xiForeword
Telling The STory of MaTh
Each module in Eureka Math builds carefully and precisely on the content learned in
the previous modules and years, weaving the knowledge learned into a coherent whole. This
produces an effect similar to reading a good novel: The storyline, even after weeks of not
reading, is easy to pick up again because the novel pulls the reader back into the plot
immediately—the need to review is minimal because the plot brings out and adds to what
has already happened. This cumulative aspect of the plot, along with its themes, character
development, and composition, are all part of the carefully thought-out design of the Eureka
Math curriculum.
So what is the storyline? One can get a sense of how the story evolves by studying the
major themes of A Story of Units, A Story of Ratios, and A Story of Functions.
A Story of Units investigates how concepts including place value, algorithms, fractions,
measurements, area, and so on can all be understood by relating and manipulating types
of units (e.g., inches, square meters, tens, fifths). For example, quantities expressed in the
same units can be added: 3 apples plus 4 apples equals 7 apples. Likewise, 3 fifths plus 4 fifths
is 7 fifths. Whole number multiplication, as in “3 fives = 15 ones,” is merely another form of
converting between different units, as when we state that “1 foot = 12 inches.” These similari-
ties between concepts drive the day-to-day theme throughout the PreK–5 curriculum: each
type of unit (or building block) is handled the same way through the common features that all
units share. Understanding the commonalities and like traits of these building blocks makes it
much easier to sharply contrast the differences. In other words, the consistency of manipula-
tion of different units helps students see the connection in topics. No longer is every new
topic separate from the previous topics studied.
A Story of Ratios moves students beyond problems that involve one-time calculations
using one or two specific measurements to thinking about proportional relationships that
hold for a whole range of measurements. The proportional relationships theme shows up
every day during middle school as students work with ratios, rates, percentages, probability,
similarity, and linear functions. A Story of Ratios provides the transition years between
students thinking of a specific triangle with side lengths 3 cm, 4 cm, and 5 cm in elementary
school to a broader view in high school for studying the set of all triangles with side lengths
in a 3:4:5 ratio (e.g., 6:8:10, 9:12:15).
A Story of Functions generalizes linear relationships learned in middle school to
polynomial, rational, trigonometric, exponential, and logarithmic functions in high school.
Students study the properties of these functions and their graphs and model with them to
move explicitly from real-world scenarios to mathematical representations. The algebra
learned in middle school is applied in rewriting functions in different forms and solving
equations derived from one or more functions. The theme drives students to finish high