CCLS Mathematics Grade 1 Curriculum Guidemvcsd.sharpschool.net/UserFiles/Servers/Server_87286/File/Satish... · mount vernon city school district ccls mathematics grade 1 curriculum

MOUNT VERNON CITY SCHOOL DISTRICT

CCLS MathematicsGrade 1

Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GRADE 1MATHEMATICS 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 1 COMMON CORE LEARNING STANDARDS ……………..7

VIII. MVCSD CCLS GRADE 1 MATHEMATICS PACING GUIDE …………....13

IX. WORD WALL …………... 31

X. SETUP OF A MATHEMATICS CLASSROOM …………... 32

XI. ELEMENTARY GRADING POLICY …………... 33

XII. SAMPLE NOTEBOOK RUBRIC …………... 34

XIII. CLASSROOM AESTHETICS …………... 35

XIV. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 36

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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.”

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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 1: Introduction

In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition,subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole numberrelationships and place value, including grouping in tens and ones; (3) developing understanding of linearmeasurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composingand decomposing geometric shapes.

1. Students develop strategies for adding and subtracting whole numbers based on their prior work with smallnumbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected toform lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning forthe operations of addition and subtraction, and to develop strategies to solve arithmetic problems with theseoperations. Students understand connections between counting and addition and subtraction (e.g., adding two is thesame as counting on two). They use properties of addition to add whole numbers and to create and use increasinglysophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problemswithin 20. By comparing a variety of solution strategies, children build their understanding of the relationshipbetween addition and subtraction.

2. Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtractmultiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problemsinvolving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especiallyrecognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense,they understand the order of the counting numbers and their relative magnitudes.

3. Students develop an understanding of the meaning and processes of measurement, including underlying conceptssuch as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivityprinciple for indirect measurement.1

4. Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral)and build understanding of part-whole relationships as well as the properties of the original and composite shapes.As they combine shapes, they recognize them from different perspectives and orientations, describe their geometricattributes, and determine how they are alike and different, to develop the background for measurement and for initialunderstandings of properties such as congruence and symmetry.

_________________1 Students should apply the principle of transitivity of measurement to make indirect comparisons, but they need not use thistechnical term.

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.

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Grade 1 Overview

Operations and Algebraic Thinking• Represent and solve problems involvingaddition and subtraction.• Understand and apply properties of operationsand the relationship between addition andsubtraction.• Add and subtract within 20.• Work with addition and subtraction equations.

Number and Operations in Base Ten• Extend the counting sequence.• Understand place value.• Use place value understanding and propertiesof operations to add and subtract.

Measurement and Data• Measure lengths indirectly and by iteratinglength units.• Tell and write time.• Represent and interpret data.

Geometry• Reason with shapes and their attributes.

Operations & Algebraic Thinking 1.OA

Represent and solve problems involving addition and subtraction.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from,

putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings,and equations with a symbol for the unknown number to represent the problem.1

2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g.,by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and subtraction.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8

= 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can beadded to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the numberthat makes 10 when added to 8. Add and subtract within 20.

Add and subtract within 20.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as

counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13– 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4= 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creatingthe known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are

true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2= 2 + 5, 4 + 1 = 5 + 2.

8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Forexample, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 =_ – 3, 6 + 6 = _.

_________________1 See Glossary, Table 1.2 Students need not use formal terms for these properties.

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Number & Operations in Base Ten 1.NBT

Extend the counting sequence.1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a

number of objects with a written numeral.

Understand place value.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the

following as special cases:a. 10 can be thought of as a bundle of ten ones — called a “ten.”b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine

ones.c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine

tens (and 0 ones).3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of

comparisons with the symbols >, =, and <.

Use place value understanding and properties of operations to add and subtract.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number

and a multiple of 10, using concrete models or drawings and strategies based on place value, properties ofoperations, and/or the relationship between addition and subtraction; relate the strategy to a written method andexplain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones;and sometimes it is necessary to compose a ten.

5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explainthe reasoning used.

6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zerodifferences), using concrete models or drawings and strategies based on place value, properties of operations,and/or the relationship between addition and subtraction; relate the strategy to a written method and explain thereasoning used.

Measurement & Data 1.MD

Measure lengths indirectly and by iterating length units.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object

(the length unit) end to end; understand that the length measurement of an object is the number of same-sizelength units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spannedby a whole number of length units with no gaps or overlaps.

Tell and write time and money.3. Tell and write time in hours and half-hours using analog and digital clocks.

Recognize and identify coins, their names, and their value.

Represent and interpret data.4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total

number of data points, how many in each category, and how many more or less are in one category than inanother.

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Geometry 1.G

Reason with shapes and their attributes.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes

(e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or

three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) tocreate a composite shape, and compose new shapes from the composite shape.1

3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves,fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, orfour of the shares. Understand for these examples that decomposing into more equal shares creates smallershares.

_________________1 Students do not need to learn formal names such as “right rectangular prism.”

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Grade 1 Cluster Emphases for Instruction

Cluster Emphases for InstructionCluster Emphasis Recommended Instructional

TimeApproximate Number of Test

PointsMajor 65–75% 70–80%

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

CCLS Standard ContentEmphasis

Operations & Algebraic Thinking1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of

adding to, taking from, putting together, taking apart, and comparing, with unknowns inall positions, e.g., by using objects, drawings, and equations with a symbol for theunknown number to represent the problem.

Major

1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is lessthan or equal to 20, e.g., by using objects, drawings, and equations with a symbol for theunknown number to represent the problem.

Major

1.OA.3 Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 +6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.(Associative property of addition.)

Major

1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 byfinding the number that makes 10 when added to 8. Add and subtract within 20.

Major

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Major

1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using therelationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 bycreating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Major

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving additionand subtraction are true or false. For example, which of the following equations are trueand which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Major

1.OA.8 Determine the unknown whole number in an addition or subtraction equation relatingthree whole numbers. For example, determine the unknown number that makes theequation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.

Major

Number & Operations in Base Ten1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals

and represent a number of objects with a written numeral.Major

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a “ten.”b. The numbers from 11 to 19 are composed of a ten and one, two, three, four,

five, six, seven, eight, or nine ones.c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four,

five, six, seven, eight, or nine tens (and 0 ones).

Major

1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits,recording the results of comparisons with the symbols >, =, and <.

Major

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CCLS Standard ContentEmphasis

1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, andadding a two-digit number and a multiple of 10, using concrete models or drawings andstrategies based on place value, properties of operations, and/or the relationship betweenaddition and subtraction; relate the strategy to a written method and explain the reasoningused. Understand that in adding two-digit numbers, one adds tens and tens, ones andones; and sometimes it is necessary to compose a ten.

Major

1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, withouthaving to count; explain the reasoning used.

Major

1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90(positive or zero differences), using concrete models or drawings and strategies based onplace value, properties of operations, and/or the relationship between addition andsubtraction; relate the strategy to a written method and explain the reasoning used.

Major

Measurement & Data1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a

third object.Major

1.MD.2 Express the length of an object as a whole number of length units, by laying multiplecopies of a shorter object (the length unit) end to end; understand that the lengthmeasurement of an object is the number of same-size length units that span it with nogaps or overlaps. Limit to contexts where the object being measured is spanned by awhole number of length units with no gaps or overlaps.

Major

1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.Recognize and identify coins, their names, and their value.

Additional

1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answerquestions about the total number of data points, how many in each category, and howmany more or less are in one category than in another.

Additional

Geometry1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus

non-defining attributes (e.g., color, orientation, overall size); build and draw shapes topossess defining attributes.

Supporting

1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles,and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, rightcircular cones, and right circular cylinders) to create a composite shape, and composenew shapes from the composite shape.

Supporting

1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares usingthe words halves, fourths, and quarters, and use the phrases half of, fourth of, andquarter of. Describe the whole as two of, or four of the shares. Understand for theseexamples that decomposing into more equal shares creates smaller shares.

Supporting

= Standards recommended for greater emphasis

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MATHEMATICS GRADE 1 PACING GUIDEThis guide using NYS Grade 1 Mathematics CCLS Modules was created to provide teachers with a time frame to complete the

Grade 1 New York State Mathematics Curriculum.

Module Title Standards Days Month i-Ready Lessons

1 Sums and Differences to 101.OA.1, 1.OA.3, 1.OA.4, 1.OA.5, 1.OA.6, 1.OA.7,

1.OA.845

Sept. 8 –Nov. 16

Topic A – 7; Topic B – 1; Topic C– 3; Topic D – 2; Topic E – 10;

Topic F – 6; Topic G – 4; Topic H– 3; Topic I – 8, 9; Topic J – 11

2Introduction to Place Value

Through Addition and SubtractionWithin 20

1.OA.1, 1.OA.2, 1.OA.3, 1.OA.4, 1.OA.6,1.NBT.2

35Nov. 17 –

Jan. 15Topic A – 14, 15; Topic B – 16;

Topic C – 13; Topic D – 12

3Ordering and Comparing Length

Measurements as Numbers1.OA.1, 1.MD.1, 1.MD.2, 1.MD.4 15

Jan. 19 –Feb. 8

Topic A – 31, 32; Topic B – 33;Topic C – 33; Topic D – 29, 30

4Place Value, Comparison,

Addition and Subtraction to 401.OA.1, 1.NBT.1, 1.NBT.2, 1.NBT.3, 1.NBT.4,

1.NBT.5, 1.NBT.635

Feb. 9 –Apr. 12

Topic A – 17, 19, 21; Topic B –22; Topic C – 20, 23; Topic D –

24; Topic E – 3;Topic F – 25

5Identifying, Composing, and

Partitioning Shapes1.MD.3, 1.G.1, 1.G.2, 1.G.3 15

Apr. 13 –May 4

Topic A – 26; Topic B – 27; TopicC – 28; Topic D – 34

6Place Value, Comparison,

Addition and Subtraction to 1001.NBT.1, 1.NBT.2, 1.NBT.3, 1.NBT.4, 1.NBT.5,

1.NBT.6, 1.MD.334

May 5 – Jun22

Topic A – 5; Topic B – 18; TopicC – 23; Topic D – 24, 25; Topic E

– 35; Topic F – 3, 5

Red – End of Module Assessment PeriodGreen – Priority Standards

Note that the curriculum assumes that each school day includes 70-75 minutes of math: one hour on the day’s Session, and 10-15minutes on Fluency activities. Designed to fit within the calendar of a typical school year, grade 1 includes a total of 153 lessons.This provides some leeway for going further with particular ideas and/or accommodating local circumstances. Although pacing willvary somewhat in response to variations in school calendars, needs of students, your school's years of experience with thecurriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from the waymathematical ideas are introduced, developed, and revisited across the year.

Required Fluency: 1.OA.6 Add and subtract within 10.

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Module Title Standards Days Month

1 Sums and Differences to 101.OA.1, 1.OA.3, 1.OA.4, 1.OA.5, 1.OA.6,

1.OA.7, 1.OA.845 Sept. 8 – Nov. 16

In this first module of Grade 1, students make significant progress towards fluency with addition and subtraction of numbers to 10(1.OA.6) as they are presented with opportunities intended to advance them from counting all to counting on which leads manystudents then to decomposing and composing addends and total amounts. In Kindergarten, students have achieved fluency withaddition and subtraction facts to 5. This means they can decompose 5 into 4 and 1, 3 and 2, and 5 and 0. They can do this withoutcounting all. They perceive the 3 and 2 embedded within the 5.

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Standards Topics and Objectives Days

1.OA.6 A Embedded Numbers and DecompositionsLesson 1: Analyze and describe embedded numbers (to 10) using 5-groups and number bonds.Lesson 2: Reason about embedded numbers in varied configurations using number bonds.Lesson 3: See and describe numbers of objects using 1 more within 5-group configurations.

3

1.OA.11.OA.51.OA.6

B Counting On from Embedded NumbersLesson 4–5: Represent put together situations with number bonds. Count on from one embedded numberor part to totals of 6 and 7 and generate all addition expressions for each total.Lesson 6–7: Represent put together situations with number bonds. Count on from one embedded numberor part to totals of 8 and 9 and generate all expressions for each total.Lesson 8: Represent all the number pairs of 10 as number bond diagrams from a given scenario andgenerate all expressions equal to 10.

5

1.OA.11.OA.61.OA.5

C Addition Word ProblemsLesson 9: Solve add to with result unknown and put together with result unknown math stories by drawing,writing equations, and making statements of the solution.Lesson 10: Solve put together with result unknown math stories by drawing and using 5-group cards.Lesson 11: Solve add to with change unknown math stories as a context for counting on by drawing, writingequations, and making statements of the solution.Lesson 12: Solve add to with change unknown math stories using 5-group cards.Lesson 13: Tell put together with result unknown, add to with result unknown, and add to with changeunknown stories from equations.

5

1.OA.51.OA.81.OA.6

D Strategies for Counting OnLesson 14–15: Count on up to 3 more using numeral and 5-group cards and fingers to track the change.Lesson 16: Count on to find the unknown part in missing addend equations such as 6 + __ = 9. Answer,“How many more to make 6, 7, 8, 9, and 10?”

3

1.OA.31.OA.7

E The Commutative Property of Addition and the Equal SignLesson 17–18: Understand the meaning of the equal sign by pairing equivalent expressions and constructingtrue number sentences.Lesson 19: Represent the same story scenario with addends repositioned (the commutative property).Lesson 20: Apply the commutative property to count on from a larger addend.

4

16


1.OA.31.OA.6

F Development of Addition Fluency Within 10Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards.Lesson22: Look for and make use of repeated reasoning on the addition chart by solving and analyzingproblems with common addends.Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problemswith the same total.Lesson 24: Practice to build fluency with facts to 10.

4

Mid-Module Assessment: Topics A–F (assessment 1 day, return 1 day, remediation or further applications1 day)

3

1.OA.11.OA.41.OA.5

G Subtraction as an Unknown Addend ProblemLesson 25: Solve add to with change unknown math stories with addition and relate to subtraction. Modelwith materials and write corresponding number sentences.Lesson 26–27: Count on using the number path to find an unknown part.

3

1.OA.11.OA.41.OA.51.OA.8

H Subtraction Word ProblemsLesson 28: Solve take from with result unknown math stories with math drawings, true number sentences andstatements, using horizontal marks to cross off what is taken away.Lesson 29: Solve take apart with addend unknown math stories with math drawings, equations andstatements, circling the known part to find the unknown.Lesson 30: Solve add to with change unknown math stories with drawings, relating addition and subtraction.Lesson 31: Solve take from with change unknown math stories with drawings.Lesson 32: Solve put together/take apart with addend unknown math stories.

5

1.OA.51.OA.61.OA.4

I Decomposition Strategies for SubtractionLesson 33: Model 0 less and 1 less pictorially and as subtraction number sentences.Lesson 34: Model n – n and n – (n – 1) pictorially and as subtraction sentences.Lesson 35: Relate subtraction facts involving fives and doubles to corresponding decompositions.Lesson 36: Relate subtraction from ten to corresponding decompositions.Lesson 37: Relate subtraction from nine to corresponding decompositions.

5

1.OA.6 J Development of Subtraction Fluency Within 10 2

17


Lesson 38: Look for and make use of repeated reasoning and structure using the addition chart to solvesubtraction problems.Lesson 39: Analyze the addition chart to create sets of related addition and subtraction facts.

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

3

Total Number of Instructional Days 45

18


2Introduction to Place Value ThroughAddition and Subtraction Within 20

1.OA.1, 1.OA.2, 1.OA.3, 1.OA.4, 1.OA.6,1.NBT.2

35 Nov. 17 – Jan. 15

Module 2 serves as a bridge from problem solving within 10 to work within 100 as students begin to solve addition and subtractionproblems involving teen numbers (1.NBT.2ab). In Module 1, students were encouraged to move beyond the Level 1 strategy ofcounting all to the more efficient counting on. Now they go beyond Level 2 to learn Level 3 decomposition and compositionstrategies, informally called make ten or take from ten.

19


1.OA.11.OA.21.OA.31.OA.6

A Counting On or Making Ten to Solve Result Unknown and Total Unknown ProblemsLesson 1: Solve word problems with three addends, two of which make ten.Lesson 2: Use the associative and commutative properties to make ten with three addends.Lessons 3–4: Make ten when one addend is 9.Lesson 5: Compare efficiency of counting on and making ten when one addend is 9.Lesson 6: Use the commutative property to make ten.Lessons 7–8: Make ten when one addend is 8.Lesson 9: Compare efficiency of counting on and making ten when one addend is 8.Lesson 10: Solve problems with addends of 7, 8, and 9.Lesson 11: Share and critique peer solution strategies for put together with total unknown word problems.

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Mid-Module Assessment: Topic A (assessment 1 day, return 1 day, remediation or further applications 1day)

3

1.OA.11.OA.31.OA.41.OA.61.OA.51.OA.7

B Counting On or Taking from Ten to Solve Result Unknown and Total Unknown ProblemsLessons 12–13: Solve word problems with subtraction of 9 from 10.Lessons 14–15: Model subtraction of 9 from teen numbers.Lesson 16: Relate counting on to making ten and taking from ten.Lessons 17–18: Model subtraction of 8 from teen numbers.Lesson 19: Compare efficiency of counting on and taking from ten.Lesson 20: Subtract 7, 8, and 9 from teen numbers.Lesson 21: Share and critique peer solution strategies for take from with result unknown and take apartwith addend unknown word problems from the teens.

10

1.OA.11.OA.31.OA.41.OA.61.OA.51.OA.71.OA.8

C Strategies for Solving Change or Addend Unknown ProblemsLesson 22: Solve put together/take apart with addend unknown word problems and relate counting on tothe take from ten strategy.Lesson 23: Solve add to with change unknown problems, relating varied addition and subtractionstrategies.Lesson 24: Strategize to solve take from with change unknown problems.Lesson 25: Strategize and apply understanding of the equal sign to solve equivalent expressions.

4

20

1.OA.11.NBT.2a1.NBT.2b1.NBT.5

D Varied Problems with Decompositions of Teen Numbers as 1 Ten and Some OnesLesson 26: Identify 1 ten as a unit by renaming representations of 10.Lesson 27: Solve addition and subtraction problems decomposing and composing teen numbers as 1 tenand some ones.Lesson 28: Solve addition problems using ten as a unit, and write two-step solutions.Lesson 29: Solve subtraction problems using ten as a unit, and write two-step solutions.

4

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

3


21


3Ordering and Comparing Length

Measurements as Numbers1.OA.1, 1.MD.1, 1.MD.2, 1.MD.4 15 Jan. 19 – Feb. 8

22


1.MD.1 A Indirect Comparison in Length MeasurementLesson 1: Compare length directly and consider importance of aligning endpoints.Lesson 2: Compare length using indirect comparison by finding objects longer than, shorter than,

and equal in length to that of a string.Lesson 3: Order three lengths using indirect comparison.

3

1.MD.11.MD.2

B Standard Length UnitsLesson 4: Express the length of an object using centimeter cubes as length units to measure with no

gaps or overlaps.Lesson 5: Rename and measure with centimeter cubes, using their standard unit name of centimeters.Lesson 6: Order, measure, and compare the length of objects before and after measuring with

centimeter cubes, solving compare with difference unknown word problems.

3

1.OA.11.MD.2

C Non-Standard and Standard Length UnitsLesson 7: Measure the same objects from Topic B with different non-standard units simultaneously to

see the need to measure with a consistent unit.Lesson 8: Understand the need to use the same units when comparing measurements with others.Lesson 9: Answer compare with difference unknown problems about lengths of two different objects

measured in centimeters.

3

1.OA.11.MD.21.MD.4

D Data InterpretationLessons 10–11: Collect, sort, and organize data, then ask and answer questions about the number of data

points.Lessons 12–13: Ask and answer varied word problem types about a data set with three categories.

4

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

2


23


4Place Value, Comparison, Addition and

Subtraction to 401.OA.1, 1.NBT.1, 1.NBT.2, 1.NBT.3, 1.NBT.4,

1.NBT.5, 1.NBT.635 Feb. 9 – Apr. 12

Module 4 builds upon Module 2’s work with place value within 20, now focusing on the role of place value in the addition and subtraction of numbers to 40.

24


1.NBT.11.NBT.21.NBT.5

A Tens and OnesLesson 1: Compare the efficiency of counting by ones and counting by tens.Lesson 2: Use the place value chart to record and name tens and ones within a two-digit number.Lesson 3: Interpret two-digit numbers as either tens and some ones or as all ones.Lesson 4: Write and interpret two-digit numbers as addition sentences that combine tens and

ones.Lesson 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit number.Lesson 6: Use dimes and pennies as representations of tens and ones.

6


B Comparison of Pairs of Two-Digit NumbersLesson 7: Compare two quantities, and identify the greater or lesser of the two given numerals.Lesson 8: Compare quantities and numerals from left to right.Lessons 9–10: Use the symbols >, =, and < to compare quantities and numerals.

4


C Addition and Subtraction of TensLesson 11: Add and subtract tens from a multiple of 10.Lesson 12: Add tens to a two-digit number.

2

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

3

1.NBT.4 D Addition of Tens or Ones to a Two-Digit NumberLessons 13–14: Use counting on and the make ten strategy when adding across a ten.Lesson 15: Use single-digit sums to support solutions for analogous sums to 40.Lessons 16–17: Add ones and ones or tens and tens.Lesson 18: Share and critique peer strategies for adding two-digit numbers.

6

1.OA.1 E Varied Problem Types Within 20Lesson 19: Use tape diagrams as representations to solve put together/take apart with total

unknown and add to with result unknown word problems.Lessons 20–21: Recognize and make use of part–whole relationships within tape diagrams when

solving a variety of problem types.

4

25

Lesson 22: Write word problems of varied types.

1.NBT.4 F Addition of Tens and Ones to a Two-Digit NumberLesson 23: Interpret two-digit numbers as tens and ones including cases with more than 9 ones.Lessons 24–25: Add a pair of two-digit numbers when the ones digits have a sum less than or equal

to 10.Lessons 26–27: Add a pair of two-digit numbers when the ones digits have a sum greater than 10.Lessons 28–29: Add a pair of two-digit numbers with varied sums in the ones.

7

End-of-Module Assessment: Topics D–F (assessment 1 day, return 1 day, remediation or furtherapplications 1 day)

3


26


5Identifying, Composing, and Partitioning

Shapes1.MD.3, 1.G.1, 1.G.2, 1.G.3 15 Apr. 13 – May 4

Throughout the year, students have explored part–whole relationships in many ways, such as their work with number bonds, tapediagrams, and their relationship to addition and subtraction. In Module 5, students consider part–whole relationships through ageometric lens.

27


1.G.1 A Attributes of ShapesLesson 1: Classify shapes based on defining attributes using examples, variants, and non-examples.Lesson 2: Find and name two-dimensional shapes including trapezoid, rhombus, and a square as a specialrectangle, based on defining attributes of sides and corners.Lesson 3: Find and name three-dimensional shapes including cone and rectangular prism, based ondefining attributes of faces and points.

3

1.G.2 B Part–Whole Relationships Within Composite ShapesLesson 4: Create composite shapes from two-dimensional shapes.Lesson 5: Compose a new shape from composite shapes.Lesson 6: Create a composite shape from three-dimensional shapes and describe the composite shapeusing shape names and positions.

3

1.G.3 C Halves and Quarters of Rectangles and CirclesLesson 7: Name and count shapes as parts of a whole, recognizing relative sizes of the parts.Lesson 8–9: Partition shapes and identify halves and quarters of circles and rectangles.

3

1.MD.31.G.3

D Application of Halves to Tell TimeLesson 10: Construct a paper clock by partitioning a circle and tell time to the hour.Lessons 11–13: Recognize halves within a circular clock face and tell time to the half hour.

4

End-of-Module Assessment: Topics A–D (assessment 1/2 day, return 1/2 day, remediation or furtherapplications 1 day)

2


28


6Place Value, Comparison, Addition and

Subtraction to 1001.NBT.1, 1.NBT.2, 1.NBT.3, 1.NBT.4,

1.NBT.5, 1.NBT.6, 1.MD.334 May 5 – Jun 22

29


1.OA.1 A Comparison Word ProblemsLesson 1: Solve compare with difference unknown problem types.Lesson 2: Solve compare with bigger or smaller unknown problem types.

2

1.NBT.11.NBT.2a1.NBT.2c1.NBT.31.NBT.5

B Numbers to 120Lesson 3: Use the place value chart to record and name tens and ones within a two-digit number up

to 100.Lesson 4: Write and interpret two-digit numbers to 100 as addition sentences that combine tens and

ones.Lesson 5: Identify 10 more, 10 less, 1 more, and 1 less than a two-digit number within 100.Lesson 6: Use the symbols >, =, and < to compare quantities and numerals to 100.Lesson 7: Count and write numbers to 120. Use Hide Zero cards to relate numbers 0 to 20 to 100

to 120.Lesson 8: Count to 120 in unit form using only tens and ones. Represent numbers to 120 as tens

and ones on the place value chart.Lesson 9: Represent up to 120 objects with a written numeral.

7

1.NBT.41.NBT.6

C Addition to 100 Using Place Value UnderstandingLesson 10: Add and subtract multiples of 10 from multiples of 10 to 100, including dimes.Lesson 11: Add a multiple of 10 to any two-digit number within 100.Lesson 12: Add a pair of two-digit numbers when the ones digits have a sum less than or equal to 10.Lessons 13–14: Add a pair of two-digit numbers when the ones digits have a sum greater than 10 using

decomposition.Lesson 15: Add a pair of two-digit numbers when the ones digits have a sum greater than 10 with

drawing. Record the total below.Lessons 16–17: Add a pair of two-digit numbers when the ones digits have a sum greater than 10 with

drawing. Record the new ten below.

8

30


1.NBT.4 D Varied Place Value Strategies for Addition to 100Lesson 18: Add a pair of two-digit numbers with varied sums in the ones, and compare results of

different recording methods.Lesson 19: Solve and share strategies for adding two-digit numbers with varied sums.

2

Mid-Module Assessment: Topics A–D (assessment 1 day, return and remediation or further applications1 day)

2

1.MD.3 E Coins and Their ValuesLesson 20: Identify pennies, nickels, and dimes by their image, name, or value. Decompose the

values of nickels and dimes using pennies and nickels.Lesson 21: Identify quarters by their image, name, or value. Decompose the value of a quarter using

pennies, nickels, and dimes.Lesson 22: Identify varied coins by their image, name, or value. Add one cent to the value of any

coin.Lesson 23: Count on using pennies from any single coin.Lesson 24: Use dimes and pennies as representations of numbers to 120.

5

1.OA.1 F Varied Problem Types Within 20Lessons 25–26: Solve compare with bigger or small unknown problem types.Lesson 27: Share and critique peer strategies for solving problems of varied types.

3

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

2

G Culminating ExperiencesLessons 28–29: Celebrate progress in fluency with adding and subtracting within 10 (and 20).

Organize engaging summer practice.Lessons 30: Create folder covers for work to be taken home illustrating the year’s learning.

3


31

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.

32

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:

33

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.”

34

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:

35

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: ____________

36

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

37

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 1 Curriculum Guidemvcsd.sharpschool.net/UserFiles/Servers/Server_87286/File/Satish... · mount vernon city school district ccls mathematics grade 1 curriculum