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Mathematics
Overview
The First Program curriculum introduces mathematical concepts using a developmentally appropriate problem-solving approach Guided by the NCTM (National Council of Teachers of Mathematics) Standards and the Common Core Standards, students are instructed through direct, hands-on experiences that deepen their conceptual understanding and increase their logical thinking skills. Concepts and ideas are explored using concrete materials and practical applications, all overseen by Dalton’s full-time Mathematics Coordinator Each House at the First Program provides a learning environment that endorses the interdisciplinary nature of mathematics learning. The children’s lives in and out of the classroom also provide opportunities for applied mathematical thinking.
Teachers allow children to make connections at their own pace and construct meaning to solve real-life problems. Teachers support each student's thinking and learning style by meeting students where they are on their educational journey Concepts, skills, and activities are designed to provide challenges and build upon students’ previous experiences A common mathematical language ensures continuity and helps children articulate their thinking processes. Common goals and common areas of study provide consistency across grade levels.
Dalton’s Mission Statement, the Dalton Plan, and the National Council of Teachers of Mathematics Standards form the basis of the First Program’s philosophy and pedagogy in mathematics instruction The First Program curriculum consists of a variety of carefully constructed assignments Teachers encourage children to problem solve and to extend mathematical awareness. Classrooms are equipped with math materials that help children move from concrete to more abstract thinking. Technology is another tool used to enhance learning. In such an environment, children work cooperatively on similar ideas in different ways, providing appropriate differentiation
At the First Program, enthusiasm for math learning is represented in various ways Math concepts and ideas are explored through children’s literature Interactive math bulletin boards encourage students, parents, and faculty to participate in mathematical discussions. Additionally, faculty members regularly participate in seminars, workshops, study groups, and other forms of professional development regarding mathematical pedagogy.
Common Goals And Areas Of Study For Grades K-3
Our primary goal is to enable all students to understand and enjoy mathematics and help them recognize its value in our world. Understanding mathematical processes enables the students to work independently on their assignments with knowledge, confidence, and enjoyment We want our students to become active problem solvers and to develop increasing confidence in their abilities to reason and communicate mathematically. Our students are engaged and excited by their explorations. We have developed a variety of cooperative learning opportunities to support the children in working constructively with others. Common areas of study include Operations and Algebraic Thinking, Geometry, Measurement & Data, and Patterns.
Instruction/Support Services
Mathematics instruction occurs individually, in small groups, and as a whole class. The House Advisors (classroom teachers) remain the primary instructors of the students. Math Specialists further support teachers and students The Math Specialists also provide additional materials, ideas, and ongoing professional development opportunities for our faculty. Additional support is given to individuals, small groups, and whole groups for both remediation and enrichment at the discretion of the House Advisors.
Kindergarten
Counting and Cardinality:
● Count to 100 by ones and by tens.
● Counts objects using one-to-one correspondence
● Match quantity to number
● Compare groups of objects (greater than, less than, is equal to).
● Write numbers from 0 to 20.
● Compare two numbers presented as written numerals.
Operations and Algebraic Thinking:
● Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
● Add and subtract whole numbers using objects, pictures, and symbols.
● Decompose numbers less than or equal to 10 into pairs in multiple ways
● Work with numbers 11–19 to gain foundations for place value.
● Compose and decompose numbers from 11 to 19 into tens and ones
Geometry:
● Identify and describe 2-dimensional shapes.
● Describe objects in the environment using names of shapes
● Analyze, compare, create, and compose shapes
Measurement and Data:
● Describe and compare measurable attributes.
● Sort objects by size, number, and other properties
● Classify objects and count the number of objects in each category
Patterns:
● Recognize patterns by attributes of size, color, shape, texture, sound, etc.
● Repeat and extend patterns
● Observe patterns relating to time: calendar work and holidays
First Grade
Operations and Algebraic Thinking:
● Use addition and subtraction to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing.
● Understand the relationship between addition and subtraction
● Add and subtract using a variety of strategies
● Read and write numbers up to 120
● Recognize the place value of numbers (ones and tens).
● Compare numbers (greater than, less than, is equal to).
● Count within 100; skip-count by 5s and 10s
● Identify even/odd numbers
Geometry:
● Build and draw 2-dimensional shapes to possess defining attributes
● Compose two-dimensional shapes to create a composite shape
● Recognize and record the line of symmetry.
● Recognize and partition shapes into halves, thirds, and fourths to show equal shares.
Measurement and Data:
● Order objects by length and compare the lengths of objects
● Use non-standard and standard measurements (inches and centimeters).
● Make bar graphs and picture graphs from experiences inside and outside of the classroom
● Organize, represent, and interpret data
● Tell and write time in hours and half-hours using analog and digital clocks.
● Use the calendar to identify seasons, months, weeks, days, and dates.
● Identify and show the value of standard coins.
Patterns:
● Recognize patterns by attributes of size, color, shape, texture, sound, etc.
● Repeat and extend number and shape patterns
Second Grade
Operations and Algebraic Thinkings:
● Use addition and subtraction to solve word problems
● Add and subtract using a variety of strategies
● Recognize the place value of numbers (ones, tens, and hundreds).
● Count within 1000; skip-count by 5s, 10s, and 100s.
● Compare numbers (greater than, less than, is equal to)
● Understands and applies the properties of odd and even numbers
● Represent and solve problems involving multiplication.
Geometry:
● Recognize similarities and differences among two-dimensional and three-dimensional shapes
● Name and identify two-dimensional and three-dimensional shapes by their attributes.
● Recognize congruency of shapes.
● Draw and locate the line of symmetry.
● Recognize and partition shapes into halves, thirds, and fourths to show equal shares
Measurement and Data:
● Recognize and use standard measurements.
● Relate geometric ideas to number, measurement, and mapping ideas.
● Make bar graphs, picture graphs, and line plots from experiences inside and outside of the classroom
● Organize, represent, and interpret data
● Tell and write time in the nearest 5 minutes using analog and digital clocks.
● Communicate and write elapsed time.
● Solve word problems involving money.
Patterns:
● Recognize patterns by attributes of size, color, shape, texture, sound, etc
● Repeat and extend patterns.
Third Grade
Operations and Algebraic Thinking:
● Recognize the place value of numbers (ones, tens, hundreds, and thousands)
● Show the value of a number in many different forms (e g , expanded form, table form)
● Rounds whole numbers to the nearest 10 or 100.
● Add and subtract using a variety of strategies.
● Represent and solve problems involving multiplication and division
● Multiply and divide within 100 using a variety of strategies
● Solve word problems involving the four operations.
● Understand and show fractional parts of a whole and groups.
● Understand fraction as a number on the number line
● Explain equivalence of fractions and compare fractions by reasoning about their size
Geometry:
● Name, label, and show attributes of two-dimensional shapes
● Recognize and construct different angles
● Recognize and draw parallel, intersecting, and perpendicular lines
● Identify multiple lines of symmetry.
Measurement and Data:
● Recognize and use standard measurements
● Organize, represent, and interpret data
● Geometric measurement: understand concepts of area and perimeter
● Solve word problems involving money.
Patterns:
● Recognize patterns by attributes of size, color, shape, texture, sound, etc.
● Repeat and extend patterns.
