# Science, Mathematics, Technology

## Science

In Lower Elementary, students learn about the origin and features of the Earth and how it impacts human life. They explore the natural order and laws of the universe, perceive the delicate balance of these natural laws, and begin to see the need for their contribution to maintain the vulnerable vitality of their environment. Topics include: the creation of the universe, the timeline of life, the composition of the Earth, the work of the sun and Earth, the role of air and water, the classifications of animals and plants, ecosystems, light, sound, magnetism and simple machines.

In Upper Elementary, topics include life science, Earth science, comparative anatomy and physical sciences. Classes are hands-on and follow the Scientific Method. Based on initial questions, each class begins with a problem to be solved, a hypothesis being made, and experimentation until a conclusion is formed. Students are encouraged to propose ideas, ask questions, and probe deeply into the subject matter. Students hone their skills of observation and develop the ability to carefully and accurately record what they see and assess any changes they discern over time.

## Technology

In Upper Elementary, students are exposed to word processing, on-line publishing, and collaborative digital communication. They conduct independent research using online resources. All work on the computers is supervised by teachers. iPads are available in most classes for on the spot research and reference use, as well as for communicating through classroom blogs or discussion groups. Students experiment with multiple forms of media to compose, edit, and share responses to books and reflect on topics discussed in their classes.

## Mathematics

The Elementary mathematics program uses Montessori materials and methodologies, Singapore Math materials and other resources. In Lower Elementary, students begin to develop proficiency in mental math and mathematical reasoning. They are encouraged to think flexibly, and to test the accuracy of their work by asking themselves what is reasonable. Topics include the history of numbers and number systems; measurement of length, weight, capacity; understanding of temperature, time, money; place value of whole numbers, common fractions and decimal fractions; ordering, rounding and estimating; addition, subtraction, multiplication and division; addition and subtraction of common fractions and decimal fractions; factors and multiples; graphing; word problem solving; mental math strategies; and commutative and associative properties of numbers.

In Upper Elementary, students develop a more sophisticated understanding of math by deepening their number sense, particularly with fractional numbers, and by deepening their understanding of basic operations. The curriculum emphasizes:

- Algorithms and procedures: In fourth grade, students practice the algorithms for addition, subtraction, multiplication and division with whole numbers as well as with fractions and decimal numbers. They move onto solving proportions, computing the area and volume of regular and irregular figures, and composing and solving algebraic equations. In sixth grade, students study the main principles of probability, data analysis and number theory, applying the skills they have mastered to these new fields.
- Flexibility: An important goal is to enable students to apply their mathematical knowledge flexibly and creatively to solve novel problems, not merely to carry out procedures for solving familiar ones. Students develop number sense by composing and decomposing numbers as they practice mental arithmetic. They develop conceptual understanding of the basic operations and their properties by breaking up and solving arithmetic problems in different ways, looking for an efficient or interesting solution. They study prime numbers, composite numbers and factors in depth to help them gain a deeper understanding of questions involving divisibility.
- Problem-Solving: Students develop confidence in approaching novel problems by gaining exposure to problems that require them to use their own judgment to choose an approach. Students also learn how to approach problems in a strategic way. They develop a repertoire of “rules of thumb” for solving problems such as by starting off with a simpler version of the original problem or drawing a diagram for representing the numerical relationships involved.
- Visualizing numerical and other mathematical relationships: Visualization is important in mathematical understanding. A simple but powerful example is the number line, in which a number’s magnitude is directly related to its position on the line. Students learn to use bar diagrams for representing numerical relationships in word problems, to understand how the slope of a line graph relates to the rate of change and do art projects in which mathematical patterns are displayed graphically.
- Communication: Students practice vervalizing their mathematical thinking in groups and in class discussions. Just as important, however, is the ability to present out one’s work neatly on paper. A student’s understanding is deepened if the student is able to reflect on and articulate his or her own problem-solving methods. Also, by laying out the work in steps on paper, the student is able to take on more and more complex problems and learn to self-correct his or her own work.

## Geometry

In the Primary classroom, children are introduced to geometric shapes and solids, learning how they appear in nature and in manmade structures. In Lower Elementary, students learn to classify shapes, and are introduced to the concepts of congruence, similarity and equivalence, which later are applied to area and volume. They work with straightedge rulers, compasses and protractors to make geometric shapes, and they are introduced to the concepts of perimeter, area and coordinate. In Upper Elementary, students learn to use geometry to understand arithmetic concepts, such as using the area model for multiplication and using graphs to understand rates of change. Additionally, students grow in their understanding of abstract geometry, beginning with points, lines, and angles. Students later learn to classify shapes according to the properties of their lines and angles, such as classifying an isosceles triangle based on the equality of its base angles. In conjunction with these geometric concepts, students learn to calculate different kinds of measurements of shapes, such as their perimeter/ circumference, and area. They also learn to use given information and geometric reasoning to draw conclusions about unknown angle and side-length measurements. The study of solids similarly includes concepts about their building blocks (vertices, edges, and faces), their classification, and their measurement (surface area and volume).