 Millhopper Montessori School
 Math Overview
"This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child's special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They can thus carryout an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations."  Maria Montessori

Beginners (ages 24)
The use of concrete materials in math allows the child to experience the concepts of size, shape, and quantity. Onetoone correspondence, simple pattern work, numeral symbols, quantity, and geometric shapes are introduced in the classroom. Activities include peg work, puzzles, counting materials, use of the long number rods, and lessons with sandpaper numerals. Counting and numeral recognition are also reinforced during large group/circle time activities.
Preschool and Preschool/Kindergarten (ages 36)
The mathematics program introduces concepts in a handson, concrete manner before moving to abstraction. Each concept is isolated and introduced to the child individually; starting with quantity, then numeral symbol, and then the correspondence between the two. This parallels the work in the practical life and sensorial areas that exposes the children to patterning, sequencing, and matching. Each new concept is introduced using stepbystep progression. After the quantities 110 are mastered using a variety of materials, the decimal system is introduced; beginning with work from 1100. This is followed by lessons using the Golden Beads to facilitate understanding of our base 10 system through the thousands. Numeral cards correspond to this work that help the child understand place and value.
The four operations of math (addition, multiplication, subtraction, and division) are presented as well as an introduction to time and money concepts and fractions (Kindergarten). Materials are available for both the conceptual understanding and memorization of basic facts. Two and three dimensional geometric figures and their names are introduced sensorially. In order for the child to move from the concrete to the abstract, much repetition is necessary. Most concepts are introduced using multiple materials, allowing the child to construct mathematical concepts through discovery, rather than through formal teaching. The children progress through the curriculum at their own pace before moving to the next lesson to allow for genuine understanding.
Lower Elementary (ages 69)
Specialized Montessori math materials provide the foundation for the math curriculum. These materials are aesthetically pleasing and reveal relationships in arithmetic, geometry, and algebra, helping students to both understand and memorize. Our materials build upon each other and have similar elements that allow students to master new work quickly. These materials give students the opportunity to have independent practice after receiving teacherdirected lessons, allowing students to progress at their own pace. The students work through the math materials learning about odd and even numbers, greater than/less than, patterning, place value, graphing, time, estimation, rounding, money, decimals, and fractions. The students learn to understand, read, and write large numbers. Our three dimensional hierarchy materials allow students to practice building numbers, combining, borrowing, and exchanging concretely. They work with these and other materials to learn the four basic mathematical operations. The materials allow students to perform operations with large numbers up to billions, an idea that is especially appealing to students at this age. Students move towards abstraction and are introduced to word problems and algebraic concepts. The geometry studies allow students to explore geometric solids, triangles and other polygons, angles, lines, parts of a circle, congruence, equivalence, symmetry, and measurement.
Upper Elementary (ages 912)
The mathematics program introduces all new concepts in a handson, concrete manner before moving to abstraction. By the time students are in upper elementary, they are ready to progress mathematically in abilitylevel groups using textbooks. The curriculum typically includes multiplication and division, multiples and factors, fraction concepts and operations, decimal concepts and operations, ratio and percent, prealgebra concepts, estimation, probability, and data analysis. Students also study geometry, including polygons, geometric solids, area, volume, lines, angles, congruence, similarity, and symmetry. Students are presented with application and computational problems. Logical reasoning, creativity, and problem solving are emphasized. There are several opportunities to apply mathematical knowledge across curriculum subjects.
Middle School (ages 1214)
Math courses utilize Prentice Hall’s Mathematics Courses 1, 2, 3, and Algebra I curriculums that use the National Council of Teachers of Mathematics standards as a basis for teaching concepts through application. There is an emphasis on reading and writing of mathematics, providing a widerange of meaningful problemsolving opportunities, and the incorporation of various technologies. This curriculum is aligned with state and nationally approved educational standards. The students continue their formal math instruction in small, abilitylevel groups. These groups occur at the same daily time block of 4070 minutes per day allowing for the integrity of developmental placement and a wider breadth of math levels to be offered.
The students are placed in groups by means of placement tests at the beginning of each school year.
The levels offered in the sixth through eighth grades are: Mathematics 1, Mathematics 2, Mathematics 3, Algebra I, and *Geometry.
Mathematics Course 1  *Prerequisite: Successful completion of Math Level 5
Mathematics Course 2  *Prerequisite: Successful completion of Mathematics Course 1
Mathematics Course 3  *Prerequisite: Successful completion of Mathematics Course 2
Algebra I  *Prerequisite: Successful completion of Mathematics Course 3 (Successful completion of this course is eligible for high school credit)
Geometry  *Prerequisite: Successful completion of Algebra I (Note: This math course is offered through Florida Virtual School to 8th graders only. Successful completion of this course is eligible for high school credit.)