2013-2014 Blended School Year-6th Grade · PDF file2013-2014 Blended School Year-6th Grade Mathematics ... FL Page 1 2013-2014 Blended School Year ... has to plan for the students

2013-2014 Blended School Year-6th Grade Mathematics

Lake County, FL Page 1

2013-2014 Blended School Year Clarification:

Students will be assessed on the Next Generation Sunshine State Standards with the FCAT 2.0.

Most of the mathematics NGSSS content is addressed within the Common Core State Standards, but not all.

Understanding Common Core State Standards for Mathematics

Read the Critical Areas of Focus for your grade level on Page 2 of this document. This explains the primary focus of the CCSSM

for your grade level. It is important to be aware of these areas during this blended year.

Look at the speaking and listening standards and writing standards on Page 3 of this document that should be integrated into

your math instruction. Plan for collaboration and writing in math based on these standards.

The Mathematical Practice Standards on Page 4 are standards that proficient math students should exhibit, but the teacher

has to plan for the students to practice with these standards during the instruction of the content standards. These should be

integrated during instruction of NGSSS or CCSM.

There are fluency standards for each grade level. These should be introduced early in the year to ensure students have

enough time and practice to develop fluency by the end of the year.

Utilizing the Scope and Sequence, NGSSS Task Card and the C² Connection Card to guide and enhance classroom instruction aligned

to NGSSS and CCSSM.

Use the Scope and Sequence Document to determine order of instruction.This document outlines:

•CCCSS that should be taught

•NGSSS Mini Assessment that should be given to assess transfer (NGSSS Standards in red do not transfer with CCSSM, therefore should be explicitely taught accoridng tho the FCAT 2.0 Specifications.)

Refer to the C² Connection Card for a deeper understanding of the Common Core Standard. This document includes:

•Deconstructed standards

•Aligned questions

•Aligned Web Links

•Elements to assist with rigorous tasks/ student engagment

Refer to the NGSSS Task Card for elements aligned to the FCAT 2.0 Assessment. This document includes:

•FCAT 2.0 Test Specifications

•Question Stems

•Summative writing tasks

•Vocabulary

•Sample Questions

Create your Differentiated Focus Calendar based on:

•Bell Ringer- (Maintaining previous benchmarks or practicing parts of current benchmark)

•Order of instruction

•School Data (Student Achievement, Instructional Look For Visit Checklist)

•Elements that would most impact instruction at your school and therefore should be included in your focus calendar

•Copy appropriate elements from the C² Connection Cards, NGSSS Task Card and Scope and Sequence documents and embed into your Focus Calendar

•Add any additional elements you would like for your school aligned to the standards

Teachers will use the differentiated focus calendar to plan instruction. The following standards should be included in each lesson plan:

•Include specific Speaking/Listening, Reading, and Writing Standards (Promotes student discourse, writing and reading across content)

•Include specific Mathematical Practice Standards to increase the rigor and student engagement.

•Include CCSSM and NGSSS aligned content standards



Critical Areas of Focus CCSSM In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. (1) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. (2) Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane. (3) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities. (4) Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.



In order for students to be College and Career ready prepared with the 21st

Century skills, it is important for them to have multiple opportunities to speak, listen, and write across content. The following are the speaking and listening standards and the writing standards that should be integrated into the math curriculum.

Speaking and Listening Reading in Science and Technical Subjects Writing in History, Science, and Technical Subjects

LACC.6.SL.1.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly. a) Come to discussions prepared, having read or

studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.

b) Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed.

c) Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion.

d) Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing.

LACC.6.SL.1.2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study. LACC.6.SL.1.3 Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not. LACC.6.SL.2.4 Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.

LACC.68.RST.1.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. LA.68.RST.2.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. LA.68.RST.3.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).

LACC.68.WHST.1.1 Write arguments focused on discipline-specific content. a) Introduce claim(s) about a topic or issue,

acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.

b) Support claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or text, using credible sources.

c) Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.

d) Establish and maintain a formal style. e) Provide a concluding statement or section that

follows from and supports the argument presented. LACC.68.WHST.2.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.



The Mathematical Practice Standards describe the expertise that mathematics teachers should develop in their students. Teachers

should consciously plan for instruction aligned with 2-3 standards embedded in each lesson.

Student Friendly Mathematical Practice Statements

MACC.K12.MP.1.1 Make sense of problems and persevere in solving them.

Make a plan!

Try different approaches when your problem is hard.

Solve your problem in more than one way.

Check whether your solution makes sense.

MACC.K12.MP.2.1 Reason abstractly and quantitatively.

Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.

MACC.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.

Explain both what to do and why it works.

Work to make sense of others’ mathematical thinking.

MACC.K.12.MP.4.1 Model with mathematics.

Apply math to real-world situations.

Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.

MACC.K12.MP.5.1 Use appropriate tools strategically.

Choose appropriate tools for your problem.

Use mathematical tools correctly and efficiently.

Estimate and use what you know to check the answers you find using tools.

MACC.K12.MP.6.1 Attend to precision.

Communicate your mathematical thinking clearly and precisely.

Use the level of precision you need for your problem.

Be accurate when you count, measure, and calculate.

MACC.K12.MP.7.1 Look for and make use of structure.

Find, extend, analyze, and create patterns.

Use patterns and structures to solve problems.

MACC.K12.MP.8.1 Look for and express regularity in repeated reasoning.

Use patterns and structures to create and explain rules and shortcuts.

Use properties, rules, and shortcuts to solve problems.

Reflect on your thinking before, during, and after you solve a problem.



Fluency Standards with Common Core Mathematics: Fluency in the standards means “fast and accurate.” When fluency is used in the

standards, it is referring to an endpoint. It is the end of that progression of learning. The fluency standards should be addressed early

in the year to provide time and practice in developing the necessary fluency skills.

Grade Fluency Standard Required Fluency

K MACC.K.OA.1.5

Add/subtract within 5

1 MACC.1.OA.3.6

Add/subtract within 10

2 MACC.2.OA.2.2 MACC.2.NBT.2.5

Add/subtract within 20 Add/subtract within 100 (pencil and paper)

3 MACC.3.OA.3.7 MACC.3.NBT.1.2

Multiply/divide within 100 Add/subtract within 1000

4 MACC.4.NBT.2.4 Add/subtract within 1,000,000

5 MACC.5.NBT.2.5

Multi‐digit multiplication

6 MACC.6.NS.2.2 MACC.6.NS.2.3

Multi-digit division Multi-digit decimal operations



*This scope and sequence is not a cross-walk. It should be used to determine order of instruction *The red NGSSS are not covered in 6th grade with the Common Core State Standards, but will need to be taught for the blended school year.

Units (Time should be adjusted

based on school data)

Common Core Focus Standards

NGSSS- Task Card Assess with Mini Benchmark

1 (5 days) MACC.6.EE.1.3 MA.6.A.3.5

2 (8 days) MACC.6.EE.1.1 MACC.6.EE.1.4 MACC.6.EE.1.2

MA.6.A.3.1

3A (10 days) MACC.6.EE.2.5 MACC.6.EE.2.7

MA.6.A.3.2

4 (5 days) MACC.6.EE.3.9 MA.6.A.3.6

3B (5 days) MACC.6.EE.2.5

MA.6.A.3.2 MA.6.A.3.3

5 (5 days) MACC.6.EE.2.5 MACC.6.EE.2.8

MA.6.A.3.2

6 (13 days) MACC.6.NS.2.3 multiplication of decimals

MA.6.A.5.3 MA.6.A.1.1 MA.6.A.1.2 MA.6.A.1.3

7 (8 days) MACC.6.NS.2.2 from 5th grade – could be reviewed before division of decimals MACC.6.NS.2.3 division of decimals

MA.6.A.5.3 MA.6.A.1.1 MA.6.A.1.2 MA.6.A.1.3

8 (10 days) MA.6.A.5.3 MA.6.A.1.1 MA.6.A.1.2 MA.6.A.1.3

9 (5 days) MACC.6.NS.1.1 MA.6.A.5.3 MA.6.A.1.1 MA.6.A.1.2 MA.6.A.1.3

10 (5 days) MACC.6.RP.1.1 MACC.6.RP.1.2 MACC.6.RP.1.3 a,b,d

MA.6.A.2.2 MA.6.A.2.1

11 (5 days) MACC.6.RP.1.3 c MA.6.A.5.1 MA.6.A.5.2 MA.6.A.5.3

12 (5 days) MA.6.G.4.1

13 (14 days) MACC.6.G.1.1 MACC.6.G.1.4

MA.6.G.4.2 MA.6.A.3.4

14 (10 days) MACC.6.G.1.2 MA.6.G.4.3

15 (5 days) MACC.6.SP.1.3 MACC.6.SP.1.1 MACC.6.SP.1.2

MA.6.S.6.1 MA.6.S.6.2

New- After FCAT 2.0

MACC.6.EE.2.6 MACC.6.SP.2.4 MACC.6.SP.2.5 MACC.6.G.1.3 MACC.6.NS.2.4 MACC.6.NS.3.5 MACC.6.NS.3.6 MACC.6.NS.3.7 MACC.6.NS.3.8

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MATHEMATICS C² CONNECTION CARD GRADE #

Domain: Larger group of related standards (Clusters fall under these domains) Each group of cards is color coded according to the cluster.

Cluster Group of related standards Associated Fluency Standard Fluency standards to be addressed with this cluster group.

These may be fluency standards from prior grade levels students have not mastered or from the current grade level they should be practicing with.

Common Core State Standard (There could be anywhere from 1-5 standards on a card because each card contains an entire cluster of standards.

Common Core State Standard

Deconstructed standard (DOK #) Deconstructed standard (DOK #) The standard is deconstructed into concise learning statements about what the students need to know and be able to do. They are organized by learning targets to make it easier to choose the correct method of instruction and assessment.

Math standards are deconstructed based on: This is the level to which teachers should teach, but may not align with the DOK for assessment. Knowledge Reasoning Demonstration Product

Suggested Mathematical Practice Standards Questions

Math Practices that should be integrated into the instruction of this cluster according to the deconstructed standards document. (Teachers may incorporate others)

Sample higher order thinking questions aligned to content and practice standards.

Vertical Progression Example Writing Connections

Prior Knowledge Upcoming knowledge in the next grade level. Example writing prompts aligned to the cluster that encourages students to explain and justify their mathematical thinking.

Web Links Common Core Task/ Assessment Next Generation Edusoft Mini-Assessment

Resources will be aligned to the cluster and sometimes aligned to multiple clusters.

Common Core Tasks and PARCC Assessment Links aligned to the cluster

Edusoft Mini-benchmark Assessment aligned to NGSSS that should be utilized to monitor transfer of knowledge. Standards in red will not transfer to CCSSM, and should therefore be explicitly taught using the NGSSS task card.

Draft 2013 Lake County Schools Academic Services Unit

MATHEMATICS C² CONNECTION CARD GRADE 6 (1 of 2)

Domain: Expressions and Equations Cluster: EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions.

Associated Fluency Standards: MACC.NS.2.2 Fluently divide multi-digit numbers, MACC.NS.2.3 Multi-digit operations with decimals

MACC.6.EE.1.1 Write and evaluate numerical expressions involving whole-number exponents.

MACC.6.EE.1.2 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. b) Identify parts of an expression using mathematical terms

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

c) Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in 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.

MACC.6.EE.1.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

MACC.6.EE.1.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

6.EE.1.1 Deconstructed standard (DOK 1)

6.EE.1.2 Deconstructed standard (DOK 2)

6.EE.1.3 deconstructed standard (DOK 2)

6.EE.1.4 deconstructed standard (DOK 1)

Knowledge

Write numerical expressions involving whole number exponents. Ex. 3⁴ = 3x3x3x3

Evaluate numerical expressions involving whole number exponents. Ex. 3⁴ = 3x3x3x3 = 81

Demonstration

Solve order of operation problems that contain exponents. Ex. 3+2² -(2 +3)=2

Knowledge

Use numbers and variables to represent desired operations.

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient.)

Identify parts of an expression as a single entity, even if not monomial.

Substitute specific values for variables

Evaluate algebraic expressions including those that arise from real-world problems.

Reasoning

Apply order of operations when there are no parentheses for expressions that include whole number exponents.

Translate written phrases into algebraic expressions.

Translate algebraic expressions into written phrases.

Knowledge

Generate equivalent expressions using the properties of operations.

Knowledge

Recognize when two expressions are equivalent.



Domain: Expressions and Equations Cluster: EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions.



MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How do you know two expressions are equivalent?

Why would you use algebraic expressions in a real world situation?

How will you use the information?

Why does that operation represent the situation?

How can numerical and algebraic expressions be used to represent real-life situations?

How can relationships be expressed with symbols?

How do number properties effect the creation of equivalent expressions?

Vertical Progression TurnOnCCMath.net K-8 Learning Trajectories

Example Writing Connection

5th

Grade

Students use order of operations and evaluate expressions.

Students write simple expressions that record calculations with numbers.

7th

Grade

Students factor and expand linear expressions with rational coefficients.

Students write equivalent expressions with fractions, decimals, percents, and integers.

Write and evaluate expressions that arise from formulas used in real-world problems.

Evaluate algebraic expressions

Translate the algebraic expression into written phrases.

Prove that the expressions are equivalent.

Explain the order of operations and how it is useful in solving mathematical and real world problems.


Common Core State Standards Mathematics: Properties of equality and inequality- P 90 6

th Grade Common Core Flip Book

Link to Depth of Knowledge (DOK) Chart

6.EE.1.1 CPALMS Resources 6.EE.1.2 CPALMS Resources 6.EE.1.3 CPALMS Resources 6.EE.1.4 CPALMS Resources

MARS Lesson: Laws of Arithmetic Illustrative Mathematics: Djinni’s Offer Illustrative Mathematics: Triangular Tables NYC Task- Grocery Shopping and the Quilt of a Math Teacher

MA.6.A.3.5 MA.6.A.3.1 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards

http://www.insidemathematics.org/index.php/commmon-core-math-intro

http://www.turnonccmath.net/

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf


http://katm.org/wp/wp-content/uploads/flipbooks/6FlipBookedited22.pdf

http://lake.k12.fl.us/Page/27614

http://www.cpalms.org/Standards/PublicPreviewBenchmark5446.aspx







http://map.mathshell.org/materials/lessons.php?taskid=484#task484

http://www.illustrativemathematics.org/illustrations/532



http://schools.nyc.gov/NR/rdonlyres/F7DD52E7-FD7E-44DC-B099-90301CAC9025/140802/NYCDOE_G6_Math_GroceryShopping_FINAL1.pdf

http://schools.nyc.gov/NR/rdonlyres/F7DD52E7-FD7E-44DC-B099-90301CAC9025/140802/NYCDOE_G6_Math_GroceryShopping_FINAL1.pdf

http://lake.k12.fl.us/site/default.aspx?PageID=1344


MATHEMATICS C² CONNECTION CARD GRADE 6 Domain: Expressions and Equations Cluster: EE.2 Reason about and solve one-variable equations and inequalities. Associated Fluency Standards:

MACC.NS.2.2 Fluently divide multi-digit numbers MACC.NS.2.3 Multi-digit operations with decimals

MACC.6.EE.2.5 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.

MACC.6.EE.2.6 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.

MACC.6.EE.2.7 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 non-negative rational numbers.

MACC.6.EE.2.8 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.

6.EE.2.5 Deconstructed standard (DOK 1) 6.EE.2.6 Deconstructed standard (DOK 2) 6.EE.2.7 deconstructed standard (DOK 2) 6.EE.2.8 deconstructed standard (DOK 2)

Knowledge

Recognize solving an equation or inequality as a process of answering “which values from a specified set, if any, make the equation or inequality true?

Know that the solutions of an equation or inequality are the values that make the equation or inequality true.

Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Knowledge

Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Knowledge

Define inverse operation.

Know how inverse operations can be used in solving one-variable equations.

Reasoning

Apply rules of the form x + p=q, and px=q, for cases in which, p, q and x are all nonnegative rational numbers, to solve real-world and mathematical problems; with only one unknown quantity.

Develop a rule for solving one-step equations using inverse operations with nonnegative rational coefficients.

Demonstration

Solve and write equations for real-world mathematical problems containing one unknown.

Knowledge

Identify the constraint or condition in a real-world or mathematical problem in order to set up an inequality.

Recognize that inequalities of the form x > c or x < c have infinitely many solutions.

Reasoning

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.

Represent solutions to inequalities or the form x > c, with infinitely many solutions, on number line diagrams.


MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

Which values from a specified set make the equation or inequality true?

Why do the quantities change in relation to one another?

Why is it important to focus on the relationship when solving the problem?

Vertical Progression

TurnOnCCMath.net K-8 Learning Trajectories


5th Grade

Students generate two numerical patterns using two given rules.

Students analyze and explain the relationship between corresponding terms in the two numerical patterns. Students graph in a coordinate plane.

7th Grade

Students fluently solve equations of the form px + q = r and p(x + q) = r with speed and accuracy.

Write to explain the strategy used to solve the problem.

Describe a problem situation that can be solved using a given equation.

Create and solve equations that are based on real world situations.


Common Core State Standards Mathematics: Properties of equality and inequality- P 90 6th Grade Common Core Flip Book


6.EE.2.5 CPALMS Resources 6.EE.2.6 CPALMS Resources 6.EE.2.7 CPALMS Resources 6.EE.2.8 CPALMS Resources

NYC Unit- Elk Street

MA.6.A.3.2 (Does not transfer to CCSSM) MA.6.A.3.3

Link to Scope and Sequence Link to Next Generation Benchmark Task Cards














http://schools.nyc.gov/NR/rdonlyres/9BC415CE-0FC0-4C97-9795-78A42276615B/140504/NYCDOE_G6_Math_ElkStreet_FINAL.pdf



MATHEMATICS C² CONNECTION CARD GRADE 6

Domain: Expressions and Equations Cluster: EE.3 Represent and analyze quantitative relationships between dependent and independent variables.

Associated Fluency Standards: MACC.NS.2.2 Fluently divide multi-digit numbers

MACC.NS.2.3 Multi-digit operations with decimals

MACC.6.EE.3.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

6.EE.3.9 Deconstructed standard (DOK 3) Knowledge

Define independent and dependent variables.

Use variables to represent two quantities in a real-world problem that change in a relationship to one another. Reasoning

Write an equation to express one quantity (dependent) in terms of the other quantity (independent.)

Analyze the relationship between the dependent variable and independent variable using tables and graphs.

Relate the data in a graph and table to the corresponding equation.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How are the dependent and independent variables related?

How is the data in the graph or table related to the corresponding equation?

As the x variable increases, how does the y variable change?



5th

Grade

Students graph points on a coordinate plane.

Students represent real world and mathematical problems by graphing points in the first quadrant.

7th

Grade

Students analyze and interpret data using measures of central tendency and measures of variability.

Given a graph, write an expression that illustrates the relationship and justify your reasoning.

Write an expression to express one quantity in terms of the other quantity and explain the expression in your own words.


Common Core State Standards Mathematics: Properties of equality and inequality- P 90 6

th Grade Common Core Flip Book


6.EE.3.9 CPALMS Resources

NYC Unit- Dance & Text Illustrative Mathematics Task- Chocolate Bars Link to Depth of Knowledge (DOK) Chart

MA.6.A.3.6 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards









http://schools.nyc.gov/NR/rdonlyres/134A0EA3-8306-474A-BB7D-A5CF809CF22F/140800/NYCDOE_G6_Math_DanceandText_FINAL1.pdf





Domain: Geometry Cluster: G.1 Solve real-world and mathematical problems involving area, surface area, and volume


MACC.6.G.1.1 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.

MACC.6.G.1.2 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.

MACC.6.G.1.3 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.

MACC.6.G.1.4 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.

6.G.1.1 Deconstructed standard (DOK 2) 6.G.1.2 Deconstructed standard (DOK 2) 6.G.1.3 deconstructed standard (DOK 2) 6.G.1.4 deconstructed standard (DOK 2) Knowledge

Recognize and know how to compose and decompose polygons into triangles and rectangles.

Reasoning

Compare the area of a triangle to the area of the composed rectangle.

Apply the techniques of composing and/or decomposing to find the area of triangles, special quadrilaterals, and polygons to solve mathematical and real world problems.

Discuss, develop and justify formulas for triangles and parallelograms.

Knowledge

Know how to calculate the volume of a right rectangular prism.

Reasoning

Apply volume formulas for right rectangular prisms to solve real-world and mathematical problems involving rectangular prisms with fractional edge lengths.

Demonstration

Model the volume of a right rectangular prism, with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.

Knowledge

Draw polygons in the coordinate plane.

Use coordinates (with the same x-coordinate or the same y-coordinate) to find the length of a side of a polygon.

Demonstration

Apply the technique of using coordinates to find the length of a side of a polygon drawn in the coordinate plane to solve real-world and mathematical problems.

Knowledge

Know that 3-D figures can be represented by nets.

Reasoning

Represent three-dimensional figures using nets made up of rectangles and triangles.

Apply knowledge of calculating the area of rectangles and triangles to a net, and combine the areas for each shape into one answer representing the surface area of a three-dimensional figure.

Demonstration

Solve real-world and mathematical problems involving surface area using nets.


MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How do you calculate________?

Why does the formula work?

How does the formula relate to the measure and the figure?

How can you use a net to calculate surface area?



5th Grade

Students find the area and volume of an object.

7th Grade

Students draw and determine the actual area based on a scale drawing.

Justify formulas for triangles and parallelograms.

Describe the shapes of the faces needed to construct_____.


6th Grade Common Core Flip Book Link to Depth of Knowledge (DOK) Chart

6.G.1.1 CPALMS Resources 6.G.1.2 CPALMS Resources 6.G.1.3 CPALMS Resources 6.G.1.4 CPALMS Resources

MARS Lesson- Security Cameras MARS Lesson- Designing Candy Cartons MARS Task- Candle Box

MA.6.G.4.1 (Does not transfer to CCSSM) MA.6.G.4.2 (Does not transfer to CCSSM) MA.6.A.3.4 MA.6.A.4.3 (Does not transfer to CCSSM) MA.6.G.6.1 (Does not transfer to CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards












http://map.mathshell.org/materials/download.php?fileid=1354

http://map.mathshell.org/materials/lessons.php

http://map.mathshell.org/materials/lessons.php

http://map.mathshell.org/materials/tasks.php?taskid=385&subpage=expert

http://map.mathshell.org/materials/tasks.php?taskid=385&subpage=expert



MATHEMATICS C² CONNECTION CARD GRADE 6 Domain: The Number System Cluster: NS.1 Apply and extend previous understandings of multiplication and division to divide fractions

by fractions. Cluster: NS.2 Compute fluently with multi-digit numbers and find common factors and multiples.



MACC.6.NS.1.1 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?

MACC.6.NS.2.2 Fluently divide multi-digit numbers using the standard algorithm.

MACC.6.NS.2.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

MACC.6.NS.2.4 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).

6.NS.1.1 Deconstructed standard (DOK 2)


6.NS.2.3 deconstructed standard (DOK 1)

6.ns.2.4 deconstructed standard (DOK 1)

Knowledge

Compute quotients of fractions divided by fractions (including mixed numbers.)

Reasoning

Interpret quotients of fractions.

Solve word problems involving division of fractions by fractions.

Demonstration

Fluently divide multi-digit numbers using the standard algorithm with speed and accuracy.

Demonstration

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation with speed and accuracy.

Demonstration

Fluently identify the factors of two whole numbers less than or equal to 100 and determine the Greatest Common Factor.

Fluently identify the multiples of two whole numbers less than or equal to 12 and determine the Least Common Multiple.

Apply the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How can you use factor lists or the prime factorizations to find the GCF?

Why is fluency with operations important?

How is the distributive property used to express a sum of two whole numbers?

If two numbers are multiples of four, will the sum of the two numbers also be a multiple of four? Why or why not?

Vertical Progression Example Writing Connection

5th Grade

Students generate equivalent fractions.

Students add, subtract, and multiply fractions.

Students divide a unit fraction by a whole number and divide a whole number by a fraction.

7th Grade

Students extend previous understanding of operations and of fractions to multiply and divide rational numbers.

Write a contextual problem for a fraction division problem.

Interpret the quotients of fractions and justify your interpretation.



6.NS.1.1 CPALMS Resources 6.NS.2.2 CPALMS Resources 6.NS.2.3 CPALMS Resources 6.NS.2.4 CPALMS Resources

NYC Unit- Share My Candy Illustrative Mathematics Task- Bake Sale

MA.6.A.5.3 (Does not transfer to CCSSM) MA.6.A.1.1 MA.6.A.1.2 MA.6.A.1.3 (Does not transfer to CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards











http://schools.nyc.gov/NR/rdonlyres/946D93E8-E911-4589-871C-97317E227C3C/141874/NYCDOE_G6_Math_SharemyCandy_FINAL.pdf

http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/258/original/illustrative_mathematics_258.pdf?1343856956





Domain: The Number System Cluster: NS.3 Apply and extend previous understandings of numbers to the system of rational numbers.



MACC.6.NS.3.5 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.

MACC.6.NS.3.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a) Recognize opposite signs of numbers as indicating

locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

b) Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

c) Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

MACC.6.NS.3.7 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.

b) Write, interpret, and explain 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 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.

d) Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represent a debt greater than 30 dollars.

MACC.6.NS.3.8 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.


MATHEMATICS C² CONNECTION CARD GRADE 6 (2 of 2) Domain: The Number System Cluster: NS.3 Apply and extend previous understandings of numbers to the system of rational

numbers. Associated Fluency Standards:

MACC.NS.2.2 Fluently divide multi-digit numbers MACC.NS.2.3 Multi-digit operations with decimals



6.NS.3.7 deconstructed standard (DOK 2)

6.ns.3.8 deconstructed standard (DOK 2)

Knowledge

Identify an integer and its opposite. Reasoning

Use integers to represent quantities in real world situations (above/below sea level, etc…)

Explain where 0 fits into a situation represented by integers.

Knowledge

Identify a rational number as a point on the number line.

Identify the location of 0 on a number line in relation to positive and negative numbers.

Recognize opposite signs of numbers as locations on opposite sides of the 0 on the number line.

Recognize the signs of both numbers in an ordered pair; indicate which quadrant of the coordinate plane the ordered pair will be located.

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.

Reasoning

Reason that the opposite of the opposite of a number is the number itself.

Reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y-axis.

Recognize that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x-axis.

Reason that when two ordered pairs differ only by signs, the locations of the points are related by reflections across both axes.

Knowledge

Order rational numbers on a number line.

Identify absolute values of rational numbers.

Reasoning

Interpret statements of inequality as statements about relative position of two numbers on a number line diagram.

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Interpret absolute value as magnitude for a positive or negative quantity.

Distinguish comparisons of absolute value from statements about order and apply to real world contexts.

Knowledge

Calculate absolute value.

Graph points in all four quadrants of the coordinate plane.

Demonstration

Solve real-world problems by graphing points in all four quadrants of the coordinate plane.

Given only coordinates, calculate the distances between two points with the same first coordinate or the same second coordinate using absolute value.


MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How would 25 feet below sea level be represented as an integer? Why?

What is the opposite of____? Justify your conclusion.

Vertical Progression Example Writing Connection

5th Grade

Students worked with positive fractions, decimals, and whole numbers.

7th Grade

Students solve real-world and mathematical problems involving the four operations with rational numbers.

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Explain where 0 fits into a situation represented by integers.



6.NS.3.5 CPALMS Resources 6.NS.3.6 CPALMS Resources 6.NS.3.7 CPALMS Resources 6.NS.3.8 CPALMS Resources

*There is no Mini-Assessment Correlation Link to Scope and Sequence Link to Next Generation Benchmark Task Cards














Domain: Ratios and Proportional Relationships Cluster: RP.1 Understand ratio concepts and use ratio reasoning to solve problems.



MACC.6.RP.1.1Understand 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.”

MACC.6.RP.1.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 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.”

MACC.RP.1.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a) Make tables of equivalent ratios relating quantities with whole-number measurements, find

missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

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

c) Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

d) Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

6.RP.1.1 Deconstructed standard (DOK 2)



Knowledge

Write ratio notation- a:b, a to b, a/b.

Know order matters when writing a ratio.

Know ratios can be simplified.

Know ratios compare two quantities; the quantities do not have to be the same unit of measure.

Recognize that ratios appear in a variety of different contexts; part-to-whole, part-to-part, and rates.

Reasoning

Generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship.

Analyze your context to determine which type of ratio is represented.

Knowledge

Identify and calculate a unit rate.

Use appropriate math terminology as related to rate.

Reasoning

Analyze the relationship between a ratio a:b and a unit rate a/b where b ≠ 0.

Knowledge

Make a table of equivalent ratios using whole numbers.

Find the missing values in a table of equivalent ratios.

Plot pairs of values that represent equivalent ratios on a coordinate plane.

Know that a percent is a ratio of a number to 100.

Find a percent of a number as a rate per 100. Reasoning

Use tables to compare proportional quantities.

Apply the concept of unit rate to solve real-world problems involving unit pricing.

Apply the concept of unit rate to solve real-world problems involving constant speed.

Apply ratio reasoning to convert measurements units in real-world and mathematical problems.

Apply ratio reasoning to convert measurement units by multiplying or dividing in real-world and mathematical problems.

Demonstrate

Solve real-world and mathematical problems involving ratio and rate.

Solve real-world problems involving finding the whole, given a part and a percent.



Domain: Ratios and Proportional Relationships Cluster: RP.1 Understand ratio concepts and use ratio reasoning to solve problems.



Suggested Mathematical Practice Standards Question

MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.8.1 Look for and express regularity in repeated reasoning. Link to Inside Mathematics 8 Mathematical Practice Standards

Compare part-part and part-whole relationships (i.e., how many pieces of fruit)?

How can you apply the concept of unit rate to solve real-world problems?

How would you use unit rate in a real-world situation?



5th

Grade

Students convert among different-sized units within a given measurement system, and use these conversions in solving multi-step real world problems.

7th

Grade

Students compute unit rates associated with ratios of fractions.

Students recognize and represent proportional relationships between quantities.

Identify and describe the ratios.

Write a comparison of the proportional quantities.


6th

Grade Common Core Flip Book Link to Depth of Knowledge (DOK) Chart

6.RP.1.1 CPALMS Resources 6.RP.1.2 CPALMS Resources 6.RP.1.3 CPALMS Resources

MARS Lesson- Traveling to School NYC Unit- Ratios and Proportional Relationships NYC Unit- Ratio Reasoning Illustrative Mathematics Task: Friends

MA.6.A.2.2 MA.6.A.2.1 MA.6.A.5.1 (Does not transfer to CCSSM) MA.6.A.5.2 (Does not transfer to CCSSM) MA.6.A.5.3 (Does not transfer to CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards










http://map.mathshell.org/materials/download.php?fileid=1366

http://schools.nyc.gov/NR/rdonlyres/A9F735CB-47E4-40F8-884F-EA54D0AB5705/0/NYCDOEG6MathRatios_Final.pdf

http://schools.nyc.gov/NR/rdonlyres/A9F735CB-47E4-40F8-884F-EA54D0AB5705/0/NYCDOEG6MathRatios_Final.pdf

http://schools.nyc.gov/NR/rdonlyres/DA04B2E8-94CE-4DE4-B902-CEE331D651FB/0/NYCDOEG6MathRatioReasoning_Final.pdf





Domain: Statistics and Probability Cluster: SP.1 Develop understanding of statistical variability. Associated Fluency Standards: MACC.NS.2.2 Fluently divide multi-digit numbers, MACC.NS.2.3 Multi-digit operations with decimals

MACC.6.SP.1.1Recognize 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.

MACC.6.SP.1.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

MACC.6.SP.1.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

6.SP.1.1 Deconstructed standard (DOK 1) 6.SP.1.2 Deconstructed standard (DOK 2) 6.SP.1.3 deconstructed standard (DOK 1) Knowledge

Recognize that data can have variability.

Recognize a statistical question (examples versus non examples.)

Knowledge

Know that a set of data has a distribution.

Describe a set of data by its center.

Describe a set of data by its spread and overall shape.

Knowledge

Recognize there are measures of central tendency for a data set.

Recognize there are measures of variances for a data set.

Recognize (measures) of central tendency for a data set. Summarize the data with a single number.

Recognize (measures) of variation for a data set. Describe how its values vary with a single number.


MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.3.1 Construct viable arguments and critique the reasoning of others. MACC.K12.MP.4.1 Model with mathematics. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure.

What is the same and what is different about________________?

How would you describe the data?

Why is data important in real-world situation?

Why does data have variability?



3rd

-5th

Grade

Students work with data on a bar graph, picture graph, line plot, and first quadrant of a coordinate plane.

7th

Grade

Students use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Describe a set of data by its center, spread, and/or overall shape.

Create a data display based on a set of data. Explain some observations that can be made from the data display?



6.SP.1.1 CPALMS Resources 6.SP.1.2 CPALMS Resources 6.SP.1.3 CPALMS Resources

MARS Task- Suzi’s Company Link to Depth of Knowledge (DOK) Chart

MA.6.S.6.1 (Does not transfer to CCSSM) MA.6.S.6.2 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards










http://map.mathshell.org/materials/tasks.php?taskid=383&subpage=apprentice




Domain: Statistics and Probability Cluster: SP.2 Summarize and describe distributions. Associated Fluency Standards: MACC.NS.2.2 Fluently divide multi-digit numbers, MACC.NS.2.3 Multi-digit operations with decimals

MACC.6.SP.2.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

MACC.6.SP.2.5 Summarize numerical data sets in relation to their context, such as by: a) Reporting the number of observations. b) Describing the nature of the attribute under investigation, including how it was measured and its

units of measurement. c) Giving quantitative measures of center (median and/or mean) and variability (interquartile range

and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

d) Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

6.SP.2.4 Deconstructed standard (DOK 2) 6.SP.2.5 Deconstructed standard (DOK 3) Knowledge

Identify the components of dot plots, histograms, and box plots.

Find the median, quartile and interquartile range of a set of data. Reasoning

Analyze a set of data to determine its variance. Product

Create a dot plot to display a set of numerical data.

Create a histogram to display a set of numerical data.

Create a box plot to display a set of numerical data.

Knowledge

Organize and display data in tables and graphs.

Report the number of observations in a data set or display.

Describe the data being collected, including how it was measured and its units of measurement.

Calculate quantitative measures of center.

Calculate quantitative measures of variance.

Identify outliers. Reasoning

Determine the effect of outliers on quantitative measures of a set of data.

Choose the appropriate measure of central tendency to represent the data.

Analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of central tendency and variability and justify why this measure is appropriate in terms of the context.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics. MACC.K12.MP.5.1 Use appropriate tools strategically. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How can you display a set of numerical data?

Why do we organize data in tables and graphs?

Why did you choose ______________ to display the set of data?

Vertical Progression

TurnOnCCMath.net K-8 Learning Trajectories


3rd-5th Grade

Students work with data on a bar graph, picture graph, line plot, and first quadrant of a coordinate plane.

7th Grade

Students use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Compare different graphs of the same data.

Justify why a measure is appropriate in terms of the context.

Analyze the data and write a detailed summary of the data.

Describe the data being collected, including how it was measured and its units of measurement.



6.SP.2.4 CPALMS Resources 6.SP.2.5 CPALMS Resources

MARS Lesson- Mean, Median, Mode, and Range Link to Depth of Knowledge (DOK) Chart

No Mini-Assessments correlate to this cluster.









http://map.mathshell.org/materials/lessons.php?taskid=486&subpage=concept

http://map.mathshell.org/materials/lessons.php?taskid=486&subpage=concept

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