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.