CCLS Mathematics Grade 6 Curriculum Guidemvcsd.sharpschool.net/UserFiles/Servers/Server_87286/File...MOUNT VERNON CITY SCHOOL DISTRICT CCLS Mathematics Grade 6 Curriculum Guide THIS

MOUNT VERNON CITY SCHOOL DISTRICT

CCLS MathematicsGrade 6

Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GRADE 6MATHEMATICS CURRICULUM IN MOUNT VERNON.

2015-2016

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Mount Vernon City School District

Board of Education

Adriane SaundersPresident

Serigne GningueVice President

Board TrusteesCharmaine FearonRosemarie Jarosz

Micah J.B. McOwenOmar McDowell

Darcy MillerWanda WhiteLesly Zamor

Superintendent of SchoolsDr. Kenneth Hamilton

Deputy SuperintendentDr. Jeff Gorman

Assistant Superintendent of BusinessKen Silver

Assistant Superintendent of Human ResourcesDenise Gagne-Kurpiewski

Administrator of Mathematics and Science (K-12)Dr. Satish Jagnandan

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TABLE OF CONTENTS

I. COVER …..……………………………………....... 1

II. MVCSD BOARD OF EDUCATION …..……………………………………....... 2

III. TABLE OF CONTENTS …..……………………………………....... 3

IV. IMPORTANT DATES …..……………………………………....... 4

V. VISION STATEMENT …..……………………………………....... 5

VI. PHILOSOPHY OF MATHEMATICS CURRICULUM ……………. 6

VII. NYS GRADE 6 COMMON CORE LEARNING STANDARDS ……………..7

VIII. MVCSD GRADE 6 MATHEMATICS PACING GUIDE …………....15

IX. WORD WALL …………... 28

X. SETUP OF A MATHEMATICS CLASSROOM …………... 29

XI. ELEMENTARY GRADING POLICY …………... 30

XII. SAMPLE NOTEBOOK RUBRIC …………... 31

XIII. CLASSROOM AESTHETICS …………... 32

XIV. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 33

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IMPORTANT DATES 2015-16

REPORT CARD – 10 WEEK PERIOD

MARKING

PERIOD

MARKING

PERIOD

BEGINS

INTERIM

PROGRESS

REPORTS

MARKING

PERIOD

ENDS

DURATION REPORT CARD

DISTRIBUTION

MP 1 September 8,

2015

October 9,

2015

November 13,

2015

10 weeks Week of

Nov. 23, 2015

MP 2 November 16,

2015

December 18,

2015

January 29,

2016

10 weeks Week of

February 8, 2016

MP 3 February 1,

2016

March 11,

2016

April 15,

2016

9 weeks Week of

April 25, 2016

MP 4 April 18,

2016

May 20,

2016

June 23,

2016

10 weeks Last Day of School

June 23, 2016

The Parent Notification Policy states “Parent(s) / guardian(s) or adult students are

to be notified, in writing, at any time during a grading period when it is apparent -

that the student may fail or is performing unsatisfactorily in any course or grade

level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during

the grading period when it becomes evident that the student's conduct or effort

grades are unsatisfactory.”

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VISION STATEMENT

True success comes from co-accountability and co-responsibility. In a coherentinstructional system, everyone is responsible for student learning and studentachievement. The question we need to constantly ask ourselves is, "How are ourstudents doing?"

The starting point for an accountability system is a set of standards andbenchmarks for student achievement. Standards work best when they are welldefined and clearly communicated to students, teachers, administrators, andparents. The focus of a standards-based education system is to provide commongoals and a shared vision of what it means to be educated. The purposes of aperiodic assessment system are to diagnose student learning needs, guideinstruction and align professional development at all levels of the system.

The primary purpose of this Instructional Guide is to provide teachers andadministrators with a tool for determining what to teach and assess. Morespecifically, the Instructional Guide provides a "road map" and timeline forteaching and assessing the Common Core Learning Standards.

I ask for your support in ensuring that this tool is utilized so students are able tobenefit from a standards-based system where curriculum, instruction, andassessment are aligned. In this system, curriculum, instruction, and assessment aretightly interwoven to support student learning and ensure ALL students have equalaccess to a rigorous curriculum.

We must all accept responsibility for closing the achievement gap and improvingstudent achievement for all of our students.

Dr. Satish Jagnandan

Administrator for Mathematics and Science (K-12)

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PHILOSOPHY OF MATHEMATICS CURRICULUM

The Mount Vernon City School District recognizes that the understanding of mathematics is

necessary for students to compete in today’s technological society. A developmentally

appropriate mathematics curriculum will incorporate a strong conceptual knowledge of

mathematics through the use of concrete experiences. To assist students in the understanding and

application of mathematical concepts, the mathematics curriculum will provide learning

experiences which promote communication, reasoning, and problem solving skills. Students will

be better able to develop an understanding for the power of mathematics in our world today.

Students will only become successful in mathematics if they see mathematics as a whole, not as

isolated skills and facts. As we develop mathematics curriculum based upon the standards,

attention must be given to both content and process strands. Likewise, as teachers develop their

instructional plans and their assessment techniques, they also must give attention to the

integration of process and content. To do otherwise would produce students who have temporary

knowledge and who are unable to apply mathematics in realistic settings. Curriculum,

instruction, and assessment are intricately related and must be designed with this in mind. All

three domains must address conceptual understanding, procedural fluency, and problem solving.

If this is accomplished, school districts will produce students who will

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.

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New York State P-12 Common Core Learning Standards forMathematics

Mathematics - Grade 6: Introduction

In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate towhole 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 thesystem of rational numbers, which includes negative numbers; (3) writing, interpreting, andusing 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. Byviewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in themultiplication table, and by analyzing simple drawings that indicate the relative size of quantities, studentsconnect their understanding of multiplication and division with ratios and rates. Thus students expand the scopeof problems for which they can use multiplication and division to solve problems, and they connect ratios andfractions. 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 betweenmultiplication 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 andthe ordering of numbers to the full system of rational numbers, which includes negative rational numbers, andin particular negative integers. They reason about the order and absolute value of rational numbers and aboutthe 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 thatcorrespond 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 ofoperations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are thevalues of the variables that make the equation true. Students use properties of operations and the idea ofmaintaining the equality of both sides of an equation to solve simple one-step equations. Students construct andanalyze 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 thinkstatistically. Students recognize that a data distribution may not have a definite center and that different ways tomeasure center yield different values. The median measures center in the sense that it is roughly the middlevalue. The mean measures center in the sense that it is the value that each data point would take on if the total ofthe data values were redistributed equally, and also in the sense that it is a balance point. Students recognize thata measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing databecause two very different sets of data can have the same mean and median yet be distinguished by theirvariability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, andsymmetry, 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 amongshapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and specialquadrilaterals 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 whosearea they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulasfor the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings andconstructions in Grade 7 by drawing polygons in the coordinate plane.

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Mathematical Practices

1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoningof 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.

Grade 6 Overview

Ratios and Proportional Relationships• Understand ratio concepts and use ratioreasoning to solve problems.

The Number System• Apply and extend previous understandings ofmultiplication and division to divide fractionsby fractions.• Compute fluently with multi-digit numbers andfind common factors and multiples.• Apply and extend previous understandings ofnumbers to the system of rational numbers.

Expressions and Equations• Apply and extend previous understandings ofarithmetic to algebraic expressions.• Reason about andsolve one-variable equationsand inequalities.• Represent and analyze quantitativerelationships between dependent andindependent variables.

Geometry• Solve real-world and mathematical problemsinvolving area, surface area, and volume.

Statistics and Probability• Develop understanding of statistical variability.• Summarize and describe distributions.

Ratios & Proportional Relationships 6.RP

Understand ratio concepts and use ratio reasoning to solve problems.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 therewas 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

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, sothere is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 perhamburger.”1

3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables ofequivalent 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 werelawns 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 whenmultiplying or dividing quantities.

_________________1 Expectations for unit rates in this grade are limited to non-complex fractions.

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The Number System 6.NS

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.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 astory context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship betweenmultiplication 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 many3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi andarea 1/2 square mi?

Compute fluently with multi-digit numbers and find common factors and multiples.2. Fluently divide multi-digit numbers using the standard algorithm.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each

operation.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 wholenumbers 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).

Apply and extend previous understandings of numbers to the system of rational numbers.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-worldcontexts, explaining the meaning of 0 in each situation.

6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axesfamiliar 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 itsown 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 byreflections across one or both axes.

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

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 numberline 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; interpretabsolute value as magnitude for a positive or negative quantity in a real-world situation. For example, foran 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 anaccount balance less than –30 dollars represents a debt greater than 30 dollars.

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 orthe same second coordinate.

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Expressions & Equations 6.EE

Apply and extend previous understandings of arithmetic to algebraic expressions.1. Write and evaluate numerical expressions involving whole-number exponents.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 usedin 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 sidesof length s = 1/2.

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

4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardlessof which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent becausethey name the same number regardless of which number y stands for.

Reason about and solve one-variable equations and inequalities.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 givennumber in a specified set makes an equation or inequality true.

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 numberin a specified set.

7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = qfor cases in which p, q and x are all nonnegative rational numbers.

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

Represent and analyze quantitative relationships between dependent and independent variables.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 independentvariables using graphs and tables, and relate these to the equation. For example, in a problem involving motionat constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to representthe relationship between distance and time.

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Geometry 6.G

Solve real-world and mathematical problems involving area, surface area, and volume.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.

2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of theappropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplyingthe edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangularprisms with fractional edge lengths in the context of solving real-world and mathematical problems.

3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of aside joining points with the same first coordinate or the same second coordinate. Apply these techniques in thecontext of solving real-world and mathematical problems.

4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find thesurface area of these figures. Apply these techniques in the context of solving real-world and mathematicalproblems.

Statistics & Probability 6.SP

Develop understanding of statistical variability.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 studentsin my school?” is a statistical question because one anticipates variability in students’ ages.

2. Understand that a set of data collected to answer a statistical question has a distribution which can be describedby its center, spread, and overall shape.

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.

Summarize and describe distributions.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.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 theoverall 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 thecontext in which the data were gathered.

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Grade 6 Common Core Mathematics Test Cluster Emphases

Cluster Emphases for Instruction on the 2013 Grade 6 Common Core Mathematics TestCluster Emphasis Recommended Instructional

TimeApproximate Number of Test

PointsMajor 65–75% 70–80%

Supporting 15–25% 10–20%Additional 5–15% 5–10%

CCLS Standard Content

Emphasis

Operations and Algebraic Thinking

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships

between corresponding terms. Form ordered pairs consisting of corresponding terms

from the two patterns, and graph the ordered pairs on a coordinate plane.

Additional

Ratios and Proportional Relationships

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship

between two quantities

Major

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use

rate language in the context of a ratio relationship

Major

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.

Major

The Number System

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

Major

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm Additional

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

algorithm for each operation

Additional

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

Additional

6.NS.5 Understand that positive and negative numbers are used together to describe quantities

having opposite directions or values; use positive and negative numbers to represent

quantities in real-world contexts, explaining the meaning of 0 in each situation

Major

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.

Major

6.NS.7 Understand ordering and absolute value of rational numbers Major

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

Major

Expressions and Equations

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. Major

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers Major

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6.EE.3 Apply the properties of operations to generate equivalent expressions. Major

6.EE.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).

Major

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

Major

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

Major

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

Major

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

Major

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.

Major

Geometry

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).

Additional

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.

Additional

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.

Supporting

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.

Supporting

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

Supporting

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.

Supporting

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Statistics and Probability

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.

Additional

Post

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

Additional

Post

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

Additional

Post

6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and

box plots

Additional

Post

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

a. Reporting the number of observations

b. Describing the nature of the attribute under investigation, including how it was

measured and its units of measurement.

c. Giving quantitative measures of center (median and/or mean) and variability

(interquartile range and/or mean absolute deviation), as well as describing any overall

pattern and any striking deviations from the overall pattern with reference to the context

in which the data were gathered.

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.

Additional

Post

= Standards recommended for greater emphasisPost = Standards recommended for instruction in May-June

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MATHEMATICS 6 PACING GUIDE

This guide using NYS Grade 6 Mathematics CCLS Modules was created to provide teachers with a time frame to complete theGrade 6 New York State Mathematics Curriculum.

Module Title Standards Days Month i-Ready Lessons

1 Ratios and Unit Rates 6.RP.1, 6.RP.2, 6.RP.3 30 Sept. 8 – Oct. 23Topic A – 1; Topic B – 3; Topic C –

2, 4; Topic D – 5

2Arithmetic Operations Including

Dividing by a Fraction6.NS.1, 6.NS.2F, 6.NS.3F, 6.NS.4 21 Oct. 26 – Nov. 24

Topic A – 6, 7; Topic B – 9, 10;Topic C – 8, 10; Topic D – 11

3 Rational Numbers 6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8 21 Nov. 25 – Jan. 5Topic A – 12; Topic B – 13; Topic

C – 14

4 Expressions and Equations6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5,

6.EE.6, 6.EE.7, 6.EE.8, 6.EE.935 Jan. 6 – Mar. 2

Topic A – 17; Topic B – 15; TopicC – 16; Topic D – 17; Topic E – 16;Topic F – 16, 17; Topic G – 18, 19;

Topic H – 20, 21

5Area, Surface Area, and Volume

Problems6.EE.2, 6.EE.5, 6.EE.6, 6.EE.7, 6.G.1,

6.G.2, 6.G.3, 6.G.423 Mar. 3 – Apr. 12

Topic A – 22; Topic B –23; Topic C– 25; Topic D – 24

NYSED GRADE 6 MATHEMATICS TEST: WEDNESDAY, APRIL 13 – FRIDAY, APRIL 15, 2016

6 Statistics 6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5 48 Apr. 18 – Jun. 17Topic A – 26, 28; Topic B –27;

Topic C – 29; Topic D – 29

Red – End of Module Assessment PeriodGreen – Priority Standards account for approximately 70-80% of number of test points.

Note that the curriculum assumes that each school day includes 70-75 minutes of math: one hour on the day’s Session, and 10-15 minutes on Fluency activities.Designed to fit within the calendar of a typical school year, grade 5 includes a total of 143 lessons. This provides some leeway for going further with particularideas and/or accommodating local circumstances. Although pacing will vary somewhat in response to variations in school calendars, needs of students, yourschool's years of experience with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from theway mathematical ideas are introduced, developed, and revisited across the year.

Required Fluency: 6.NS.2 Multi-digit division & 6.NS.3 Multi-digit decimal operations.

16


1 Ratios and Unit Rates 6.RP.1, 6.RP.2, 6.RP.3 30 Sept. 8 – Oct. 23 Topic A – 1; Topic B – 3; Topic C – 2, 4; Topic D – 5

In this module, students are introduced to the concepts of ratio and rate. Their previous experience solving problems involvingmultiplicative comparisons, such as “Max has three times as many toy cars as Jack,” (4.OA.2) serves as the conceptual foundation forunderstanding ratios as a multiplicative comparison of two or more numbers used in quantities or measurements (6.RP.1). Studentsdevelop fluidity in using multiple forms of ratio language and ratio notation. They construct viable arguments and communicatereasoning about ratio equivalence as they solve ratio problems in real world contexts (6.RP.3). As the first topic comes to a close,students develop a precise definition of the value of a ratio a:b, where b ≠ 0 as the value a/b, applying previous understanding offraction as division (5.NF.3). They can then formalize their understanding of equivalent ratios as ratios having the same value.

Standards Topics Days

6.RP.16.RP.3a

A Representing and Reasoning About RatiosLessons 1-2: RatiosLessons 3-4: Equivalent RatiosLessons 5-6: Solving Problems by Finding Equivalent RatiosLesson 7: Associated Ratios and the Value of a RatioLesson 8: Equivalent Ratios Defined Through the Value of a Ratio

8

6.RP.3a B Collections of Equivalent RatiosLesson 9: Tables of Equivalent RatiosLesson 10: The Structure of Ratio Tables: Additive and MultiplicativeLesson 11: Comparing Ratios Using Ratio TablesLesson 12: From Ratio Tables to Double Number Line DiagramsLesson 13: From Ratio Tables to Equations Using the Value of the RatioLesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on theCoordinate PlaneLesson 15: A Synthesis of Representations of Equivalent Ratio Collections

7

6.RP.2 C Unit Rates 7

17

6.RP.3b6.RP.3d

Lesson 16: From Ratios to RatesLesson 17: From Rates to RatiosLesson 18: Finding a Rate by Dividing Two QuantitiesLessons 19-20: Comparison Shopping—Unit Price and Related Measurement ConversionsLessons 21-22: Getting the Job Done—Speed, Work, and Measurement UnitsLesson 23: Problem-Solving Using Rates, Unit Rates, and Conversions

6.RP.3c D PercentLesson 24: Percent and Rates per 100Lesson 25: A Fraction as a PercentLesson 26: Percent of a QuantityLessons 27-29: Solving Percent Problems

6

End-of-Module Assessment: Topics A through D (assessment 1 day, remediation or furtherapplications 1 day)

2

Total Number of Instructional Days 30

Mid-Module Assessment: Topics A through B should be given for homework (weekend).

18


2Arithmetic Operations Including

Dividing by a Fraction6.NS.1, 6.NS.2F, 6.NS.3F, 6.NS.4 21 Oct. 26 – Nov. 24

Topic A – 6, 7; Topic B – 9, 10;Topic C – 8, 10; Topic D – 11

In Module 1, students used their existing understanding of multiplication and division as they began their study of ratios and rates. InModule 2, students complete their understanding of the four operations as they study division of whole numbers, division by a fractionand operations on multi-digit decimals. This expanded understanding serves to complete their study of the four operations withpositive rational numbers, thereby preparing students for understanding, locating, and ordering negative rational numbers (Module 3)and algebraic expressions (Module 4).


6.NS.1 A Dividing Fractions by FractionsLessons 1–2: Interpreting Division of a Whole Number by a Fraction—Visual ModelsLessons 3–4: Interpreting and Computing Division of a Fraction by a Fraction—More ModelsLesson 5: Creating Division StoriesLesson 6: More Division StoriesLesson 7: The Relationship Between Visual Fraction Models and EquationsLesson 8: Dividing Fractions and Mixed Numbers

8

6.NS.3 B Multi-Digit Decimal Operations—Adding, Subtracting, and MultiplyingLesson 9: Sums and Differences of DecimalsLesson 10: The Distributive Property and Product of DecimalsLesson 11: Fraction Multiplication and the Products of Decimals

3

6.NS.26.NS.3

C Dividing Whole Numbers and DecimalsLesson 12: Estimating Digits in a QuotientLesson 13: Dividing Multi-Digit Numbers Using the AlgorithmLesson 14: The Division Algorithm—Converting Decimal Division into Whole NumberDivision Using FractionsLesson 15: The Division Algorithm—Converting Decimal Division into Whole Number

4

19

Division Using Mental Math

6.NS.4 D Number Theory—Thinking Logically About Multiplicative ArithmeticLesson 16: Even and Odd NumbersLesson 17: Divisibility Tests for 3 and 9Lesson 18: Least Common Multiple and Greatest Common FactorLesson 19: The Euclidean Algorithm as an Application of the Long Division Algorithm

4


2



20


3 Rational Numbers 6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8 21 Nov. 25 – Jan. 5 Topic A – 12; Topic B – 13; Topic C – 14

Students are familiar with the number line and determining the location of positive fractions, decimals, and whole numbers fromprevious grades. Students extend the number line (both horizontally and vertically) in Module 3 to include the opposites of wholenumbers. The number line serves as a model to relate integers and other rational numbers to statements of order in real-worldcontexts. In this module’s final topic, the number line model is extended to two-dimensions, as students use the coordinate plane tomodel and solve real-world problems involving rational numbers.


6.NS.C.56.NS.C.6a6.NS.C.6c

A Understanding Positive and Negative Numbers on the Number LineLesson 1: Positive and Negative Numbers on the Number Line—Opposite Direction and ValueLessons 2–3: Real-World Positive and Negative Numbers and ZeroLesson 4: The Opposite of a NumberLesson 5: The Opposite of a Number’s OppositeLesson 6: Rational Numbers on the Number Line

6

6.NS.C.6c6.NS.C.7

B Order and Absolute ValueLessons 7–8: Ordering Integers and Other Rational NumbersLesson 9: Comparing Integers and Other Rational NumbersLesson 10: Writing and Interpreting Inequality Statements Involving Rational NumbersLesson 11: Absolute Value—Magnitude and DistanceLesson 12: The Relationship Between Absolute Value and OrderLesson 13: Statements of Order in the Real World

7

6.NS.C.6b6.NS.C.6c6.NS.C.8

C Rational Numbers and the Coordinate PlaneLesson 14: Ordered PairsLesson 15: Locating Ordered Pairs on the Coordinate PlaneLesson 16: Symmetry in the Coordinate PlaneLesson 17: Drawing the Coordinate Plane and Points on the Plane

6

21

Lesson 18: Distance on the Coordinate PlaneLesson 19: Problem-Solving and the Coordinate Plane


2



22


4Expressions and

Equations6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5,

6.EE.6, 6.EE.7, 6.EE.8, 6.EE.935 Jan. 6 – Mar. 2

Topic A – 17; Topic B – 15; Topic C – 16; Topic D –17; Topic E – 16; Topic F – 16, 17; Topic G – 18, 19;

Topic H – 20, 21

In Module 4, students extend their arithmetic work to include using letters to represent numbers. Students understand that letters aresimply “stand-ins” for numbers and that arithmetic is carried out exactly as it is with numbers. Students explore operations in terms ofverbal expressions and determine that arithmetic properties hold true with expressions because nothing has changed—they are stilldoing arithmetic with numbers. Students determine that letters are used to represent specific but unknown numbers and are used tomake statements or identities that are true for all numbers or a range of numbers. Students understand the importance of specifying

units when defining letters. Students say, “Let Karolyn’s weight in pounds” instead of “Let Karolyn’s weight” becauseweight cannot be a specific number until it is associated with a unit, such as pounds, ounces, grams, etc. They also determine that it is

inaccurate to define as Karolyn because Karolyn is not a number. Students conclude that in word problems, each letter (or variable)represents a number and its meaning is clearly stated.


6.EE.A.3 A Relationships of the OperationsLesson 1: The Relationship of Addition and SubtractionLesson 2: The Relationship of Multiplication and DivisionLesson 3: The Relationship of Multiplication and AdditionLesson 4: The Relationship of Division and Subtraction

4

6.EE.A.16.EE.A.2c

B Special Notations of OperationsLesson 5: ExponentsLesson 6: The Order of Operations

2

6.EE.A.2c6.EE.A.4

C Replacing Letters and NumbersLesson 7: Replacing Letters with NumbersLesson 8: Replacing Numbers with Letters

2

6.EE.A.2a6.EE.A.2b

D Expanding, Factoring, and Distributing ExpressionsLesson 9: Writing Addition and Subtraction Expressions

6

23

6.EE.A.36.EE.A.4

Lesson 10: Writing and Expanding Multiplication ExpressionsLesson 11: Factoring ExpressionsLesson 12: Distributing ExpressionsLessons 13–14: Writing Division Expressions

6.EE.A.2b E Expressing Operations in Algebraic FormLesson 15: Read Expressions in Which Letters Stand for NumbersLessons 16–17: Write Expressions in Which Letters Stand for Numbers

2

6.EE.A.26.EE.A.2c6.EE.B.5

F Writing and Evaluating Expressions and FormulasLesson 18: Writing and Evaluating Expressions—Addition and SubtractionLesson 19: Substituting to Evaluate Addition and Subtraction ExpressionsLesson 20: Writing and Evaluating Expressions—Multiplication and DivisionLesson 21: Writing and Evaluating Expressions—Multiplication and AdditionLesson 22: Writing and Evaluating Expressions—Exponents

5

6.EE.B.56.EE.B.66.EE.B.7

G Solving EquationsLessons 23–24: True and False Number SentencesLesson 25: Finding Solutions to Make Equations TrueLesson 26: One-Step Equations—Addition and SubtractionLesson 27: One-Step Equations—Multiplication and DivisionLesson 28: Two-Step Problems—All OperationsLesson 29: Multi-Step Problems—All Operations

7

6.EE.B.56.EE.B.66.EE.B.76.EE.B.86.EE.C.9

H Applications of EquationsLesson 30: One-Step Problems in the Real WorldLesson 31: Problems in Mathematical TermsLesson 32: Multi-Step Problems in the Real WorldLesson 33: From Equations to InequalitiesLesson 34: Writing and Graphing Inequalities in Real-World Problems

5

End-of-Module Assessment: Topics A through H (assessment 1 day, remediation or further applications 1day)

2


Mid-Module Assessment: Topics A through E should be given for homework (weekend).

24


5Area, Surface Area, and

Volume Problems6.EE.2, 6.EE.5, 6.EE.6, 6.EE.7,

6.G.1, 6.G.2, 6.G.3, 6.G.448 Apr. 18 – Jun. 17

Topic A – 26, 28; Topic B –27; Topic C– 29; Topic D – 29

NYSED GRADE 6 MATHEMATICS TEST: WEDNESDAY, APRIL 13 – FRIDAY, APRIL 15, 2016

Starting in Grade 1, students compose and decompose plane and solid figures (1.G.A.2). They move to spatial structuring ofrectangular arrays in Grade 2 (2.G.A.2) and continually build upon their understanding of arrays to ultimately apply their knowledgeto two- and three-dimensional figures in Grade 4 (4.MD.A.3) and Grade 5 (5.MD.C.3, 5.MD.C.5). Students move from buildingarrays to using arrays to find area and eventually move to decomposing three-dimensional shapes into layers that are arrays of cubes.In this module, students utilize their previous experiences in shape composition and decomposition in order to understand and developformulas for area, volume, and surface area.


6.G.A.1 A Area of Triangles, Quadrilaterals, and PolygonsLesson 1: The Area of Parallelograms Through Rectangle FactsLesson 2: The Area of Right TrianglesLessons 3–4: The Area of All Triangles Using Height and BaseLesson 5: The Area of Polygons Through Composition and DecompositionLesson 6: Area in the Real World

6

6.G.A.3 B Polygons on the Coordinate PlaneLesson 7: Distance on the Coordinate PlaneLesson 8: Drawing Polygons in the Coordinate PlaneLesson 9: Determining Perimeter and Area of Polygons on the Coordinate PlaneLesson 10: Distance, Perimeter, and Area in the Real World

4

6.G.A.2 C Volume of Right Rectangular PrismsLesson 11: Volume with Fractional Edge Lengths and Unit CubesLesson 12: From Unit Cubes to the Formulas for VolumeLesson 13: The Formulas for Volume

5

25

Lesson 14: Volume in the Real World

6.G.A.26.G.A.4

D Nets and Surface AreaLesson 15: Representing Three-Dimensional Figures Using Nets 213Lesson 16: Constructing Nets 246Lesson 17: From Nets to Surface Area 262Lesson 18: Determining Surface Area of Three-Dimensional FiguresLesson 19: Surface Area and Volume in the Real World 288

Lesson 19a: Addendum Lesson for Modeling―Applying Surface Area and Volume to Aquariums

6

End-of-Module Assessment: Topics C through D (assessment 1 day, remediation or furtherapplications 1 day)

2



26

Module Title Standards Days Monthi-ReadyLessons

6 Statistics 6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5 32 Apr. 27 – Jun. 11

In Grade 5, students used bar graphs and line plots to represent data and then solved problems using the information presented in theplots (5.MD.B.2). In this module, students move from simply representing data into analysis of data. In Topic A, students begin tothink and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data (6.SP.A.1).Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center,variability, and shape (6.SP.A.2). Beginning in Topic A, and throughout the module, students see and represent data distributionsusing dot plots and histograms (6.SP.B.4).


6.SP.A.16.SP.A.26.SP.B.4

6.SP.B.5b

A Understanding DistributionsLesson 1: Posing Statistical QuestionsLesson 2: Displaying a Data DistributionLesson 3: Creating a Dot PlotLesson 4: Creating a HistogramLesson 5: Describing a Distribution Displayed in a Histogram

10

6.SP.A.26.SP.A.36.SP.B.46.SP.B.5

B Summarizing a Distribution that is Approximately Symmetric Using the Mean and MeanAbsolute Deviation

Lesson 6: Describing the Center of a Distribution Using the MeanLesson 7: The Mean as a Balance PointLesson 8: Variability in a Data DistributionLesson 9: The Mean Absolute Deviation (MAD)Lessons 10–11: Describing Distributions Using the Mean and MAD

11

Mid-Module Assessment: Topics A through B (assessment 1 day, remediation or furtherapplications 2 days)

3

6.SP.A.26.SP.A.3

C Summarizing a Distribution that is Skewed Using the Median and the Interquartile RangeLesson 12: Describing the Center of a Distribution Using the Median

10

27

6.SP.B.46.SP.B.5

Lesson 13: Describing Variability Using the Interquartile Range (IQR)Lesson 14: Summarizing a Distribution Using a Box PlotLesson 15: More Practice with Box PlotsLesson 16: Understanding Box Plots

6.SP.B.46.SP.B.5

C Summarizing and Describing Distributions () 187Lesson 17: Developing a Statistical ProjectLesson 18: Connecting Graphical Representations and Numerical SummariesLesson 19: Comparing Data DistributionsLesson 20: Describing Center, Variability, and Shape of a Data Distribution from a GraphicalRepresentationLesson 21: Summarizing a Data Distribution by Describing Center, Variability, and ShapeLesson 22: Presenting a Summary of a Statistical Project

11

End-of-Module Assessment: Topics C through D (assessment 1 day, remediation or furtherapplications 2 days)

3


WORD WALLS ARE DESIGNED …

to promote group learning support the teaching of important general principles about words and how they work Foster reading and writing in content area Provide reference support for children during their reading and writing Promote independence on the part of young students as they work with words Provide a visual map to help children remember connections between words

and the characteristics that will help them form categories Develop a growing core of words that become part of their vocabulary

Important Notice A Mathematics Word Wall must be present in every mathematics classroom.

Math Word Wall

Create a math wordwall

Place math words onyour current wordwall but highlightthem in some way.

29

SETUP OF THE MATHEMATICS CLASSROOM

I. Prerequisites for a Mathematics Classroom Teacher Schedule Class List Seating Chart Code of Conduct / Discipline Grade Level Common Core Learning Standards (CCLS) Updated Mathematics Student Work Mathematics Grading Policy Mathematics Diagrams, Charts, Posters, etc. Grade Level Number Line Grade Level Mathematics Word Wall Mathematics Portfolios Mathematics Center with Manipulatives (Grades K - 12)

II. Updated Student WorkA section of the classroom must display recent student work. This can be of anytype of assessment, graphic organizer, and writing activity. Teacher feedback mustbe included on student’s work.

III. Board Set-UpEvery day, teachers must display the Lesson # and Title, Objective(s), CommonCore Learning Standard(s), Opening Exercise and Homework. At the start ofthe class, students are to copy this information and immediately begin on theFluency Activity or Opening Exercise.

IV. Spiraling HomeworkHomework is used to reinforce daily learning objectives. The secondary purposeof homework is to reinforce objectives learned earlier in the year. Theassessments are cumulative, spiraling homework requires students to reviewcoursework throughout the year.

Student’s Name: School:

Teacher’s Name: Date:

Lesson # and Title:

Objective(s)

CCLS:

Opening Exercise:

30

ELEMENTARY MATHEMATICS GRADING POLICYThis course of study includes different components, each of which are assigned the followingpercentages to comprise a final grade. I want you--the student--to understand that your gradesare not something that I give you, but rather, a reflection of the work that you give to me.

COMPONENTS OF OVERALL GRADE

LEVEL 1 (0-54%), LEVEL 2 (55-74%), LEVEL 3 (75-89%) AND LEVEL 4 (90-100%)

1. End of Module Assessments → 35%

2. Mid Module Assessments → 15%

3. Homework → 20%

4. Notebook and/or Journal → 15%

5. Classwork / Class Participation → 15%

o Class participation will play a significant part in the determination of your grade.Class participation will include the following: attendance, punctuality to class,contributions to the instructional process, effort, contributions during small groupactivities and attentiveness in class.

PERFORMANCE LEVEL DESCRIPTORS

Level 4 Student demonstrates an in-depth understanding of concepts, skills and processestaught in this reporting period and exceeds the required performance

Level 3 Student consistently demonstrates an understanding of concepts, skills and processestaught in this reporting period

Level 2 Student is beginning to demonstrate an understanding of concepts, skills andprocesses taught during this reporting period

Level 1 Student does not yet demonstrate an understanding of concepts, skills and processestaught in this reporting period and needs consistent support

NE Not evaluated at this time

IMPORTANT NOTICE

As per MVCSD Board Resolution 06-71, the Parent Notification Policy states “Parent(s) /guardian(s) or adult students are to be notified, in writing, at any time during a grading periodwhen it is apparent - that the student may fail or is performing unsatisfactorily in any course orgrade level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during thegrading period when it becomes evident that the student's conduct or effort grades areunsatisfactory.”

31

SAMPLE NOTEBOOK SCORING RUBRIC

Student Name:______________________________________________

Teacher Name:___________________________________________

Criteria 4 3 2 1 Points

Completion ofRequired Sections

All requiredsections arecomplete.

One requiredsection ismissing.

Two or threerequired sections

are missing.

More than threerequired sections

are missing.

Missing SectionsNo sections of

the notebook aremissing.

One sections ofthe notebook is

missing.

Two sections of thenotebook are

missing.

Three or moresections of thenotebook are

missing.

Headers / Footers

No requiredheader(s) and/or

footer(s) aremissing within

notebook.

One or tworequired

header(s) and/orfooter(s) are

missing withinnotebook.

Three or fourrequired header(s)and/or footer(s) are


More than fourrequired header(s)and/or footer(s) are


Organization

All assignmentand/or notes arekept in a logical

or numericalsequence.

One or twoassignments

and/or notes arenot in a logical or

numericalsequence.

Three or Fourassignments and/ornotes are not in a

logical ornumericalsequence.

More than fourassignments and/ornotes are not in a

logical ornumericalsequence.

NeatnessOverall notebookis kept very neat.

Overall notebookis kept in asatisfactorycondition.

Overall notebook iskept in a below

satisfactorycondition.

Overall notebook isunkept and very

disorganized.

Total

Teacher’s Comments:

32

CLASSROOM AESTHETICS

“PRINT–RICH” ENVIRONMENT CONDUCIVE TO LEARNING

TEACHER NAME: _________________________________________________________

COURSE / PERIOD: _________________________________________________________

ROOM: _________________________________________________________

CHECKLISTYES NO

Teacher Schedule

Class List

Seating Chart

Code of Conduct / Discipline

Grade Level Mathematics CCLS

Mathematics Grading Policy

Mathematics Diagrams, Posters, Displays, etc.

Grade Level Number Line

Updated Student Work (Projects, Assessments, Writing, etc.)

Updated Student Portfolios

Updated Grade Level Mathematics Word-Wall

Mathematics Centers with Manipulatives

Organization of Materials

Cleanliness

Principal Signature: _________________________________________ Date: ____________

Asst. Pri. Signature: _________________________________________ Date: ____________

33

SYSTEMATIC DESIGN OF A MATHEMATICS LESSON

What are the components of an Elementary Mathematics Block?

ComponentFluency Practice Information processing theory supports the view that automaticity in math facts is

fundamental to success in many areas of higher mathematics. Without the ability to retrievefacts directly or automatically, students are likely to experience a high cognitive load as theyperform a range of complex tasks. The added processing demands resulting from inefficientmethods such as counting (vs. direct retrieval) often lead to declarative and procedural errors.Accurate and efficient retrieval of basic math facts is critical to a student’s success inmathematics.

Opening Exercise - Whole Group This can be considered the motivation or Do Now of the lesson It should set the stage for the day's lesson Introduction of a new concept, built on prior knowledge Open-ended problemsConceptual Development - Whole Group (Teacher Directed, Student Centered) Inform students of what they are going to do. Refer to Objectives. Refer to the Key Words

(Word Wall) Define the expectations for the work to be done Provide various demonstrations using modeling and multiple representations (i.e. model a

strategy and your thinking for problem solving, model how to use a ruler to measure items,model how to use inch graph paper to find the perimeter of a polygon,)

Relate to previous work Provide logical sequence and clear explanations Provide medial summaryApplication Problems - Cooperative Groups, Pairs, Individuals, (Student Interaction &Engagement, Teacher Facilitated) Students try out the skill or concept learned in the conceptual development Teachers circulate the room, conferences with the students and assesses student work (i.e.

teacher asks questions to raise the level of student thinking) Students construct knowledge around the key idea or content standard through the use of

problem solving strategies, manipulatives, accountable/quality talk, writing, modeling,technology applied learning

Student Debrief - Whole Group (Teacher Directed, Student Centered) Students discuss their work and explain their thinking Teacher asks questions to help students draw conclusions and make references Determine if objective(s) were achieved Students summarize what was learned Allow students to reflect, share (i.e. read from journal)Homework/Enrichment - Whole Group (Teacher Directed, Student Centered) Homework is a follow-up to the lesson which may involve skill practice, problem solving

and writing

34

Homework, projects or enrichment activities should be assigned on a daily basis. SPIRALLING OF HOMEWORK - Teacher will also assign problems / questions pertaining to

lessons taught in the past

Remember: Assessments are on-going based on students’ responses.Assessment: Independent Practice (It is on-going! Provide formal assessment whennecessary / appropriate) Always write, use and allow students to generate Effective Questions for optimal learning Based on assessment(s), Re-teach the skill, concept or content using alternative strategies

and approaches

Important Notice

All lessons must be numbered with corresponding homework. For example, lesson #1 will

corresponded to homework #1 and so on.

Writing assignments at the end of the lesson (closure) bring great benefits. Not only do they

enhance students' general writing ability, but they also increase both the understanding of

content while learning the specific vocabulary of the disciplines.

Spiraling Homework

o Homework is used to reinforce daily learning objectives. The secondary purpose of

homework is to reinforce objectives learned earlier in the year. The assessments are

cumulative, spiraling homework requires students to review coursework throughout the

year.

Manipulative must be incorporated in all lessons. With students actively involved in

manipulating materials, interest in mathematics will be aroused. Using manipulative

materials in teaching mathematics will help students learn:

a. to relate real world situations to mathematics symbolism.

b. to work together cooperatively in solving problems.

c. to discuss mathematical ideas and concepts.

d. to verbalize their mathematics thinking.

e. to make presentations in front of a large group.

f. that there are many different ways to solve problems.

g. that mathematics problems can be symbolized in many different ways.

h. that they can solve mathematics problems without just following teachers' directions.

Documents

CCLS Mathematics Grade 6 Curriculum Guidemvcsd.sharpschool.net/UserFiles/Servers/Server_87286/File...MOUNT VERNON CITY SCHOOL DISTRICT CCLS Mathematics Grade 6 Curriculum Guide THIS