Upper Elementary Curriculum

(grades 4, 5 & 6)

Upper Elementary: A Defining Period for Intellectual Exploration

Montessori described the upper elementary child as entering the world of reason and emerging into a rich, new world of the abstract. While at the children’s school, they were interested in things, and now they will begin to focus mainly on the how and the why. Elementary students want to use their evolving powers of reason to come to their own conclusions. Teachers present ideas, spark motivation and introduce materials that allow children to access the richness of the world's knowledge. 





The Decimal System: The Four Operations of Arithmetic in Upper Elementary

Fractions, Decimals, Percents, Money, and Ratio and Probability in Upper Elementary

Powers of Numbers and Roots of Numbers in Upper Elementary

Measurement in Upper Elementary

Statistics and Graphs during the six Elementary years
Summary of Upper Elementary Mathematical Fields of Study

Geometry in Upper Elementary

Cultural: History

Cultural: Science

Life Science

Physical Science

Earth Science

Scientific Reasoning and Technology


Writing with clarity and reading with fluency are important goals of the language curriculum.  In reading, students continue to grow skills of decoding and fluency, semantics and syntax, vocabulary, literature and genres, and research skills. With a more sophisticated level of language comes greater refinement in its use. While students continue to benefit from concrete experience with concepts in grammar and mechanics, they also explore the study of language as an ongoing creative process of research, ideas, and imagination.

Reading: Upper elementary students meet multiple times per week in small Literature Circles. In a roundtable format, they discuss a text, ask questions, and explore challenging literary concepts such as symbolism, theme, character, and plot development. During each session, students take on roles (e.g., summarizer, discussion director, word finder, connector) that empower them to participate, lead discussions, and gain multiple perspectives. Literature Circles help strengthen reading comprehension through discussion of open-ended questions, making predictions, reviewing character traits, identifying foreshadowing, and drawing inferences and conclusions. They also heighten awareness of author’s craft and how those elements can benefit a student’s own writing. Reading fluency is boosted through Reader’s Theater and other proven methods. We highly encourage reading aloud in school as well as at home. Supplemental reading also occurs with many Montessori “works”. The children frequently work with Grammar boxes, Sky Scrapers, and S.R.A. Reading Laboratory stories.


Writing: The continued development of 6-Trait Writing, and the steps in the writing process, including drafting and editing, span the upper elementary years. The skills are taught in context as students explore various types of writing. Character and setting descriptions are among the more refined writing techniques introduced during the Upper Elementary years. More challenging poetic and prose forms are explored. Advanced punctuation, keyboarding and word processing skills are also taught. Students learn how to organize and write a logical essay. They have opportunities to write expository and persuasive essays, and to read their writing aloud to their peers. Interwoven in our study of writing, a more advanced classification of all the parts of speech is undertaken. Principal parts of the verb, such as infinitives and participles, are introduced along with their advanced grammar symbols. By using these colorful grammar symbols, the study of style in writing comes alive visually for the children. Compound and complex sentences are studied and the classification of phrases and clauses are presented. The students are also introduced to the art of sentence diagramming. All the areas of word study undertaken in Lower Elementary classrooms are explored at a deeper level. More complex word derivations (especially Latin and Greek), analogies, figures of speech, and literary expressions are introduced systematically over the three years.


An understanding of the process takes precedence over memorization in the upper elementary math curriculum.  Concepts are first presented in the most concrete way possible with materials.  This supports students as they grow to understand facts and concepts and eventually shift to abstraction.  In addition to Montessori math manipulatives, they work with complementary written assignments and curricular materials that reinforce specific math concepts and skills. Students meet with teachers in small skills-based groups throughout the week to receive direct instruction. As they progress through the curriculum, gain momentum, and make developmental strides, we help them build the critical skills and strategies of mathematical problem-solving. This further supports students as they prepare for the rigors of the Middle School mathematics program.  Advanced topics include estimation, fractions, and decimals, solving for an unknown, lines and angles, plane figures, math facts tables, squares and cubes, positive and negative integers, mixed numbers, triangles and circles, calculation of area, the volume of prisms, and the theorem of Pythagoras.


The Decimal System: The Four Operations of Arithmetic in Upper Elementary

Students tackle more complex problems such as using two and three-digit multipliers and divisors. They still use materials when needed, but are now often working solely on paper. Practice with the four operations of arithmetic continues as they work on their speed and accuracy. Non-decimal bases are also explored with beginning with manipulative materials. As students now move towards greater abstraction, they also work in a math workbooks and take periodic mastery tests.


Fractions, Decimals, Percents, Money, and Ratio and Probability in Upper Elementary

Upper Elementary students learn the more complex operations with fractions, such as division of a fraction by a fraction. These are first explored with manipulatives and then the rules of the operations are memorized. Working with decimals and percents and their conversions to fractions is a focus of the Upper Elementary years. Money problems such as calculating a tip, sales tax, interest problems are undertaken. Students learn about the concepts of ratio and proportion and problem solve using these concepts. Probability is also explored.


Powers of Numbers and Roots of Numbers in Upper Elementary

Further exploration of the powers of ten in the Upper Elementary classroom leads to the study of scientific notation. Squaring and cubing work prepares students for the extraction of square roots and cube roots. They may explore other polynomials according to interest. Montessori mathematics materials allow students to do this complex work in a very concrete way and gradually work their way towards abstraction.


Measurement in Upper Elementary

US customary and metric measures are memorized and the temperature scales are introduced. Students explore the concepts of area and volume and derive formulae using hands-on Montessori materials. Unit conversions within and between systems are learned and practiced.

Statistics and Graphs during the six Elementary years

Data collecting and organization begins at the Lower Elementary level with surveys and learning to find the mean. Students learn how to represent data using a variety of graphs. At the Upper Elementary level, students learn other central tendency measures such as mode and median, and the interpretation and reading of all kinds of graphs.


Summary of Upper Elementary Mathematical Fields of Study Include:

Reading and writing numbers

  • Ones, tens, hundreds, thousands, millions, billions

  • Comparing numbers

  • Greater than, less than

  • Introduction to estimation  


Rounding: Ones, tens, hundreds, thousands, millions, billion


Static and Dynamic Division

  • Divisibility

  • Estimation

  • Word problems


Static and Dynamic Multiplication

  • Geometric multiplication

  • Powers of numbers

  • Ten to the power 1-6

  • Powers of two cube

  • Explore powers

  • Exponential notation

  • One set of multiples 1-6

  • More than one set of multiples

  • Least Common Multiple


Problem-solving/word problems

  • One step

  • Two step

  • Multiple step



  • Greatest common factors

  • Factor trees

  • Prime factors Fractions

  • Equivalence • Simplifying

  • Changing improper fractions to mixed numbers and vice versa

  • Adding and subtracting like denominators

  • Adding and subtracting mixed numbers with like denominators

  • Adding and subtracting with different denominators

  • Multiplying fractions and mixed numbers

  • Dividing fractions and mixed numbers





  • Reading and writing decimals, tenths—billionths

  • Addition, subtraction, multiplication, division

  • Changing decimals to fractions and fractions to decimals



  • Fraction to decimal

  • Decimal to percent

  • Percent to fraction

  • Word problems


Ratio and Proportion

  • Concept, language, and notation

  • Ratios as an indicated division

  • Problem-solving



  • Number line

  • Negative snake addition

  • Negative snake subtraction

  • Comparing integers


Rules for functions Introduction to Algebra

  • Concept of equation, balancing equations

  • Isolating the unknowns

  • Order of operations

  • Word problems

Geometry in Upper Elementary

The formulae for area and volume are derived and mastered during the Upper Elementary years. These formulae are a point of arrival after much exploration, not a point of departure. The work involves a lot of investigation of the equivalency relationships of various figures and includes a deep study of the Pythagorean Theorem (arithmetical, geometrical and Euclidean proofs) using Montessori materials specially prepared for this purpose. Students learn to describe their proofs using precise terminology. They also practice a graduated series of geometric constructions using compass and straight edge. Once the number line is mastered, students are introduced to the concept of the coordinate plane. The concepts of ordered pairs, slope and intercept are presented.

Cultural: History

The history and social studies curriculum strives to introduce ideas that students can really ponder. The Great Lessons, developed by Maria Montessori, offer a panoramic view of the universe and a sense of humanity across time as the basis for learning. The great questions that arise from this view then serve as a blueprint for further study in all cultural areas. The origin of the universe, the formation of Earth, the fundamental needs of human beings, the history of writing, the measurement of time, early and modern humans, ancient civilizations, and American history are all introduced and studied.


IMS presents a school-wide, three-year cycle of content so special events such as cultural festivals, assemblies, field trips, and reading lists can be thematically planned for the whole school. The three-year cycle of Cultural Studies content—covering Ancient, American and World Civilizations. Each level delves into the year's subject according to its appropriate developmental capabilities. Students continue to study geography in more detail.  The structure of the Earth, physical geography, political geography, and mapping are included in the Elementary curriculum. 

Cultural: Science

Students are introduced to numerous ideas and topics in science over the course of the Upper Elementary years.  Some introductory topics include chemistry, physics, astronomy, geology, and meteorology.  More advanced study includes the scientific method, the periodic table of elements, atomic structure, biochemistry, photosynthesis, mechanics, electricity, and human biophysics.  Topics in biology include the comparative study of vertebrates, botany, classification, microbiology, evolutionary biology, and human biology.


Life Science

  • Environments

  • Food and nutrition

  • Biology: Human, plant and animal


Physical Science

  • Physics of sound

  • Magnetism and electricity

  • Levers and pulleys

  • Mixtures and solutions


Earth Science

  • Solar energy

  • Land forms


Scientific Reasoning and Technology

  • Variables

  • Measurement

  • Models and design​