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Elementary Mathematics

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Grade 1 Module 1: Sums and Differences to 10
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In this first module of Grade 1, students make significant progress towards fluency with addition and subtraction of numbers to 10 as they are presented with opportunities intended to advance them from counting all to counting on which leads many students then to decomposing and composing addends and total amounts.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
05/11/2013
Grade 1 Module 2:  Introduction to Place Value Through Addition and Subtraction Within 20
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Module 2 serves as a bridge from students' prior work with problem solving within 10 to work within 100 as students begin to solve addition and subtraction problems involving teen numbers. Students go beyond the Level 2 strategies of counting on and counting back as they learn Level 3 strategies informally called "make ten" or "take from ten."

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/05/2013
Grade 1 Module 3: Ordering and Comparing Length Measurements as Numbers
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Module 3 begins by extending students’ kindergarten experiences with direct length comparison to indirect comparison whereby the length of one object is used to compare the lengths of two other objects.  Longer than and shorter than are taken to a new level of precision by introducing the idea of a length unit.  Students then explore the usefulness of measuring with similar units. The module closes with students representing and interpreting data.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/31/2013
Grade 1 Module 4:  Place Value, Comparison, Addition and Subtraction to 40
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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.  Students study, organize, and manipulate numbers within 40.  They compare quantities and begin using the symbols for greater than (>) and less than (<).  Addition and subtraction of tens is another focus of this module as is the use of familiar strategies to add two-digit and single-digit numbers within 40.  Near the end of the module, the focus moves to new ways to represent larger quantities and adding like place value units as students add two-digit numbers.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/25/2013
Grade 1 Module 5: Identifying, Composing, and Partitioning Shapes
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In Module 5, students consider part–whole relationships through a geometric lens. The module opens with students identifying the defining parts, or attributes, of two- and three-dimensional shapes, building on their kindergarten experiences of sorting, analyzing, comparing, and creating various two- and three-dimensional shapes and objects. Students combine shapes to create a new whole: a composite shape. They also relate geometric figures to equal parts and name the parts as halves and fourths. The module closes with students applying their understanding of halves to tell time to the hour and half hour.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
10/20/2013
Grade 1 Module 6: Place Value, Comparison, Addition and Subtraction to 100
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In this final module of the Grade 1 curriculum, students bring together their learning from Module 1 through Module 5 to learn the most challenging Grade 1 standards and celebrate their progress. As the module opens, students grapple with comparative word problem types. Next, they extend their understanding of and skill with tens and ones to numbers to 100. Students also extend their learning from Module 4 to the numbers to 100 to add and subtract. At the start of the second half of Module 6, students are introduced to nickels and quarters, having already used pennies and dimes in the context of their work with numbers to 40 in Module 4. Students use their knowledge of tens and ones to explore decompositions of the values of coins. The module concludes with fun fluency festivities to celebrate a year's worth of learning.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
12/30/2013
Grade 2 Module 1: Sums and Differences to 20
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Module 1 sets the foundation for students to master the sums and differences to 20 and to  subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using place value understandings, properties of operations and the relationship between addition and subtraction.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
05/11/2013
Grade 2 Module 2: Addition and Subtraction of Length Units
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In this 12-day Grade 2 module, students engage in activities designed to deepen their conceptual understanding of measurement and to relate addition and subtraction to length.  Their work in Module 2 is exclusively with metric units in order to support place value concepts.  Customary units will be introduced in Module 7.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
05/11/2013
Grade 2 Module 3: Place Value, Counting, and Comparison of Numbers to 1,000
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In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana?1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/25/2012
Grade 2 Module 4:  Addition and Subtraction Within 200 with Word Problems to 100
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In Module 4, students develop place value strategies to fluently add and subtract within 100; they represent and solve one- and two-step word problems of varying types within 100; and they develop conceptual understanding of addition and subtraction of multi-digit numbers within 200.  Using a concrete to pictorial to abstract approach, students use manipulatives and math drawings to develop an understanding of the composition and decomposition of units, and they relate these representations to the standard algorithm for addition and subtraction.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/05/2013
Grade 2 Module 5: Addition and Subtraction Within 1,000 with Word Problems to 100
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In Module 4, students developed addition and subtraction fluency within 100 and began developing conceptual understanding of the standard algorithm via place value strategies. In Module 5, students build upon their mastery of renaming place value units and extend their work with conceptual understanding of the addition and subtraction algorithms to numbers within 1,000, always with the option of modeling with materials or drawings. Throughout the module, students continue to focus on strengthening and deepening conceptual understanding and fluency.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
10/28/2013
Grade 2 Module 6: Foundations of Multiplication and Division
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Module 6 lays the conceptual foundation for multiplication and division in Grade 3 and for the idea that numbers other than 1, 10, and 100 can serve as units.  Topics in this module include:  Formation of Equal Groups, Arrays and Equal Groups, Rectangular Arrays as a Foundation for Multiplication and Division, and The Meaning of Even and Odd Numbers.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
12/30/2013
Grade 2 Module 7:  Problem Solving with Length, Money, and Data
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Module 7 presents an opportunity for students to practice addition and subtraction strategies within 100 and problem-solving skills as they learn to work with various types of units within the contexts of length, money, and data.  Students represent categorical and measurement data using picture graphs, bar graphs, and line plots.  They revisit measuring and estimating length from Module 2, though now using both metric and customary units.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/01/2014
Grade 2 Module 8: Time, Shapes, and Fractions as Equal Parts of Shapes
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In Module 8, the final module of the year, students extend their understanding of part–whole relationships through the lens of geometry.  As students compose and decompose shapes, they begin to develop an understanding of unit fractions as equal parts of a whole.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/01/2014
Grade 3 Mathematics Module 5: Fractions as Numbers on the Number Line
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In this 35-day Grade 3 module, students extend and deepen second grade practice with "equal shares" to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/03/2013
Grade 3 Module 2:  Place Value and Problem Solving with Units of Measure
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Module 2 uses place value to unify measurement, rounding skills, and the standard algorithms for addition and subtraction.  The module begins with plenty of hands-on experience using a variety of tools to build practical measurement skills and conceptual understanding of metric and time units.  Estimation naturally surfaces through application; this transitions students into rounding.  In the module’s final topics students round to assess whether or not their solutions to problems solved using the standard algorithms are reasonable.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/05/2013
Grade 3 Module 3: Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10
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This 25-day module builds directly on students’ work with multiplication and division in Module 1. Module 3 extends the study of factors from 2, 3, 4, 5, and 10 to include all units from 0 to 10, as well as multiples of 10 within 100. Similar to the organization of Module 1, the introduction of new factors in Module 3 spreads across topics. This allows students to build fluency with facts involving a particular unit before moving on. The factors are sequenced to facilitate systematic instruction with increasingly sophisticated strategies and patterns.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
08/01/2013
Grade 3 Module 4: Multiplication and Area
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In this 20-day module students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure.  They come to understand that the space can be tiled with unit squares without gaps or overlaps.  They make predictions and explore which rectangles cover the most area when the side lengths differ.  Students progress from using square tile manipulatives to drawing their own area models and manipulate rectangular arrays to concretely demonstrate the arithmetic properties. The module culminates with students designing a simple floor plan that conforms to given area specifications.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
10/18/2013
Grade 3 Module 6: Collecting and Displaying Data
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This 10-day module builds on Grade 2 concepts about data, graphing, and line plots. The two topics in this module focus on generating and analyzing categorical and measurement data.  By the end of the module, students are working with a mixture of scaled picture graphs, bar graphs, and line plots to problem solve using both categorical and measurement data.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
12/11/2013
Grade 3 Module 7: Geometry and Measurement Word Problems
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This 40-day final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter.  The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations.  Next students explore geometry.  Students tessellate to bridge geometry experience with the study of perimeter.  Line plots, familiar from Module 6, help students draw conclusions about perimeter and area measurements.  Students solve word problems involving area and perimeter using all four operations.  The module concludes with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/01/2014
Grade 4 Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction
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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).  They recognize 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).

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
05/11/2013
Grade 4 Module 2:  Unit Conversions and Problem Solving with Metric Measurement
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Module 2 uses length, mass and capacity in the metric system to convert between units using place value knowledge.  Students recognize patterns of converting units on the place value chart, just as 1000 grams is equal 1 kilogram, 1000 ones is equal to 1 thousand.  Conversions are recorded in two-column tables and number lines, and are applied in single- and multi-step word problems solved by the addition and subtraction algorithm or a special strategy.  Mixed unit practice prepares students for multi-digit operations and manipulating fractional units in future modules.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/05/2013
Grade 4 Module 3: Multi-Digit Multiplication and Division
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In this 43-day module, students use place value understanding and visual representations to solve multiplication and division problems with 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.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
08/30/2013
Grade 4 Module 4: Angle Measure and Plane Figures
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This 20-day module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in their work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation. Through decomposition and composition activities as well as an exploration of symmetry, students recognize specific attributes present in two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures based on them.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
10/20/2013
Grade 4 Module 5: Fraction Equivalence, Ordering, and Operations
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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 mixed numbers.  This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models.  Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes.  Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
01/17/2014
Grade 4 Module 6: Decimal Fractions
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This 20-day module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms.  Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/01/2014
Grade 4 Module 7: Exploring Measurement with Multiplication
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In this 20-day 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.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/01/2014
Grade 5 Math Module 1
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In Module 1, students’ understanding of the patterns in the base ten system are extended from Grade 4’s work with place value of multi-digit whole numbers and decimals to hundredths to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves it one place value to the right. Toward the module’s end students apply these new understandings as they reason about and perform decimal operations through the hundredths place.

Subject:
Measurement and Data
Material Type:
Activity/Lab
Assessment
Lesson Plan
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
03/13/2015
Grade 5 Module 2:  Multi-Digit Whole Number and Decimal Fraction Operations
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In Module 2 students apply patterns of the base ten system  to mental strategies and a sequential study of multiplication via area diagrams and the distributive property leading to fluency with the standard algorithm.  Students move from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products. Multiplication is explored as a method for expressing equivalent measures in both whole number and decimal forms.  A similar sequence for division begins concretely with number disks as an introduction to division with multi-digit divisors and leads student to divide multi-digit whole number and decimal dividends by two-digit divisors using a vertical written method.  In addition, students evaluate and write expressions, recording their calculations using the associative property and parentheses.  Students apply the work of the module to solve multi-step word problems using multi-digit multiplication and division with unknowns representing either the group size or number of groups.  An emphasis on the reasonableness of both products and quotients, interpretation of remainders and reasoning about the placement of decimals draws on skills learned throughout the module, including refining knowledge of place value, rounding, and estimation.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/05/2013
Grade 5 Module 3: Addition and Subtraction of Fractions
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In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/27/2012
Grade 5 Module 4: Multiplication and Division of Fractions and Decimal Fractions
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Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/15/2013
Grade 5 Module 5: Addition and Multiplication with Volume and Area
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In this 25-day module, students work with two- and three-dimensional figures.  Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms.  The second half of the module turns to extending students’ understanding of two-dimensional figures.  Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths.  They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes.  This module fills a gap between Grade 4’s work with two-dimensional figures and Grade 6’s work with volume and area.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
01/17/2014
Grade 5 Module 6: Problem Solving with the Coordinate Plane
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In this 40-day module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems.  Students use the familiar number line as an introduction to the idea of a coordinate, and they construct two perpendicular number lines to create a coordinate system on the plane.  Students see that just as points on the line can be located by their distance from 0, the plane’s coordinate system can be used to locate and plot points using two coordinates.  They then use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the rules that generate them.  This study culminates in an exploration of the coordinate plane in real world applications.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/01/2014
Grade K Module 2:  Two-Dimensional and Three-Dimensional Shapes
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Module 2 explores two-dimensional and three-dimensional shapes.  Students learn about flat and solid shapes independently as well as how they are related to each other and to shapes in their environment.  Students begin to use position words when referring to and moving shapes.  Students learn to use their words to distinguish between examples and non-examples of flat and solid shapes.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/05/2013
Grade K Module 3: Comparison of Length, Weight, Capacity, and Numbers to 10
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After students observed, analyzed, and classified objects by shape into pre-determined categories in Module 2, they now compare and analyze length, weight, volume, and, finally, number in Module 3. The module supports students’ understanding of amounts and their developing number sense. The module culminates in a three-day exploration, one day devoted to each attribute: length, weight, and volume.

Subject:
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
08/01/2013
Grade K Module 4: Number Pairs, Addition and Subtraction to 10
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Module 4 marks the next exciting step in math for kindergartners, addition and subtraction! They begin to harness their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers to reason about and solve addition and subtraction expressions and equations. In Topics A and B, decomposition and composition are taught simultaneously using the number bond model so that students begin to understand the relationship between parts and wholes before moving into formal work with addition and subtraction in the rest of the module.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/26/2013
Grade K Module 6: Analyzing, Comparing, and Composing Shapes
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Kindergarten comes to a close with another opportunity for students to explore geometry in Module 6. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
11/28/2013
Kindergarten Mathematics Module 5: Numbers 10?20; Count to 100 by Ones and Tens
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Up to this point in Grade K, students have worked intensively within 10 and have often counted to 30 using the Rekenrek during fluency practice. This work sets the stage for this module where students clarify the meaning of the 10 ones and some ones within a teen number and extend that understanding to count to 100.

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
02/05/2013