EngageNY Math Resources Collection Resources (21)

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Criteria for Resources Aligned to Common Core State Standards in Mathematics
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Developed by one of the authors of the Common Core State Standards, ...

Developed by one of the authors of the Common Core State Standards, the seven criteria for resources outlined in this document should guide development of curriculum modules and accompanying materials. Seven criteria are: Promote Effectiveness, Quality Materials, Develop Mathematical Practices, Balance of Approach, Capacity-building, Content Alignment, Comprehensiveness.

Subject:
Education
Mathematics
Material Type:
Teaching/Learning Strategy
Provider:
EngageNY
OER Commons
Provider Set:
Common Core Reference Collection
Author:
Jason Zimba
Grade 7 Mathematics
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In order to assist educators with the implementation of the Common Core, ...

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The full year of Grade 7 Mathematics curriculum is available from the module links.

Subject:
Mathematics
Material Type:
Full Course
Homework/Assignment
Lesson Plan
Textbook
Unit of Study
Provider:
New York State Education Department
Provider Set:
EngageNY
Grade 6 Mathematics
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In order to assist educators with the implementation of the Common Core, ...

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The full year of Grade 6 Mathematics curriculum is available from the module links

Subject:
Mathematics
Material Type:
Full Course
Lesson Plan
Textbook
Unit of Study
Provider:
New York State Education Department
Provider Set:
EngageNY
New York State Common Core Mathematics Curriculum: Algebra 1
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In order to assist educators with the implementation of the Common Core, ...

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The full year of Algebra I curriculum is available below.

Subject:
Mathematics
Algebra
Material Type:
Full Course
Provider:
New York State Education Department
Provider Set:
EngageNY
New York State Common Core Mathematics Curriculum: Geometry (Module 1)
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In order to assist educators with the implementation of the Common Core, ...

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The Geometry curriculum is available below.

Subject:
Mathematics
Geometry
Material Type:
Full Course
Provider:
New York State Education Department
Provider Set:
EngageNY
Grade 8 Mathematics Module 1: Integer Exponents and Scientific Notation
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In Grade 8 Module 1, students expand their basic knowledge of positive ...

In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for any integer exponent.  Next, students work with numbers in the form of an integer multiplied by a power of 10 to express how many times as much one is than the other.  This leads into an explanation of scientific notation and continued work performing operations on numbers written in this form. 

Subject:
Numbers and Operations
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Grade 7 Mathematics Module 1: Ratios and Proportional Relationship
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In this 30-day Grade 7 module, students build upon sixth grade reasoning ...

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality.  Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions.  Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
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 ...

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
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 ...

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
Grade 5 Math Module 1
Conditions of Use:
No Strings Attached
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In Module 1, students’ understanding of the patterns in the base ten ...

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
Grade 6 Mathematics Module 1: Ratios and Unit Rates 
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Students begin their sixth grade year investigating the concepts of ratio and ...

Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.

Subject:
Ratios and Proportions
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Grade 5 Math Module 1
Conditions of Use:
No Strings Attached
Rating

In Module 1, students’ understanding of the patterns in the base ten ...

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
Prekindergarten Mathematics Module 5: Addition and Subtraction Stories and Counting to 20
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Module 5 is the culmination of children’s work with number in the ...

Module 5 is the culmination of children’s work with number in the Pre-K year.  Throughout Modules 1 and 3, they had extensive counting experiences with numbers 0–10.  In Module 4, they examined the relationships between numbers 1–5 through comparison.  In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples).  They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5.  Students will also learn to write numerals 0-5 and explore patterns in this final module.

Subject:
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Prekindergarten Mathematics Module 4: Comparison of Length, Weight, Capacity, and Numbers to 5 
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In the first half of this module, students identify measurable attributes of ...

In the first half of this module, students identify measurable attributes of objects in terms of length, weight, and capacity.  Students learn words such as small, big, short, tall, empty, full, heavy, and light so that they will have the vocabulary needed to describe objects (PK.MD.1).  The comparison of length, weight, and capacity naturally leads to discussions about quantity and number.  In the second half, measurement is connected to quantity as students reason if there are enough, more than, less than, or the same number of objects in a set using matching and counting strategies (PK.CC.5).  Comparing concrete sets leads to comparing quantities and abstract numbers.  Children will also focus on identifying first and last in quantities up to 5 and 10 in different configurations (PK.CC.6).

Subject:
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Geometry Module 5: Circles With and Without Coordinates
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This module brings together the ideas of similarity and congruence and the ...

This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year.  It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story.  This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Algebra II Module 1: Polynomial, Rational, and Radical Relationships
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Students connect polynomial arithmetic to computations with whole numbers and integers. Students ...

Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations. 

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Algebra II Module 2
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Module 2 builds on students’ previous work with units and with functions ...

Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Algebra II Module 3: Exponential and Logarithmic Functions
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In this module, students synthesize and generalize what they have learned about ...

In this module, students synthesize and generalize what they have learned about a variety of function families.  They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4).  They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions.  They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3).  Students identify appropriate types of functions to model a situation.  They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit.  The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module.  In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY