Engage NY
MATH CURRICULUM
What is it?
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EngageNY math curriculum was developed by the New York State Education Department
and written by teachers for teachers to support the implementation of the Common Core
State Standards. It is our interim math curriculum for the next two years. Engage NY will
help students develop a deeper understanding of subject matter, learn how to think
critically and apply what they have learned to the real world. This curriculum supports the
district’s goal of college and career readiness.
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EngageNY uses a balanced approach to layered instruction. Fluency, concept
development and application are layered to guide students through the mathematics.
There is a deliberate progression of material to support complex understanding of
concepts.
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Each lesson is structured to incorporate fluency activities along with the development of
conceptual understanding, procedural skills, and problem solving. Components are taught
from concrete to abstract (sometimes the concrete level has been covered in a prior
grade level so the lesson will move from the abstract to the pictorial or concrete).
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There are 5 to 7 modules for the year for each grade level that focus on the major work of
each grade. Many lessons are taught within each module focusing on the grade level
standards.
Major Work in Each Grade:
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K–2
Addition and subtraction – concepts, skills, and
problem solving; place value
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3 -5
Multiplication and division of whole numbers and
fractions – concepts, skills, and problem solving
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6
Ratios and proportional relationships; arithmetic of
rational numbers
Focus Grade Level Standards:
Kindergarten
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Know number names and the count sequence
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Count to tell the number of objects
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Compare numbers
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Work with numbers 11-19 to gain foundations for place value
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Understand addition as putting together and adding to and
understand subtraction as taking apart and taking from
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Describe and compare measurable attributes
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Classify objects and count the number of objects in each category
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Identify and describe shapes
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Analyze, compare, create, and compose shapes
Grade 1 
Represent and solve problems involving addition and subtraction
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Understand and apply properties of operations and the relationship between addition and
subtraction
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Add and subtract within 20
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Work with addition and subtraction equations
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Extend the counting sequence
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Understand place value
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Measure lengths indirectly and by iterating length units
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Tell and write time
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Represent and interpret data
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Reason with shapes and their attributes
Grade 2 
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Represent and solve problems involving addition and subtraction
Add and subtract within 20
Work with equal groups of objects to gain foundations for multiplication
Understand place value
Use place value understanding and properties of operations to add and subtract
Measure and estimate lengths in standard units
Relate addition and subtraction to length
Work with time and money
Represent and interpret data
Reason with shapes and their attributes
Grade 3 
Represent and solve problems involving multiplication and division
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Understand properties of multiplication and the relationship between multiplication and division
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Multiply and divide within 100
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Solve problems involving the four operations, and identify and explain patterns in arithmetic
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Use place value understanding and properties of operations to perform multi-digit arithmetic
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Develop understanding of fractions as numbers
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Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects
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Represent and interpret data
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Geometric measurement: understand concepts of area and relate are to multiplication and to addition
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Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between
linear and area measures
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Reason with shapes and their attributes
Grade 4 
Use the four operations with whole numbers to solve problems
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Gain familiarity with factors and multiples
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Generate and analyze patterns
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Generalize place value understanding for multi-digit whole numbers
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Use place value understanding and properties of operations to perform multi-digit arithmetic
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Extend understanding of fraction equivalence and ordering
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Build fractions from unit fractions by applying and extending previous understandings of operations on whole
numbers
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Understand decimal notation for fractions, and compare decimal fractions
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Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
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Represent and interpret data
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Geometric measurement: understand concepts of angle and measure angles
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Draw and identify lines and angles, and classify shapes by properties of their lines and angles
Grade 5 
Write and interpret numerical expressions
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Analyze patterns and relationships
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Understand the place value system
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Perform operations with multi-digit whole numbers and with decimals to hundredths
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Use equivalent fraction as a strategy to add and subtract fractions
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Apply and extend previous understandings of multiplication and division to multiply and divide
fractions
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Convert like measurement: understand concepts of volume and relate volume to multiplication
and to addition
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Graph points on the coordinate plane to solve real-world and mathematical problems
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Classify two-dimensional figures into categories based on their properties
Grade 6 
Understand ratio concepts and use ratio reasoning to solve problems
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Apply and extend previous understandings of multiplication and division to divide fractions by fractions
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Compute fluently with multi-digit numbers and find common factors and multiples
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Apply and extend previous understandings of numbers to the system of rational numbers
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Apply and extend previous understandings of arithmetic to algebraic expressions
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Reason about and solve one-variable equations and inequalities
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Represent and analyze quantitative relationships between dependent and independent variables
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Solve real-world and mathematical problems involving area, surface, and volume
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Develop understanding of statistical variability
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Summarize and describe distributions
Lesson structure:
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Fluency Practice – Promotes automaticity and focuses on recognizing patters and
connections.
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Application Problem – Students choose and apply the correct mathematics concept to
solve real problems that cause them to think creatively and quantitatively and use
patterns. There are a range of problems from single-step word problems to multi-step
word problems. The application problems are directly related to the Concept
Development.
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Concept Development – The major portion of instruction where new learning is
introduced. Sequencing of standards and topics within modules ensures students have
the understanding they need to access new learning goals and integrate them.
Problem sets and homework reinforce the learning that was introduced.
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Student Debrief – Students reflect back on the lesson and analyze their learning. They
make connections between parts of the lesson, concepts, strategies, and tools on their
own. The goal is for students to see and hear multiple perspectives from their
classmates as they share their work.
The 8 mathematical practices are
integrated into the curriculum
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Make sense of problems and persevere in solving them.
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Reason abstractly and quantitatively
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Construct viable arguments and critique the reasoning of others.
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Model with mathematics.
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Use appropriate tools strategically.
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Attend to precision.
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Look for and make use of structure.
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Look for and express regularity in repeated reasoning.
Fact Families: A fact family is made up of three numbers. Just as in any family
the members, or numbers, are related and there are always at least four
math facts to be made with them. Take, for example, these members of a
fact family: 6, 4, and 10.
6 + 4 = 10
4 + 6 = 10
You can also switch the first two numbers, using the commutative property of
addition and subtraction and still get the same answer.
10 - 4 = 6
10 - 6 = 4
Number Towers: Number towers or number stairs – one more and one
less within tens.
Numbers towers are used primarily in kindergarten.
Tape Diagrams: are defined in the Common Core Standards as drawings that
look like a segment of tape, used to illustrate number relationship.
An array: is a systematic arrangement of objects, usually in rows and columns.
In math, an array refers to a set of numbers or objects that will follow a
specific pattern.
Number Bonds: are different pairs of numbers which make up the same
number. For instance, the number bonds for 10 are 1+9, 2+8, 3+7, 4+6 and
5+5. Number bond is typically represented using a picture consisting of 3
circles connected by 2 lines.
RDW Term = Read, Draw and Write – Read the problem,
draw a picture and write an explanation of your answer.
Commutative Property –
Commutative Laws" say we can swap numbers over and still get the same
answer ...
Distributive Property –
Distributive Law" is the BEST one of all, but needs careful attention.
This is what it lets us do:
3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4
So, the 3× can be "distributed" across the 2+4, into 3×2 and 3×4
Associative Property “Associative Laws" say that it doesn't matter how we group the numbers
(i.e. which we calculate first) ..
... when we add:
(a + b) + c = a + (b + c)
Number Line 
Children build fluency with addition and subtraction, preparing them for
more advanced operations.
Place Value Chart
They add and subtract within 1000, using concrete models or drawings and
strategies based on place value.
236 is showing on the model.
Arrow Notation
Students use arrow notation to record their mental math. First, they add a
multiple of 100, and then count on by multiples of 10 to find the total (as
shown at right).
Kindergarten Sample Problem
First Grade Sample Problem
2nd Grade Sample Problem
3rd Grade Sample Problem
4th Grade Sample Problem
5th Grade Sample Problem
6th Grade Sample Problem
How many quarter hours are in 5 hours?
Solution: inverse fraction for ¼ = 4/1
5 x 4/1 = 20 (there are 4 quarter hours in each hour – 15 minutes).
So 5 hours multiplied by 4/1 = 20
Answer: There are 20 quarter hours in 5 hours.
Go Out to the Community!
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Please share with the community that this curriculum will provide rigor and
the skills and knowledge needed to prepare our students for T-2-4:
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They will be ready to attend either a Technical, 2-year, or 4-year
college/university.
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We will get them Ready, In, and Through!