE Holt McDougal: 304–307, 308–309, 310, EP13 Curriculum Companion: CC6, CC17, CC18 CC196.SP.5b– SE Holt McDougal: Curriculum Companion: CC16, CC17, CC18, CC196.SP.5c– SE Holt McDougal: Curriculum Companion: CC12, CC13, CC14, CC15, CC16, CC17, CC18, CC196.SP.5d – SE Holt McDougal: Curriculum Companion: CC16, CC17, CC18, CC19Supplemental Text Connections: List other school-purchased curriculum resources.Other materials available: List other useful resources, teacher-created, online, etc.TEXT RESOURCES:Teaching the Common Core Math Standards with Hands-On Activities (Jossey-Bass Teacher Gr 6-8) pp 65-77.“How to Assess While You Teach Math Formative Assessment Practices and Lessons”, Dana Islas, Math Solutions






Integration of Technology: Specific examples that apply the technology standards in the content.ET06-S2C1-01: Communicate digitally with others by selecting and using a variety of appropriate communication tools. (6.SP.1)Math Example: document.docx Page 41


Students learn to rank survey questions. Teacher provides survey questions (To extend learning opportunity have students create questions.)

for students to rank based on widest to narrowest range of data results. Students will utilize full program capability and explain reasoning for ranking status. Have students compare their rankings with other students, small groups and compare their rankings

with the whole class. Intel Education K12 Thinking Tools: Visual Ranking Tool

ET06-S3C2-04: Use appropriate digital tools to synthesize research information to develop new ideas and/or create new understanding. (6.SP.4)Math Examples:

Use a spreadsheet (web-based or offline) to process data and display data using appropriate graphApplication and Web Resources:Create a Spreadsheet Circle Graph

ET06-S3C2- 05: Follow copyright laws when using text, images, videos and/or other sources and obtain permission to use the work of others and cite resources appropriately. (6.SP.4)Math Examples:

Organize students in teams of 4-5 Students design and conduct a survey, of at least 30 students, about their use (frequency & quantity:

minutes/pages/words) of media content in research projects in any subject.Survey Generator

One of the media content types is assigned to each team(6 teams). Media content may come from varied sources and includes: Motion Media, Text, Poetry, Music/Lyrics/Video, Photos/Illustrations, numerical data.

Students then present the survey result in a spreadsheet and generate a graph that shows the mean percentage of the use of the given media being investigated.

Student then compare these results based on the fair use guidelines as follows: Motion Media - 10% or 3 minutesText - 10% or 1000 wordsPoetry - 250 words, no more than 3 from same authorMusic, Lyrics, Video 10% or 30 secPhotos & Illustrations - 5 images from one authorNumerical Data Sets - 10% of 2500 fields or cells

ET06-S5C1-06: Exhibit legal and ethical behavior when using technology and discuss consequences of misuse. (6.SP.4)Math Examples:

Organize students in teams of 4-5 Students design and conduct a survey, of at least 30 students, about their use (frequency & quantity:

minutes/pages/words) of media content in research projects in any subject.Survey Generator

One of the media content types is assigned to each team(6 teams). Media content may come from varied sources and includes: Motion Media, Text, Poetry, Music/Lyrics/Video, Photos/Illustrations, numerical data.

Students then present the survey result in a spreadsheet and generate a graph that shows the mean percentage of the use of the given media being investigated.

Student then compare these results based on the fair use guidelines as follows: Motion Media - 10% or 3 minutesText - 10% or 1000 wordsPoetry - 250 words, no more than 3 from same authorMusic, Lyrics, Video 10% or 30 secPhotos & Illustrations - 5 images from one authorNumerical Data Sets - 10% of 2500 fields or cells


http://www.surveymonkey.com/

http://www.surveymonkey.com/

http://www.shodor.org/interactivate/activities/CircleGraph/

http://nces.ed.gov/nceskids/createagraph/default.aspx

http://www.intel.com/about/corporateresponsibility/education/k12/tools.htm





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