 ### Mathematics (Upper Elementary)

Upper Elementary students do their basic computations abstractly, as they use advanced Montessori manipulatives to explore more challenging concepts.

Increasingly capable of abstract thought, Upper Elementary students begin to do their basic computations abstractly, leaving materials behind. However, they also extend the concrete work of their earlier years. They carry the experiences from previous work into more challenging areas: expanding polynomials, computing square and cube roots, and exploring calculations in various numeration bases.

Montessori manipulatives help them understand concepts and procedures for work with fractions and decimals, and enable them to derive formulas for calculating areas, volumes and surface areas. Students explore preliminary concepts of algebra.

Geometry lessons involve nomenclature of polygons and geometric solids. Students are introduced to the etymology of geometry terms. The concepts of similarity, congruence, and equivalency are presented in numerous ways. Students work to establish equivalency theorems and cover perimeter, area, and volume. Contrary to traditional educational approaches, students learn to develop geometric theorems through hands-on exploration.

The Montessori curriculum allows the student to explore and make meaning in our world. It encourages students to become independent, lifelong learners who are ready to assume responsibility in the greater community.

The curriculum is organized around the following objectives:

• Acquisition of the concepts of number and quantity, including fractions, decimal fractions, improper fractions and mixed numbers, squares and square roots, cubes and cube roots, and irrational numbers.
• Use of numeration symbols and mathematical notation including: reading decimal fractions; using a “radical” symbol; comparing numbers; using the associative and distributive properties with polynomials; and using positive and negative numbers.
• Development of number theory including studies of multiples and factors and understanding decimal fractions.
• Using of the concept of place value to express numbers in expanded and exponential notation.
• Development of a vocabulary of mathematical terms, including key words for operations, fractions; nomenclature of plane figures, solids, angles, and lines.
• Ability to perform abstract operations on whole numbers, fractions and decimal fractions; using order of operations.
• Memorization of math facts
• Data collection and representation including use of line plots, bar graphs and line graphs; applying the basic concepts of probability.
• Evaluation and use of a variety of problem solving strategies
• Understanding of measurement units: derivation and use of formulas for the calculation of perimeters, circumferences, areas of circles, surface areas and volumes of solids.
• Use of nomenclature of geometric shapes and solids including plane figures; congruence/similarity/equivalence; solid geometric figures; and the Pythagorean theorem.