Our math program consists of multiple approaches, including “skill development,” which provides students with direct instruction in math strategies and then time to practice those strategies in the Singapore Math® books. Singapore Math® materials focus on place value to provide deep knowledge of numbers. As students work with and manipulate numbers, they work towards fluency by learning and using mental math strategies.
When students have opportunities to work extensively with operations and representations in a variety of ways, they develop a more thorough understanding of the properties of math. We are dedicated to developing students’ conceptual understanding of mathematics so that they are able to apply their knowledge to problems in a multitude of contexts.
We strive to help students view themselves as mathematicians by focusing on developing a growth mindset and offering ample opportunities for students to share their “math thinking” with peers. By engaging in long-form math explorations (i.e. problems or challenges that require flexible thinking to solve) students learn to represent their thinking in various ways and gain an appreciation for the many pathways to a solution.
Using a variety of assessment tools, we gauge students’ facility with each concept and support them accordingly. We aim to meet each student where they are, to help them develop math skills that they may be struggling with while providing challenges that will extend their thinking on concepts with which they have demonstrated proficiency.
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Kindergarten math focuses on:
Sorting and Patterning
Counting, including skip counting
Numeral Recognition and Writing
Operations, with an emphasis on Addition and Subtraction
Place Value
Geometry
Measurement
Kindergarten uses the Developing Roots curriculum, which provides a developmentally appropriate introduction to the Singapore Math® approach. Direct instruction is supplemented calendar activities and a variety of math materials that invite play and flexibility to support the learning of the concepts listed above.
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In first grade, students explore the following topics:
Place Value to 100
Addition and Subtraction within 100
Number Bonds
Shapes
Ordinal Numbers
Measurement (length)
Comparing Numbers
Grouping and Sharing
Fractions
Time
Money
To gain number sense, first grade students are taught to make connections between topics. While first graders will still work on “fact families,” Singapore Math® also uses a pictorial representation called a “Number Bond” to help students see the connections between addition and subtraction.
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Second grade students explore:
Place Value to 1000
Addition and Subtraction (with regrouping)
Measurement (length, weight, capacity)
Multiplication and Division (by a single digit number)
Mental Calculations
Shapes
Graphing
Time
Money
In second grade, students are introduced to a level of abstraction in their manipulatives. They begin to utilize place value disks. These concrete manipulatives represent different place values and provide a bridge between one-to-one correspondence and more abstract representations of values. They also gain exposure to drawing bar models, a key component of our upper-elementary math curriculum.
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In third grade, students explore:
Place Value to 10,000
Addition and Subtraction
Mental Calculations
Estimation
Multiplication (with regrouping)
Measurement (length, weight, capacity)
Division (with and without remainders)
Mental Calculations
Graphs and Tables
Fractions (equivalence, simplifying, comparing, adding, subtracting)
Measurement
Geometry
Area and Perimeter
Time
Money
Third grade students continue to use place value disks with increasingly complex numbers and operations. They gain facility with using bar models to represent word problems. This method of problem-solving is a hallmark of the Singapore Math® approach. Bar models allow students to use pictorial representations to solve complex word problems that would otherwise require algebraic equations. By representing the problem visually, they gain a deeper understanding of the relationship between a word problem and a mathematical equation.
We also start to work with students on their “multiplication facts.” We encourage students to learn and remember these facts as they are able, but do not expect them to memorize them all yet!
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In fourth grade, students explore:
Place Value to 1,000,000
Prime numbers
Addition and Subtraction
Factors and multiples of whole numbers within 100
Commutative, Associative, and Distributive Properties
Multiplication (by a 1 & 2 digit number)
Division (up to 4 digit quotients)
Fractions (equivalence, mixed numbers, improper fractions, adding, subtracting, multiplying)
Rounding
Graphs and Plots
Measurement Conversion
Area and Perimeter
Decimals (converting fractions, adding, subtracting, multiplying, dividing)
Geometry (angles, quadrilaterals, cuboids)
Fourth grade students are working with much larger and much smaller numbers, as they delve into decimals. They are more fully immersed in using pictorial representations to solve math problems. Although concrete manipulatives may still be used on occasion, students are usually ready and able to solve problems using only pictorials and algorithms.
Students continue working on their “multiplication facts.” We encourage students to learn and remember these facts but do not expect them to have memorized them all yet!
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In fifth grade, students explore:
Place Value to 1,000,000,000
Order of Operations
Prime numbers
Multiplication (within 10,000 by a 2-digit number)
Division (within 10,000 by a 2-digit divisor)
Factors and multiples of whole numbers within 100
Greatest/Lowest common factors within 100
Fractions (addition, subtraction, multiplication, division)
Review of Area and Perimeter
Area of a Triangle
Volume of Solid Figures
Decimals (rounding, addition, subtraction, multiplication, division)
Geometry (Angles, triangle, quadrilaterals)
Data Analysis and Graphing
Ratio
Rate
Percentage
In fifth grade, students are working with a wider variety of mathematical concepts. Our fifth-grade curriculum is rich and comprehensive, giving students exposure to, and practice with, concepts that would typically be taught in middle school. Students are challenged to solve complex, multi-step problems that require algebraic reasoning while continuing to represent their thinking through bar models. This helps them develop a deeper understanding of underlying concepts, while also promoting flexible thinking.