2025-26 Course Descriptions - Catalog - Page 8
MATHEMATICS
IONS
As students join the Field community as 6th
graders, they are wrestling with ideas both
mathematical and personal: Who am I as a
mathematician? What does it mean to be part of
a math community at Field? In the IONS (Integers,
Operations, and Number Sense) course, they
begin answering this question with a study of
data representation and visualization to support
their understanding of statistics that may come
up in history and science classes, and to begin
to use mathematics to help make sense of
the world around them. Students then explore
ratios and proportional relationships across a
variety of contexts, solving complex problems
that apply to life outside the classroom. In other
investigations they extend their understanding
of computation with positive whole numbers to
deep understanding of operations with fractions,
decimals, and negative numbers. In geometry,
students go beyond memorizing names of shapes
to deriving the formulas for area, surface area,
volume, and angle measure of polygons and
polyhedra. Throughout the year they begin to
make sense of equalities and inequalities with
algebraic notation and learn to think and work like
mathematicians—collaborating on teams, making
conjectures and gathering supporting evidence,
and communicating their ideas to each other and
the wider community.
ALGEBRA A
The main throughline for Algebra A is “Math is
about relationships,” which has both personal
and mathematical meanings. On the personal
level, students re昀氀ect on their own identity as
mathematicians and practice the skills important
to functioning as a community: collaborating on
teams, using evidence to support arguments,
communicating their ideas and evaluating the
ideas of others. Mathematically, they delve into
these skills as they develop deep understanding
of independent and dependent variables,
proportional relationships, and equations and
inequalities. Throughout the year, students apply
these concepts to complex, open-ended problems
across a variety of contexts. Through a study of
percentages, they investigate the question, “How
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does math help us make better decisions?” In a
unit on geometry, they build upon previous work
with polygons as they explore, not as an irrational
number but as a representation of the ratio of
circumference to diameter. In other investigations,
students examine what the word “opposite” means
in math, including inverse operations and positive
and negative integers, decimals, and fractions. In
all units, students look for patterns across problems
and make explicit connections among the models,
algebraic equations, and graphs that represent
mathematical situations they will encounter both in
future math and science classes and in their lived
experiences.
