Mathematics Overview

The mathematics curriculum at Friends School Haverford is based on the National Council of Teachers of Math Principles and Standards for School Mathematics (2001) and the Common Core State Standards for Mathematics (2011). Sense making and thinking are core to all aspects of the curriculum. Students explore real world topics, solve problems, investigate space and time, practice computation and communicate their thinking through discussion and writing. They work cooperatively and independently on tasks based on their own developmental levels. Calculators and computers are used in all grade levels from K-8.

Friends School Haverford uses Math Trailblazers (published by Kendall/Hunt) as their main resource for math instruction in grades Kindergarten through 4. The Middle School uses Math Trailblazers, Connected Math (published by Prentice Hall) and a variety of other resources as they move into a formal study of algebra.

Lower School Mathematics


The preschool math curriculum builds a foundation for our youngest students’ number sense, number symbol identification, and general mathematical reasoning. Preschoolers are invited to use number sense and mathematical reasoning to make sense of the world. Students discuss the daily class schedule using ordinal numbers; they are encouraged to seek linear patterns in nature and create their own using beads, colored cubes, or other materials; they play games that develop basic logic, reasoning, and spatial awareness. Preschool teachers introduce students to mathematical tools like clocks, calendars, graphs, and diagrams. Some additional units of mathematical study include shape identification, more and less than, zero/null sets, sorting, and symmetry.


The primary goal of pre-k math is foundational understanding. In order to build our students’ understanding of numbers and their relationship to the world, the curriculum explores mathematical concepts through concrete, hands-on demonstrations, and individual and group experimentation with multi-sensory play. Some math concepts include patterning, sorting, spatial relationships, geometry, and measurement. In addition to the daily math curriculum, the weekly math question gives the class the opportunity to further discuss numbers and their relationships to one another.


Kindergarten math capitalizes on our students’ curiosity and wonder at the world around them. Through experiential learning, independent exploration, and cooperative investigation, our students become knowledgeable about the world and versatile in expressing how they understand math in their everyday lives. Kindergarten math is integrated across the academic curriculum and takes place inside the classroom, out in the playgrounds and fields, and during cooperative service learning projects. Whether inside the classroom or out, students learn about the world by sorting, graphing, tallying, counting, and constructing. Multi-sensory, hands-on activities encourage every kindergartner to actively participate. Kindergarten is the first year students participate in the school-wide Math Trailblazers curriculum.

First Grade

First grade mathematics centers on building a core understanding of numbers, shapes, and patterns. The curriculum is exciting and vital: the skills first graders develop, and the knowledge they gain, form the basis for all subsequent mathematical thinking. Students learn about measurement, time, money, place value, and the relationships between numbers. Math class consists of teacher-directed lessons, math workshop, and work places. During work places, students explore games and activities that extend and enhance the concepts first graders learn during their math lessons. Students develop their mathematical abilities and expand their mathematical knowledge independently, in pairs, and in groups.

Second Grade

In second grade math, students follow the Trailblazers curriculum, which emphasizes differentiated instruction and hands-on learning. The curriculum focuses on foundational math concepts such as building number sense, working with data, and developing math “tool kits.” Second graders are encouraged to use these tool kits to solve problems, explain their thinking, and expand their available strategies. Math class provides students opportunities to work independently, in partnerships, and in small and large groups.

Third Grade

The third grade mathematics curriculum enables students to investigate new mathematical concepts and learn the basic operations of addition, subtraction, multiplication, and division. Third grade students develop their mathematical understanding through the use of manipulatives, guided exploration, and teacher-directed activities. Students learn to quickly and accurately solve equations and to apply their knowledge to problem solving. Our students learn that while computations have one right answer, many mathematical problems have a number of valid solutions, and that multiple strategies may be used to discover these solutions. Problem solving strategies include sorting, classifying, making graphs, exploring geometric relationships, making predictions, and interpreting statistical information.

Fourth Grade

Fourth grade mathematics emphasizes problem solving, verbal and written communication, and establishing links between previous learning and new concepts. The fourth grade Math Trailblazers curriculum continues to integrate math with science and language arts. Students explore patterns in multiplication and place value, probability, fractions, data prediction, geometry, and more, with an interdisciplinary problem solving focus. Fourth grade’s daily math class includes teacher instruction and supplemental math games. Students learn to use new tools like calculators and computers to help with class work.


Middle School Mathematics

Middle school math functions as a bridge. On one side lies the foundational math education of the primary grades, consisting of concrete work in number sense, calculation, and problem solving; on the other side rests the abstract, generalized language and methods of high school-level Algebra. Each student enters middle school math with an idiosyncratic understanding of primary-level math foundations. At FSH, our Math teachers create a personalized bridge for each student, tailored to her or his mathematical strengths and weaknesses, that ensures each student enters high school prepared and eager to tackle algebra, geometry, and courses beyond.

Middle school students at FSH begin their math coursework by filling any remaining gaps in their foundational math knowledge. Fifth and sixth grade Math Workshop allows students the time to finish developing this foundational base, while also encouraging students to challenge themselves and enter unfamiliar math territory. Units of study include factors and multiples; fraction and decimal operations; ratio and proportion; two-dimensional geometry; and basic probability. Students work collaboratively, constructing new understanding through collective, empirical investigation. Groups of students develop algorithms and methods of problem-solving through scaffolded, hands-on activities, after which their learning is formalized in reflective, class-wide discussion.

In the seventh and eighth grade Math Workshop, students work develop more advanced algebraic and geometrical understanding. Units of study include: statistics; three-dimensional geometry; linear, exponential, and quadratic relationships; the language of algebraic expressions; and function families. Students who have mastered the middle school math curriculum are provided with the opportunity to begin high school-level algebra coursework.