CCLS Mathematics Grade 4 Curriculum...

MOUNT VERNON CITY SCHOOL DISTRICT

CCLS MathematicsGrade 4

Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GRADE 4MATHEMATICS CURRICULUM IN MOUNT VERNON.

2015-2016

2

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

3

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 4 COMMON CORE LEARNING STANDARDS ……………..7

VIII. MVCSD GRADE 4 MATHEMATICS PACING GUIDE …………....14

IX. WORD WALL …………... 34

X. SETUP OF A MATHEMATICS CLASSROOM …………... 35

XI. ELEMENTARY GRADING POLICY …………... 36

XII. SAMPLE NOTEBOOK RUBRIC …………... 37

XIII. CLASSROOM AESTHETICS …………... 38

XIV. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 39

4

IMPORTANT DATES 2015-16

REPORT CARD – 10 WEEK PERIOD

MARKINGPERIOD

MARKINGPERIODBEGINS

INTERIMPROGRESSREPORTS

MARKINGPERIOD

ENDS

DURATION REPORT CARDDISTRIBUTION

MP 1 September 8,2015

October 9,2015

November 13,2015

10 weeks Week ofNov. 23, 2015

MP 2 November 16,2015

December 18,2015

January 29,2016

10 weeks Week ofFebruary 8, 2016

MP 3 February 1,2016

March 11,2016

April 15,2016

9 weeks Week ofApril 25, 2016

MP 4 April 18,2016

May 20,2016

June 23,2016

10 weeks Last Day of SchoolJune 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.”

5

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)

6

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.

7

New York State P-12 Common Core Learning Standards forMathematics

Mathematics - Grade 4: Introduction

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency withmulti-digit multiplication, and developing understanding of dividing to find quotients involving multi-digitdividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with likedenominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can beanalyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular anglemeasures, and symmetry.

1. Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbersin each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, areamodels), place value, and properties of operations, in particular the distributive property, as they develop,discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit wholenumbers. Depending on the numbers and the context, they select and accurately apply appropriate methods toestimate or mentally calculate products. They develop fluency with efficient procedures for multiplying wholenumbers; understand and explain why the procedures work based on place value and properties of operations;and use them to solve problems. Students apply their understanding of models for division, place value,properties of operations, and the relationship of division to multiplication as they develop, discuss, and useefficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They selectand accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remaindersbased upon the context.

2. Students develop understanding of fraction equivalence and operations with fractions. They recognize that twodifferent fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizingequivalent fractions. Students extend previous understandings about how fractions are built from unit fractions,composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning offractions and the meaning of multiplication to multiply a fraction by a whole number.

3. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, andanalyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensionalobjects and the use of them to solve problems involving symmetry.

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.

8

Grade 4 Overview

Operations and Algebraic Thinking• Use the four operations with whole numbers tosolve problems.• Gain familiarity with factors and multiples.• Generate and analyze patterns.

Number and Operations in Base Ten• Generalize place value understanding for multidigitwhole numbers.• Use place value understanding and properties ofoperations to perform multi-digit arithmetic.

Number and Operations—Fractions• Extend understanding of fraction equivalenceand ordering.• Build fractions from unit fractions by applyingand extending previous understandings ofoperations on whole numbers.• Understand decimal notation for fractions, andcompare decimal fractions.

Measurement and Data• Solve problems involving measurement andconversion of measurements from a larger unit toa smaller unit.• Represent and interpret data.• Geometric measurement: understand concepts ofangle and measure angles.

Geometry• Draw and identify lines and angles, and classifyshapes by properties of their lines and angles.

Operations & Algebraic Thinking 4.OA

Use the four operations with whole numbers to solve problems.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as

many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons asmultiplication equations.

2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings andequations with a symbol for the unknown number to represent the problem, distinguishing multiplicativecomparison from additive comparison.1

3. Solve multistep word problems posed with whole numbers and having whole-number answers using the fouroperations, including problems in which remainders must be interpreted. Represent these problems usingequations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mentalcomputation and estimation strategies including rounding.

Gain familiarity with factors and multiples.4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of

each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Generate and analyze patterns.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were

not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms inthe resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explaininformally why the numbers will continue to alternate in this way.

_________________1 See Glossary, Table 2.

9

Number & Operations in Base Ten¹ 4.NBT

Generalize place value understanding for multi-digit whole numbers.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the

place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols torecord the results of comparisons.

3. Use place value understanding to round multi-digit whole numbers to any place.

Use place value understanding and properties of operations to perform multi-digit arithmetic.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers,

using strategies based on place value and the properties of operations. Illustrate and explain the calculation byusing equations, rectangular arrays, and/or area models.

6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, usingstrategies based on place value, the properties of operations, and/or the relationship between multiplication anddivision. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

_________________1Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000

Number & Operations—Fractions¹ 4.NF

Extend understanding of fraction equivalence and ordering.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with

attention to how the number and size of the parts differ even though the two fractions themselves are the samesize. Use this principle to recognize and generate equivalent fractions.

2. Compare two fractions with different numerators and different denominators, e.g., by creating commondenominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisonsare valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols>, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit fractions by applying and extending previous understandings of operations onwhole numbers.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the samewhole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recordingeach decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with anequivalent fraction, and/or by using properties of operations and the relationship between addition andsubtraction.

d. Solve word problems involving addition and subtraction of fractions referring to the same whole andhaving like denominators, e.g., by using visual fraction models and equations to represent the problem.

4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as

the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a

whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing thisproduct as 6/5. (In general, n × (a/b) = (n × a)/b.)

10

c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visualfraction models and equations to represent the problem. For example, if each person at a party will eat 3/8of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will beneeded? Between what two whole numbers does your answer lie?

Understand decimal notation for fractions, and compare decimal fractions.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique

to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add3/10 + 4/100 = 34/100.

6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describea length as 0.62 meters; locate 0.62 on a number line diagram.

7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid onlywhen the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <,and justify the conclusions, e.g., by using a visual model.

_________________1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.2 Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general.But addition and subtraction with unlike denominators in general is not a requirement at this grade.

Measurement & Data 4.MD

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml;

hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of asmaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times aslong as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listingthe number pairs (1, 12), (2, 24), (3, 36), ...

2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses ofobjects, and money, including problems involving simple fractions or decimals, and problems that requireexpressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantitiesusing diagrams such as number line diagrams that feature a measurement scale.

3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example,find the width of a rectangular room given the area of the flooring and the length, by viewing the area formulaas a multiplication equation with an unknown factor.

Represent and interpret data.4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems

involving addition and subtraction of fractions by using information presented in line plots. For example, from aline plot find and interpret the difference in length between the longest and shortest specimens in an insectcollection.

Geometric measurement: understand concepts of angle and measure angles.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and

understand concepts of angle measurement:a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by

considering the fraction of the circular arc between the points where the two rays intersect the circle. Anangle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle

measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems tofind unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with asymbol for the unknown angle measure.

11

Geometry 4.G

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

Identify these in two-dimensional figures.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the

presence or absence of angles of a specified size. Recognize right triangles as a category, and identify righttriangles.

3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can befolded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

12

Grade 4 Cluster Emphases for Instruction

Cluster Emphases for Instruction on the 2013-14 Grade 4 Common Core Mathematics Testand 2013-14 Local Measure

Cluster Emphasis Recommended InstructionalTime

Approximate Number of TestPoints

Major 65–75% 70–80%

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

CCLS Standard ContentEmphasis

Operations and Algebraic Thinking4.OA.1 Interpret a multiplication equation as a comparison. Represent verbal statements

of multiplicative comparisons as multiplication equations.Major

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison Major

4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in whichremainders must be interpreted. Represent these problems using equations with aletter standing for the unknown quantity. Assess the reasonableness of answersusing mental computation and estimation strategies including rounding.

Major

4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that awhole number is a multiple of each of its factors. Determine whether a givenwhole number in the range 1–100 is a multiple of a given one-digit number.Determine whether a given whole number in the range 1–100 is prime orcomposite.

Supporting

4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparentfeatures of the pattern that were not explicit in the rule itself.

Additional

Number and Operations in Base Ten4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten

times what it represents in the place to its rightMajor

4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, numbernames, and expanded form. Compare two multi-digit numbers based on meaningsof the digits in each place, using >, =, and <

Major

4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Major

4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm Major

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, andmultiply two two-digit numbers, using strategies based on place value and theproperties of operations. Illustrate and explain the calculation by using equations,rectangular arrays, and/or area models.

Major

4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends andone-digit divisors, using strategies based on place value, the properties ofoperations, and/or the relationship between multiplication and division. Illustrateand explain the calculation by using equations, rectangular arrays, and/or areamodels.

Major

Number and Operations--Fractions4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using

visual fraction models, with attention to how the number and size of the partsdiffer even though the two fractions themselves are the same size. Use thisprinciple to recognize and generate equivalent fractions.

Major

13

CCLS Standard ContentEmphasis

4.NF.2 Compare two fractions with different numerators and different denominators.Recognize that comparisons are valid only when the two fractions refer to thesame whole. Record the results of comparisons with symbols >, =, or <, andjustify the conclusions.

Major

4.NF.3 Understand a fraction a/b with a>1 as a sum of fractions 1/b. Major

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fractionby a whole number.

Major

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction withdenominator 100, and use this technique to add two fractions with respectivedenominators 10 and 100.

MajorPost

4.NF.6 Use decimal notation for fractions with denominators 10 or 100. Major Post

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognizethat comparisons are only valid when the two decimals refer to the same whole.Record the results of comparisons with the symbols >, =, or < and justify theconclusions

Major Post

Measurement and Data3.MD.4 Generate measurement data by measuring using rulers marked with halves and

fourths of an inch. Show the data by making a line plotSupporting

3.MD.8 Solve real world and mathematical problems involving perimeters of polygons Additional

4.MD.1 Know relative sizes of measurement units within one system of units includingkm, m, cm, kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system ofmeasurement, express measurements in a larger unit in terms of a smaller unit.Record measurement equivalents in a two-column table.

SupportingPost

4.MD.2 Use the four operations to solve word problems involving distances, intervals oftime, liquid volumes, masses of objects, and money, including problems involvingsimple fractions or decimals, and problems that require expressing measurementsgiven in a larger unit in terms of a smaller unit. Represent measurement quantitiesusing diagrams such as number line diagrams that feature a measurement scale.

SupportingPost

4.MD.3 Apply the area and perimeter formulas for rectangles in real world andmathematical problems

Supporting

4.MD.4 Make a line plot to display a data set of SupportingGeometry

3.G.1 Understand that shapes in different categories may share attributes and that theshared attributes can define a larger category.

Supporting

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as aunit fraction of the whole.

Supporting

4.G.1 Draw points, lines, line segments, rays, angles, and perpendicular and parallellines. Identify these in two-dimensional figures

Additional

4.G.2 Classify two-dimensional figures based on the presence or absence of parallel orperpendicular lines, or the presence or absence of angles of a specified size.Recognize right triangles as a category, and identify right triangles

Additional

4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across thefigure such that the figure can be folded along the line into matching parts.Identify line-symmetric figures and draw lines of symmetry.

Additional

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

14

MVCSD GRADE 4 MATHEMATICS PACING GUIDE

This guide using NYS Grade 4 Mathematics CCLS Modules was created to provide teachers with a time frame to complete theGrade 4 New York State Mathematics Curriculum.

Module Title Standards Days Month i-Ready Lessons

1Place Value, Rounding, and Algorithms

for Addition and Subtraction4.OA.3, 4.NBT.1, 4.NBT.2, 4.NBT.3,

4.NBT.425 Sept. 8 – Oct. 16

Topic A – 1; Topic B – 2;Topic C – 4; Topic D – 3;

Topic E – 3; Topic F – 9, 10

2Unit Conversions and Problem Solving

with Metric Measurement4.MD.1, 4.MD.2 7 Oct. 19 – Oct. 27 Topic A – 23; Topic B – 25

3 Multi-Digit Multiplication and Division4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4,

4.NBT.5, 4.NBT.6, 4.MD.337 Oct. 28 – Dec. 23

Topic A – 5, 26; Topic B – 11;Topic C – 11; Topic D – 6;Topic E – 12; Topic F – 7;

Topic G – 12; Topic H – 11

4 Angle Measure and Plane Figures4.MD.5, 4.MD.6, 4.MD.7, 4.G.1, 4.G.2,

4.G.319 Jan. 4 – Jan. 29

Topic A – 31; Topic B – 28,29; Topic C – 30; Topic D –

32, 33

5Fraction Equivalence, Ordering, and

Operations

4.OA.5, 4.NF.1, 4.NF.2, 4.NF.3a,4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4a,4.NF.4b, 4.NF.4c, 4.MD.2, 4.MD.4

40 Feb. 1 – Apr. 12

Topic A – 15; Topic B – 13;Topic C – 14; Topic D – 16;Topic E – 17; Topic F – 17;

Topic G – 18, 19, 27; Topic H– 8

NYSED GRADE 4 MATHEMATICS TEST: WEDNESDAY, APRIL 13 – FRIDAY, APRIL 15, 2016

6 Decimal Fractions 4.NF.5, 4.NF.6, 4.NF.7, 4.MD.2 25 Apr. 18 – May 23Topic A – 21; Topic B – 20;Topic C – 22; Topic D – 20;

Topic E – 24

7 Exploring Multiplication 4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5 21 May 24 – Jun. 22 Topic A – 23; Topic B – 25;Topic C – 25

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 4 includes a total of 149 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: 4.NBT.4 Add and subtract within 1,000,000

15


1Place Value, Rounding, andAlgorithms for Addition and

Subtraction

4.OA.3, 4.NBT.1, 4.NBT.2,4.NBT.3, 4.NBT.4

25 Sept. 8 – Oct. 16Topic A – 1; Topic B – 2; TopicC – 4; Topic D – 3; Topic E – 3;

Topic F – 9, 10

In this 25-day module of Grade 4, students extend their work with whole numbers. They begin with large numbers using familiar units (hundreds and thousands)and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart (4.NBT.1). Theyrecognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand,million, billion).

16

Standards Topics and Objectives Days

4.NBT.14.NBT.24.OA.1

A Place Value of Multi-Digit Whole NumbersLesson 1: Interpret a multiplication equation as a comparison.Lesson 2: Recognize a digit represents 10 times the value of what it represents in the place to its

right.Lesson 3: Name numbers within 1 million by building understanding of the place value chart and

placement of commas for naming base thousand units.Lesson 4: Read and write multi-digit numbers using base ten numerals, number names, and

expanded form.

4

4.NBT.2 B Comparing Multi-Digit Whole NumbersLesson 5: Compare numbers based on meanings of the digits, using >,<, or = to record the

comparison.Lesson 6: Find 1, 10, and 100 thousand more and less than a given number.

2

4.NBT.3 C Rounding Multi-Digit Whole NumbersLesson 7: Round multi-digit numbers to the thousands place using the vertical number line.Lesson 8: Round multi-digit numbers to any place using the vertical number line.Lesson 9: Use place value understanding to round multi-digit numbers to any place value.Lesson 10: Use place value understanding to round multi-digit numbers to any place value using real

world applications.

4

Mid-Module Assessment: Topics A–C (review content 1 day, assessment ½ day, return ½ day,remediation or further applications 1 day)

3

4.OA.34.NBT.44.NBT.14.NBT.2

D Multi-Digit Whole Number AdditionLesson 11: Use place value understanding to fluently add multi-digit whole numbers using the

standard addition algorithm and apply the algorithm to solve word problems using tapediagrams.

Lesson 12: Solve multi-step word problems using the standard addition algorithm modeled with tapediagrams and assess the reasonableness of answers using rounding.

2

4.OA.3 E Multi-Digit Whole Number Subtraction 4

17


4.NBT.44.NBT.14.NBT.2

Lesson 13: Use place value understanding to decompose to smaller units once using the standardsubtraction algorithm, and apply the algorithm to solve word problems using tapediagrams.

Lesson 14: Use place value understanding to decompose to smaller units up to 3 times using thestandard subtraction algorithm, and apply the algorithm to solve word problems usingtape diagrams.

Lesson 15: Use place value understanding to fluently decompose to smaller units multiple times inany place using the standard subtraction algorithm, and apply the algorithm to solve wordproblems using tape diagrams.

Lesson 16: Solve two-step word problems using the standard subtraction algorithm fluently modeledwith tape diagrams and assess the reasonableness of answers using rounding.

4.OA.34.NBT.14.NBT.24.NBT.4

F Addition and Subtraction Word ProblemsLesson 17: Solve additive compare word problems modeled with tape diagrams.Lesson 18: Solve multi-step word problems modeled with tape diagrams and assess the

reasonableness of answers using rounding.Lesson 19: Create and solve multi-step word problems from given tape diagrams and equations.

3

End-of-Module Assessment: Topics A through F (review content 1 day, assessment ½ day, return ½day, remediation or further application 1 day)

3

Total Number of Instructional Days 25

18


2Unit Conversions and Problem Solving

with Metric Measurement4.MD.1, 4.MD.2 7 Oct. 19 – Oct. 27 Topic A – 23; Topic B – 25

Students have become accustomed to thinking of 250 as 2 hundreds 5 tens, but the idea of a mixed unit shows up in many variedcontexts, such as 2 hr 5 min, $2.50, 2 km 5 m, 2’ 5”, 2 5/8 (hours and minutes, dollars and cents, kilometers and meters, feet andinches, ones and eighths). While the context and the units may vary greatly, there are many common threads present in any mixedunit calculation. Consider the connections and similarities between the following equalities:

2,437 2 thousands 437 ones = 2,437 ones2 km 437 m 2,437 m 2 kilometers 437 meters = 2,437 meters2 kg 437 g 2,437 g 2 kilograms 437 grams = 2,437 grams

2 L 437 mL 2,437 mL 2 liters 437 milliliters = 2,437 milliliters

In order to explore the process of working with mixed units, Module 2 focuses on length, mass, and capacity in the metric system,where place value serves as a natural guide for moving between larger and smaller units.

19


4.MD.14.MD.2

A Metric Unit ConversionsLesson 1: Express metric length measurements in terms of a smaller unit; model and solve

addition and subtraction word problems involving metric length.Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve

addition and subtraction word problems involving metric mass.Lesson 3: Express metric capacity measurements in terms of a smaller unit; model and solve

addition and subtraction word problems involving metric capacity.

3

4.MD.14.MD.2

B Application of Metric Unit ConversionsLesson 4: Know and relate metric units to place value units in order to express measurements

in different units.Lesson 5: Use addition and subtraction to solve multi-step word problems involving length,

mass, and capacity.

2

End-of-Module Assessment: Topics A–B (assessment ½ day, return ½ day, remediation or furtherapplications 1 day)

2


20


3 Multi-Digit Multiplication and Division4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4,

4.NBT.5, 4.NBT.6, 4.MD.337 Oct. 28 – Dec. 23

Topic A – 5, 26; Topic B – 11;Topic C – 11; Topic D – 6;Topic E – 12; Topic F – 7;

Topic G – 12; Topic H – 11

In this 37-day module, students use place value understanding and visual representations to solve multiplication and division problemswith multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends.

21


4.OA.14.OA.24.MD.34.OA.3

A Multiplicative Comparison Word ProblemsLesson 1: Investigate and use the formulas for area and perimeter of rectangles.Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter

formulas.Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi-step real

world problems.

3

4.NBT.54.OA.14.OA.2

4.NBT.1

B Multiplication by 10, 100, and 1,000Lesson 4: Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and

numerically.Lesson 5: Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns.Lesson 6: Multiply two-digit multiples of 10 by two-digit multiples of 10 with the area model.

3

4.NBT.54.OA.2

4.NBT.1

C Multiplication of up to Four Digits by Single-Digit NumbersLesson 7: Use place value disks to represent two-digit by one-digit multiplication.Lesson 8: Extend the use of place value disks to represent three- and four-digit by one-digit

multiplication.Lessons 9–10: Multiply three- and four-digit numbers by one-digit numbers applying the standard

algorithm.Lesson 11: Connect the area model and the partial products method to the standard algorithm.

4

4.OA.14.OA.24.OA.3

4.NBT.5

D Multiplication Word ProblemsLesson 12: Solve two-step word problems, including multiplicative comparison.Lesson 13: Use multiplication, addition, or subtraction to solve multi-step word problems.

2

22


4.NBT.64.OA.3

E Division of Tens and Ones with Successive RemaindersLesson 14 Solve division word problems with remainders.Lesson 15: Understand and solve division problems with a remainder using the array and area

models.Lesson 16: Understand and solve two-digit dividend division problems with a remainder in the ones

place by using number disks.Lesson 17: Represent and solve division problems requiring decomposing a remainder in the tens.Lesson 18: Find whole number quotients and remainders.Lesson 19: Explain remainders by using place value understanding and models.Lesson 20: Solve division problems without remainders using the area model.Lesson 21: Solve division problems with remainders using the area model.

8

4.OA.4 F Reasoning with DivisibilityLesson 22: Find factor pairs for numbers to 100 and use understanding of factors to define prime and

composite.Lesson 23: Use division and the associative property to test for factors and observe patterns.Lesson 24: Determine whether a whole number is a multiple of another number.Lesson 25: Explore properties of prime and composite numbers to 100 by using multiples.

4

4.OA.34.NBT.64.NBT.1

G Division of Thousands, Hundreds, Tens, and OnesLesson 26: Divide multiples of 10, 100, and 1,000 by single-digit numbers.Lesson 27: Represent and solve division problems with up to a three-digit dividend numerically and

with number disks requiring decomposing a remainder in the hundreds place.Lesson 28: Represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5

numerically.Lesson 29: Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5,

decomposing a remainder up to three times.Lesson 30: Solve division problems with a zero in the dividend or with a zero in the quotient.Lesson 31: Interpret division word problems as either number of groups unknown or group size

unknown.Lesson 32: Interpret and find whole number quotients and remainders to solve one-step division

word problems with larger divisors of 6, 7, 8, and 9.Lesson 33: Explain the connection of the area model of division to the long division algorithm for

8

23


three- and four-digit dividends.4.NBT.54.OA.34.MD.3

H Multiplication of Two-Digit by Two-Digit NumbersLesson 34: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart.Lesson 35: Multiply two-digit multiples of 10 by two-digit numbers using the area model.Lesson 36: Multiply two-digit by two-digit numbers using four partial products.Lessons 37–38: Transition from four partial products to the standard algorithm for two-digit by two-

digit multiplication.

4

End-of-Module Assessment: Topics A–H 1Total Number of Instructional Days 37

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

24


4 Angle Measure and Plane Figures4.MD.5, 4.MD.6, 4.MD.7, 4.G.1, 4.G.2,

4.G.319 Jan. 4 – Jan. 29

Topic A – 31; Topic B – 28,29; Topic C – 30; Topic D –

32, 33

This 19-day module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and definethese geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role intheir work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. Inthese problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning throughthe solving of an equation. This connection between the measurement tool and the numerical work lays an important foundation for success with middle schoolgeometry and algebra. Through decomposition and composition activities as well as an exploration of symmetry, students recognize specific attributes presentin two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures based on them.

25


4.G.1 A Lines and AnglesLesson 1: Identify and draw points, lines, line segments, rays, and angles and recognize them

in various contexts and familiar figures.Lesson 2: Use right angles to determine whether angles are equal to, greater than, or less than

right angles. Draw right, obtuse, and acute angles.Lesson 3: Identify, define, and draw perpendicular lines.Lesson 4: Identify, define, and draw parallel lines.

4

4.MD.54.MD.6

B Angle MeasurementLesson 5: Use a circular protractor to understand a 1-degree angle as 1/360 of a turn. Explore

benchmark angles using the protractor.Lesson 6: Use varied protractors to distinguish angle measure from length measurement.Lesson 7: Measure and draw angles. Sketch given angle measures and verify with a

protractor.Lesson 8: Identify and measure angles as turns and recognize them in various contexts.

4

Mid-Module Assessment: Topics A–B (assessment ½ day, return ½ day) 1

4.MD.7 C Problem Solving with the Addition of Angle MeasuresLesson 9: Decompose angles using pattern blocks.Lessons 10–11: Use the addition of adjacent angle measures to solve problems using a symbol

for the unknown angle measure.

3

4.G.14.G.24.G.3

D Two-Dimensional Figures and SymmetryLesson 12: Recognize lines of symmetry for given two-dimensional figures; identify line-

symmetric figures and draw lines of symmetry.Lesson 13: Analyze and classify triangles based on side length, angle measure, or both.Lesson 14: Define and construct triangles from given criteria. Explore symmetry in triangles.Lesson 15: Classify quadrilaterals based on parallel and perpendicular lines and the presence

or absence of angles of a specified size.Lesson 16: Reason about attributes to construct quadrilaterals on square or triangular grid

paper.

5

26


End-of-Module Assessment: Topics A–D (assessment ½ day, return ½ day, remediation or furtherapplication 1 day)

2


27


5Fraction Equivalence, Ordering, and

Operations

4.OA.5, 4.NF.1, 4.NF.2, 4.NF.3a,4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4a,4.NF.4b, 4.NF.4c, 4.MD.2, 4.MD.4

40 Feb. 1 – Apr. 12

Topic A – 15; Topic B – 13;Topic C – 14; Topic D – 16;Topic E – 17; Topic F – 17;

Topic G – 18, 19, 27; Topic H– 8

NYSED GRADE 4 MATHEMATICS TEST: WEDNESDAY, APRIL 13 – FRIDAY, APRIL 15, 2016

In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixednumbers. This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models. Benchmark fractions play animportant part in students’ ability to generalize and reason about relative fraction and mixed number sizes. Students then have the opportunity to apply what theyknow to be true for whole number operations to the new concepts of fraction and mixed number operations.

28


4.NF.3b4.NF.4a4.NF.3a

A Decomposition and Fraction EquivalenceLessons 1–2: Decompose fractions as a sum of unit fractions using tape diagrams.Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit

fraction using tape diagrams.Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.Lesson 5: Decompose unit fractions using area models to show equivalence.Lesson 6: Decompose fractions using area models to show equivalence.

6

4.NF.14.NF.3b

B Fraction Equivalence Using Multiplication and DivisionLessons 7–8: Use the area model and multiplication to show the equivalence of two fractions.Lessons 9–10: Use the area model and division to show the equivalence of two fractions.Lesson 11: Explain fraction equivalence using a tape diagram and the number line, and relate that to

the use of multiplication and division.

4

4.NF.2 C Fraction ComparisonLessons 12–13: Reason using benchmarks to compare two fractions on the number line.Lessons 14–15: Find common units or number of units to compare two fractions.

3

4.NF.3a4.NF.3d4.NF.14.MD.2

D Fraction Addition and SubtractionLesson 16: Use visual models to add and subtract two fractions with the same units.Lesson 17: Use visual models to add and subtract two fractions with the same units, including

subtracting from one whole.Lesson 18: Add and subtract more than two fractions.Lesson 19: Solve word problems involving addition and subtraction of fractions.Lessons 20–21: Use visual models to add two fractions with related units using the denominators 2, 3, 4,

5, 6, 8, 10, and 12.

6

Mid-Module Assessment: Topics A–D (assessment ½ day, return ½ day) 1

4.NF.14.NF.24.NF.3

E Extending Fraction Equivalence to Fractions Greater than 1Lesson 22: Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number

using decomposition and visual models.

6

29


4.NBT.64.NF.4a4.MD.4

Lesson 23: Add and multiply unit fractions to build fractions greater than 1 using visual models.Lessons 24–25: Decompose and compose fractions greater than 1 to express them in various forms.Lesson 26: Compare fractions greater than 1 by reasoning using benchmark fractions.Lesson 27: Compare fractions greater than 1 by creating common numerators or denominators.Lesson 28: Solve word problems with line plots.

4.NF.3c4.NF.3d4.MD.44.MD.2

F Addition and Subtraction of Fractions by DecompositionLesson 29: Estimate sums and differences using benchmark numbers.Lesson 30: Add a mixed number and a fraction.Lesson 31: Add mixed numbers.Lesson 32: Subtract a fraction from a mixed numberLesson 33: Subtract a mixed number from a mixed number.Lesson 34: Subtract mixed numbers.

6

4.NF.44.MD.44.OA.24.MD.2

G Repeated Addition of Fractions as MultiplicationLessons 35–36: Represent the multiplication of n times a/b as (n × a)/b using the associative property and

visual models.Lessons 37–38: Find the product of a whole number and a mixed number using the distributive property.Lesson 39: Solve multiplicative comparison word problems involving fractions.Lesson 40: Solve word problems involving the multiplication of a whole number and a fraction

including those involving line plots.

5

4.OA.5 H ExplorationLesson 41: Find and use a pattern to calculate the sum of all fractional parts between 0 and 1. Share

and critique peer strategies.

1

End-of-Module Assessment: Topics A–H (assessment ½ day, return ½ day, remediation or furtherapplications 1 day)

2


30


6 Decimal Fractions 4.NF.5, 4.NF.6, 4.NF.7, 4.MD.2 25 Apr. 18 – May 23Topic A – 21; Topic B – 20;Topic C – 22; Topic D – 20;

Topic E – 24

This 25-day module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity inboth fraction and decimal forms. Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimalnumbers, building a solid foundation for Grade 5 work with decimal operations. Previously referred to as whole numbers, all numbers written in the base tennumber system with place value units that are powers of 10 are henceforth referred to as decimal numbers, a set which now includes tenths and hundredths, e.g.1, 15, 248, 0.3, 3.02, and 24.345.

31


4.NF.64.NBT.14.MD.1

A Exploration of TenthsLesson 1: Use metric measurement to model the decomposition of one whole into tenths.Lesson 2: Use metric measurement and area models to represent tenths as fractions greater than 1 anddecimal numbers.Lesson 3: Represent mixed numbers with units of tens, ones, and tenths with number disks, on thenumber line, and in expanded form.

4

4.NF.54.NF.6

4.NBT.14.NF.14.NF.74.MD.1

B Tenths and HundredthsLesson 4: Use meters to model the decomposition of one whole into hundredths. Represent and counthundredths.Lesson 5: Model the equivalence of tenths and hundredths using the area model and number disks.Lesson 6: Use the area model and number line to represent mixed numbers with units of ones, tenths,and hundredths in fraction and decimal forms.Lesson 7: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expandedform and on the place value chart.Lesson 8: Use understanding of fraction equivalence to investigate decimal numbers on the place valuechart expressed in different units.

6

Mid-Module Assessment: Topics A–B (assessment 1 day, return ½ day, remediation or furtherapplications ½ day)

2

4.NF.74.MD.14.MD.2

C Decimal ComparisonLesson 9: Use the place value chart and metric measurement to compare decimals and answercomparison questions.Lesson 10: Use area models and the number line to compare decimal numbers, and record comparisonsusing <, >, and =.Lesson 11: Compare and order mixed numbers in various forms.

4

4.NF.54.NF.64.NF.3c

D Addition with Tenths and HundredthsLesson 12: Apply understanding of fraction equivalence to add tenths and hundredths.Lesson 13: Add decimal numbers by converting to fraction form.

4

32


4.MD.1 Lesson 14: Solve word problems involving the addition of measurements in decimal form.

4.MD.24.NF.54.NF.6

E Money Amounts as Decimal NumbersLesson 15: Express money amounts given in various forms as decimal numbers.Lesson 16: Solve word problems involving money.

3

End-of-Module Assessment: Topics A–E (assessment 1 day, return ½ day, remediation or furtherapplications ½ day)

2


33


7 Exploring Multiplication 4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5 21 May 24 – Jun. 22 Topic A – 23; Topic B – 25;Topic C – 25

In this module, students build their competencies in measurement as they relate multiplication to the conversion of measurement units.Throughout the module, students will explore multiple strategies for solving measurement problems involving unit conversion.

34


4.OA.14.OA.24.MD.14.NBT.54.MD.2

A Measurement Conversion TablesLessons 1–2: Create conversion tables for length, weight, and capacity units using measurementtools, and use the tables to solve problems.Lesson 3: Create conversion tables for units of time, and use the tables to solve problems.Lesson 4: Solve multiplicative comparison word problems using measurement conversion tables.Lesson 5: Share and critique peer strategies.

5

4.OA.24.OA.34.MD.14.MD.24.NBT.54.NBT.6

B Problem Solving with MeasurementLesson 6: Solve Problems involving mixed units of capacity.Lesson 7: Solve problems involving mixed units of length.Lesson 8: Solve problems involving mixed units of weight.Lesson 9: Solve problem involving mixed units of time.Lessons 10–11: Solve multi-step measurement word problems.

6

4.OA.34.MD.14.MD.24.NBT.54.NBT.6

C Investigation of Measurements Expressed as Mixed NumbersLessons 12–13: Use measurement tools to convert mixed number measurements to smaller units.Lesson 14: Solve multi-step word problems involving converting mixed number measurements to asingle unit.

3

End-of-Module Assessment: Topics A–C (assessment 1 day, ½ day return, remediation or further application ½ day) 2

Lessons 15–16: Create and determine the area of composite figures.Lesson 17: Practice and solidify Grade 4 fluency.Lesson 18: Practice and solidify Grade 4 vocabulary.

5


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.

36

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:

37

ELEMENTARY MATHEMATICS GRADING POLICY

This 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.”

38

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:

39

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: ____________

40

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

41

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.

CCLS Mathematics Grade 4 Curriculum...

Documents

Transcript of CCLS Mathematics Grade 4 Curriculum...