Preschool to Kindergarden: In Pre-Kindergarten and Kindergarten students are beginning to understand how to represent the physical world with mathematical language and symbols. With teacher assistance, students are able to use these representations to solve simple problems including drawing pictures to represent problems, creating and solving one-step story problems and solving addition and subtraction work problems.

Lower School: Students use appropriate mathematical vocabulary, symbols, and notation to communicate mathematical ideas. Students use developing reasoning skills to identify patterns and relationships, select appropriate strategies, solve problems and justify and test solutions. By fifth grade, students are able to use trial and error and the process of elimination to solve problems, write a number sentence or symbolic expression based on a problem, communicate mathematical thinking, select appropriate math vocabulary in oral and written form and use various visual aids (lists, tables, graphs) to solve problems and communicate results.

Middle School: After the completion of middle school, students will also be able to use inductive and deductive reasoning in mathematical situations and applications, solve word problems using individual and collaborative methods to investigate and comprehend mathematical content and its applications, and use the precise language and special symbols of mathematics.

Preschool to Kindergarden: In Pre-Kindergarten and Kindergarten, students grasp the relationship between number and quantity which allow counting, simple addition and subtraction, and comparing. Students are able to count objects with a one-to-one correspondence to 100, understand place value, perform simple addition and subtraction and understand basic fraction concepts.

Lower School: By the end of third grade, the student has a strong understanding of number concepts and now has a good understanding of place value. The student understands and can easily perform the four basic operations with whole numbers as well as understand the simple relationship between whole numbers, simple fractions, and decimals. By the end of fifth grade, among many other skills, students are able to identify and distinguish among whole numbers, integers, fractions, decimals, proportions, and percents, apply basic number theory concepts (e.g. positive and negative numbers, odd and even numbers, prime and composite numbers, factors, multiples, divisibility), write the family of equations using inverse operations for a given set of numbers, divide with and without remainders using 3-/2-digit combination, illustrate quotient as a remainder, fraction, or decimal, calculate squares and square roots, represent exponents and powers as repeated multiplication, interpret equivalent forms of basic percents, fractions, and decimals and when one form of a number might be more useful than another, demonstrate how fractions relate to decimals and percents, recognize and apply basic concepts or ratio, proportion, and percent and compare how ratios and proportions are related to fractions and percents.

Middle School: After the completion of middle school, students should have achieved mastery of the topics covered in Algebra I, including the ability to define and apply algebraic properties of equality and inequality to real numbers (commutative, associative, distributive, additive inverse, multiplicative inverse, additive identity, multiplicative identity, zero product, transitive, reflexive, symmetric), use the symbols of inclusion: absolute value, negative numbers, opposites, order of operations, parentheses, braces, brackets, perform operations with exponents including operations with positive, negative, and fractional exponents, demonstrate conversion to scientific notation, simplify numerical expressions by applying properties of real numbers, explain and apply the inverse operations to simplify computations and solve problems, select and apply appropriate methods and tools for computing in a problem situation and compute square roots, cube roots, fourth roots, and roots of large numbers.

Preschool to Kindergarden: At this age, students are aware that objects have properties that can be described and compared. They are able to measure time and money in simple units, including the ability to use appropriate vocabulary to describe various measurements, compare, order and measure objects according to a given attribute (e.g., size, length, weight, volume, etc.), interpret a calendar using appropriate vocabulary, tell time (to the hour) using appropriate vocabulary, recognize and name currency (penny, nickel, dime, and one dollar bill) by sight and identify the value of coins (penny, nickel, dime) and dollar bill.

Lower School: With a broader set of vocabulary and tools to quantify properties of objects, students can measure quantities with the appropriate units and use these measurements to compare quantities. With an ability to grasp the concept of equivalence, students are able to understand and use conversion charts. By third grade, some specific skills include the ability to compare and order objects according to a given attribute, solve word problems involving measurement concepts and skills, understand use of conversion charts (e.g., feet to inches, yards to feet, etc.), investigate perimeter and area relationships, compare, estimate, and measure volume of objects using standard and metric system and compare, estimate, and measure temperature using both the Fahrenheit and Celsius scale. By the end of lower school, some specific skills and content areas include the ability to explain basic types of measures (perimeter, area, capacity, volume, weight, angle, circumference, temperature, and time), demonstrate the conversion of units (i.e. standard or metric), compare and estimate perimeter (or circumference) and area of regular and complex polygons, circles, triangles, parallelograms, and trapezoids using standard and metric system, describe the relationship between area and perimeter and develop strategies and use formulas to determine the circumference of circles and the area of circles, triangles, parallelograms, and trapezoids, determine the volume of selected prisms, pyramids, cones, and cylinders.

Middle School: After the completion of middle school, in addition to the previous skills, students will be able to approach every concept from four different perspectives: analytic, numeric, graphical, and verbal, convert between customary and metric units of length, area, and volume, apply estimation techniques in a variety of real-life situations and select and use appropriate units and tools depending on degree of accuracy required to find measurement.

Preschool to Kindergarden: In Preschool and Kindergarden, students understand and use simple vocabulary to describe physical space as well as identify common shapes and features. They are able to understand the meaning of terms of orientation and position (e.g., inside, outside, between, left, right, etc.), name and understand the basic properties (e.g., number of sides, corners, angles, etc.) of common geometric shapes (circles, squares, and triangles), draw common geometric shapes, and identify lines of symmetry.

Lower School: As students move through the lower school, they will be able to understand the basic properties of, and similarities and differences among, a variety of shapes, understand line of symmetry and use motion geometry to investigate concepts of symmetry, similarity, and congruence, solve problems involving spatial relationships (e.g., perimeter area, tessellations, symmetry). By the time they complete lower school, they will, among other skills, be able to relate map scales to relative size and distance, use correct terminology for describing various shapes, and figures, and their attributes, draw geometric shapes and solids, compare, classify, and measure geometric shapes, draw, define, and identify the characteristics of points, lines, segments, rays, and angles, and represent and solve problems relating to size, shape, perimeter (circumference), and area of rectangles, triangles, and circles using geometric models.

Middle School: After the completion of middle school, in addition to the previous skills, students will be able to classify and measure geometric shapes, apply coordinate geometry to locate and explore points, lines, slopes, and geometric figures algebraically, explain the concept of parallel and perpendicular lines and how their slopes are related, use the Pythagorean Theorem to find missing sides of triangles and determine a right triangle and use trigonometric ratios to find the missing side or angle of a right triangle.

Preschool to Kindergarden: In Preschool and Kindergarden, students recognize patterns and are able to copy or construct simple patterns. Some specific skills include the ability to understand that patterns can be made by putting different shapes or objects together, copy and construct designs and patterns, identify and extend basic patterns (using number or objects), and manipulate patterns.

Lower School: As students mature and build upon their skills, they will be able to recognize basic number patterns, make, copy, and extend patterns, find common attributes among figures in a set, read, work with, and represent time, write amounts of money using appropriate signs and decimal points, and make change using as few coins as possible. By the end of fifth grade, students will be able to recognize, explore, model, and describe a variety of patterns, and identify the rules that explain them, describe how a pattern can be developed into a series represented geometrically or numerically, define variables that stand for one or more numbers, learn appropriate use of symbols and apply the basic concept and use of comparison signs (<.>.=) and parenthesis and solve simple open sentences involving operations (e.g., missing addends and/or symbols).

Middle School: After the completion of middle school, students will have completed all the content of High School Algebra I, enabling them to begin their High School career with Geometry. Some of the important skills they will acquire include the ability to generalize patterns using defined and repeating functions, use patterns and functions to solve problems, distinguish between relations and functions, represent situations and mathematical relationships that involve variable quantities with expressions, equations, and inequalities, evaluate algebraic expressions, examine and simplify expressions containing integral exponents, solve equations and inequalities, solve systems of (mostly linear) equations and inequalities, apply algebraic techniques to solve rate problems and solve rational equations.

Preschool to Kindergarden: At this age, students are able to collect and organize information about objects or events in their environment. Students are able to collect and organize simple data, understand simple graphs, understand that observations about objects or events can be organized or displayed in simple graphs (e.g., calendar, temperature, weather graphs, shapes, etc.), interpret graphs (e.g., answer simple questions regarding the data they contain) and describe things as similar or not similar.

Lower School: As students continue into the lower school, they will be able to collect, classify, organize, and compare data, understand that observations about objects or events can be organized or displayed in graphs, charts, and diagrams, read and interpret a variety of tables, graphs, charts, and diagrams, and understand that one can find out about a group of things by studying just a few of its members. As they complete the lower school program, students will be able to categorize data in various forms and illustrate that collecting, organizing, and displaying data can be done in various ways, create appropriate graphs given the data to be analyzed, collect and organize data for graphical representation (pictographs, line graphs, bar and circle graphs; pie charts), read and interpret pictographs, line graphs, bar graphs, and pie charts, use the concept of probability and samples to predict events and outcomes, analyze historical data and make a statistical prediction, classify samples by describing sets and data and make valid inferences, predictions, and arguments based on simple data analysis.

Middle School: By the end of middle school, in addition to the skills above, students will be able to construct and interpret representations of data, interpret and make predictions from data, use sampling procedures and understand the concept of bias in sampling, use counting techniques to compute probability including simple probability, independent events, and product of probabilities, summarize data using measures of central tendency and understand the meaning of measurement data and categorical data, of univariate and bivariate data and of the term variable.