Philosophy
Our mathematical philosophy is to provide students with a deep conceptual understanding of math through a variety of engaging and effective strategies. This is accomplished through the collaboration of classroom teachers and math AIS providers who skillfully integrate our research-based K-5 math program (Into Math) and math fluency program (Building Fact Fluency) along with our digital platforms (i-Ready and IXL) into daily lessons.
Our Approach
Central to this approach is the CRA (Concrete-Representational-Abstract) method, which guides students from hands-on experiences to representational models, then abstract thinking; helping learners connect the “why” to the “how.” Small group and station teaching further enhance learning by allowing targeted instruction and collaborative problem-solving. We work to provide engaging experiences that connect math to real-world scenarios, inspire curiosity and highlight the relevance of math in everyday life.
Mathematical Mindsets
Building a positive math mindset is critical and empowers our young mathematicians to approach challenges with confidence and resilience. Additionally, through meaningful math discussions and the integration of academic vocabulary, students develop the language needed to articulate their reasoning and participate in rich mathematical conversations. All of this is done while we encourage flexible thinking so learners can approach problems from multiple perspectives, fostering creativity and adaptability. Together, these strategies cultivate a supportive and dynamic learning environment where students thrive as life-long critical thinkers and problem solvers. Meaningful research has pointed to the crucial role of healthy mindset in mathematics education. To learn more about this, visit YouCubed at the Stanford Graduate School of Education.
Mathematical Practices
All mathematics courses from K-12 emphasize the development of a set of expertise called “Mathematical Practices.” These practices are the underpinning of all content learning and are key proficiencies students need to become strong problem solvers. The practices we seek to develop in our students are:
- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning
Mathematical Concepts Across K-5
Our coursework is grounded in the New York State Next Generation Mathematics Learning Standards. The topics students will encounter each year are described below:
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Units & Concepts: K-5 Mathematics
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Kindergarten
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Classify, Count, & Set Objects
Analyze & Compare Two-Dimensional Shapes
Analyze & Compare Three Dimensional Shapes
Describe Positions of Objects
Represent Numbers to 5 with Objects
Represent Numbers Within 5
Matching and Counting Numbers to 5
Represent Numbers 6 to 10 With Objects
Represent Numbers 6 to 10 With Written Numerals
Compare Numbers to 10
Add To Within 10
Use the Count Sequence to Count to 100
Take from Within 10
Word Problems
Ways to Make Numbers to 10
Place Value Foundations: Represent Numbers to 20
Place Value Foundations: Represent Numbers to 20 with Written Numerals
Explore Coins
Length and Height
Weight
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Grade 1
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Addition Strategies
Subtraction Strategies
Properties of Operations
Apply the Addition and Subtraction Relationship
Three-Dimensional Shapes
Two-Dimensional Shapes
Understand “Add To” and “Take Apart From” Problems
Understand “Put Together” and “Take Apart” Problems
Data
Understand “Compare” Problems
Understand Place Value
Count and Represent Numbers
Compare Numbers
Understand Addition and Subtraction with Tens and Ones
Measure Length
Measure Time
Fraction Foundations
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Grade 2
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Fluency and Addition and Subtraction Within 20
Even & Odd Numbers
Equal Groups, Arrays
Understanding Place Value
Read, Write, Show Numbers to 1,000
Use Place Value, Add/Subtract 10 or 100, Compare Three-Digit Numbers
Coins
Dollar Amounts
Time
Data
Addition and Subtraction Counting Strategies
Regrouping, Adding and Subtraction of Two-and Three-Digit Numbers
Develop Addition and Subtraction Fluency
Word Problems
Two- and Three-Dimensional Shapes
Understand Fractions
Measurement: Length
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Grade 3
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Multiplication and Area
Multiplication Strategies
Read, Write, and Show Numbers to 1,000
Understand Division
Relate Multiplication and Division
Applications of Multiplication and Division
Addition and Subtraction Strategies & Applications within 1,000
Understand Fractions as Numbers (Fractions on a Number Line, Fractions of a Whole, Fractions Greater than 1)
Compare Fractions, Understanding Equivalent Fractions
Relate Shapes, Fractions, and Area
Time
Representing and Interpreting Data
Geometry: Perimeter
Geometry: Two-Dimensional Shapes
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Grade 4
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Place Value of Whole Numbers
Addition and Subtraction of Whole Numbers
Interpret & Solve Word Problems, Multistep Problems
Mental Math & Estimation Strategies
Multiply by 1-Digit Numbers
Division by 1-Digit Numbers
Number Theory: Factors, Multiples, Prime, and Composite Numbers
Fraction Equivalence & Comparison
Add/Subtract Fractions and Mixed Numbers With Like Denominators
Multiply Fractions by Whole Numbers
Geometry: Perimeter & Area
Geometry: Using Fractions to Understand Angles
Geometry: Two Dimensional Figures
Geometry: Symmetry and Patterns
Customary Measurement Units (Length, Weight, Volume)
Relative Sizes and Comparison of Measurement Units
Problem Solving with Time & Measurement
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Grade 5
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Whole Number and Decimal Place Value
Whole Number Multiplication, including multi digit numbers
Understand Division of Whole Numbers
Expressions
Volume
Adding & Subtracting Mixed Numbers
Multiplication of Fractions
Multiplication of Mixed Numbers
Division with Whole Numbers and Unit Fractions
Multiplication and Division with Decimals
Measurement
Geometry: Graphs and Patterns
Geometry: Two-Dimensional Figures
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