Math
The Lower School mathematics program helps all children deeply understand fundamental ideas of number and operations, geometry, data, measurement and early algebra. The program emphasizes developing a strong conceptual foundation and mathematical skills in students by following a developmentally appropriate sequence, by spiraling back to concepts over the years, and by emphasizing the construction of in-depth understanding. Children collaborate on solving worthwhile problems that have rich mathematical underpinnings. Problems can be solved on a variety of levels, have multiple entry points, and therefore are accessible to the abilities of all students in a class. Children use both real life materials and math manipulatives, they think mathematically, they apply concepts and strategies flexibly, and they examine the patterns and relationships of math. Emphasis is placed on the presentation and communication of mathematics in written, oral, graphic and symbolic forms. Our program results in students who develop perseverance and a sense of ownership of mathematics. Children are strong in mental mathematics, and also develop computational fluency. Ongoing review and practice, as well as homework are an integrated part of the program.
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The Fours are constantly engaged in exploring the world around them and math is a natural part of this. Through their activities in the classroom and explorations with math materials, the Fours investigate a range of math concepts including counting, patterning, sorting, and graphing. Specific activities throughout the school day help children practice these concepts such as discussing the lunch chart graph, counting cups during snack set-up, noticing shape relationships in blocks, and sorting art and recycled materials, among many others. Block building offers the Fours many rich opportunities to explore various math and science concepts such as balance, symmetry, patterning, gravity, shape recognition and counting. Children also use math language to describe their work. By using a variety of materials and games, children strengthen their conceptual understanding and gain confidence in their knowledge of these mathematical concepts.
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Kindergartners engage in meaningful opportunities to develop their sense of numbers and quantities through a variety of concrete experiences. They use the counting sequence to connect number names with written numbers and the quantities they represent. As students develop accurate counting strategies, they also deepen their understanding of how numbers and quantities are related within the counting sequence. Children also focus on data collection and interpretation, exploration of shapes, and the development of number sense through beginning addition and subtraction. By using a variety of materials and games, children work independently and in small groups to strengthen their skills and gain confidence in their knowledge of these mathematical concepts and skills. In their work with blocks, children explore spatial relationships and describe their experience using geometric language. Through block building activities, the Kindergartners hone new strategies as they work on balance, symmetry, and geometry.
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First graders begin to move from concrete understandings of number to abstract concepts such as the meaning and application of mathematical symbols. To develop foundational number sense, first graders practice counting by ones, twos, fives, tens and develop an understanding of addition and subtraction. They solve story problems, compose and decompose quantities in different ways, and add and subtract numbers up to 20. First graders learn to count on to combine two quantities, subtract one quantity from another, and become fluent with combinations of 10. In geometry, first graders identify, describe, draw, and compare 2-D shapes, with an emphasis placed on developing an understanding of triangles. As beginning data analysts, first graders sort related objects according to particular attributes. They gradually construct standard forms of representation including picture graphs, tallies, charts, and bar graphs. They carry out their own data investigation, developing a question and then collecting, representing, describing and interpreting the data. First graders develop a foundation of skills for accurate linear measurement and measurement of area. They measure both objects and distances, explore what happens when something is measured with different sized units, and learn that when something is measured twice with the same unit, the same results should be obtained.
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Second graders explore the composition of numbers to 100 and develop an understanding of the base-10 structure of our number system. By the end of the year, students are expected to be fluent with the addition combinations to 10+10; to add and subtract two-digit numbers accurately. Activities support development of these skills. They also work with repeating patterns that provide an opportunity to think about skip-counting with various starting points and to ponder odd and even numbers deeply. In measurement, second graders employ linear units to measure and compare the lengths of different objects. They use nonstandard (e.g. cubes) and standard (e.g. inches, feet, centimeters) units of measure. Students also measure time as they practice naming, notating and telling time on digital and analog clocks.
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Third graders are encouraged to become deep and flexible mathematical thinkers by the introduction of skills and concepts that students explore through problem solving, games and activities. They are exposed to challenging, meaningful problems that allow them students of varying levels to be appropriately challenged and feel successful. The emphasis is on developing and practicing different strategies for finding solutions, rather than on getting the right answer. Students often work with a partner or group during math. Rich mathematical conversations are promoted by encouraging students to present and explain their strategies to their peers, who then respond with thoughts or questions. In this way, multiple approaches to a solution are considered.
Third grade math units include: an extensive study of place value and two- and three-digit addition and subtraction; an exploration of measurement, area, perimeter, and two-dimensional shapes; an introduction to the concept of multiplication and its relationship to division; an introduction to fractions; and a study of patterns, functions, and change. Throughout each unit, third graders are encouraged to record their ideas and strategies in clear and organized ways, as well as communicate their thinking verbally and in writing.
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Fourth Grade work with whole numbers and operations focuses on multiplication and division, and on extending knowledge of the base-ten number system to 10,000. Students use models, representations, and story contexts to help them understand and solve multiplication and division problems. By the end of the year, students are expected to solve multi-digit addition and subtraction problems efficiently, know their multiplication combinations to 12 x 12, and use the related division facts. Students work with fractions in the context of area, as a group, and on a number line. Fourth graders reason about fraction comparisons, order fractions on a number line, and use representations and reasoning to add fractions. Measurement work includes linear measurement (with both U.S. standard and metric units), area, angle measurement, and volume. Children work together to solve real world problems using a variety of strategies. Accuracy, efficiency, and flexibility are the goals throughout the mathematics curriculum.
