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# EngageNY Mathematics

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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
10/28/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
12/30/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
02/01/2014
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
02/01/2014
Conditional Remix & Share Permitted
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This 25-day module begins the year by building on students fluency with addition and knowledge of arrays.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
05/11/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
02/03/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
07/05/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
08/01/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
10/18/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
12/11/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Geometry
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
02/01/2014
Conditional Remix & Share Permitted
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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).

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
05/11/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
07/05/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
08/30/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Geometry
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
10/20/2013
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
01/17/2014
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
02/01/2014
Conditional Remix & Share Permitted
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Measurement and Data
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
02/01/2014
Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Assessment
Lesson Plan
Provider:
New York State Education Department
Provider Set:
EngageNY
03/13/2015
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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.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY