Major MatheMatICal theMeS In eaCh Grade Band | 17polynomials. In Precalculus, students may compare the advantages of carrying out
simulations using manipulatives (e.g., coins or dice) versus creating a simulation using
a graphing calculator or computer software. In Module 2, students use calculators and
computer software to solve systems of three equations and three unknowns using
matrices. Computer software is also used to help students visualize three-dimensional
changes on a two-dimensional screen and in the creation of video games.mp.6. attend to precision.
Students are asked to attend to precision in all modules when they are precise in defining
variables and when they use appropriate vocabulary and terminology when
communicating with each other.
In Module 1 of Algebra I, students formalize descriptions of what they learned before
(e.g., variables, solution sets, numerical expressions, algebraic expressions) as they build
equivalent expressions and solve equations.
In Geometry, a clear application of this standard is found throughout the modules when
students carry out constructions. Precision in carrying out the steps in a construction is
critical in establishing and verifying geometric properties. This holds true for precisely
measuring line segments and angles. In Module 3, students formalize definitions, using
explicit language to define terms, such as right rectangular prism, that have been
informal and more descriptive in earlier grades.
One example where precision is apparent in the Algebra II curriculum is in describing
functions. The curriculum requires students to distinguish the attributes of a function,
including its equation, inputs, outputs, domain, and range, and to identify the graph of
the function and its features. It is important, for instance, for students to understand
that transformations are applied to the graphs of functions and that fx()= 2 x is an
equation representing linear function f whose inputs are represented by x, whose
outputs are represented by 2x, and whose graph passes through the origin.mp.7. Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. They
can see algebraic expressions as single objects or as a composition of several objects.
In Module 4 of Algebra I, two explicit cases illustrate how the Eureka Math curriculum
supports students’ making use of structure. First, in Lesson 2, several exercises require
students to multiply binomials, and the structural similarities of the expanded products
help students recognize patterns that enable them to factor quadratic trinomials into a
product of two binomials. Several lessons in Topic C provide opportunities to explore
the relationship between the structure of a function equation and the relationship to its
graph. Specifically, students recognize how changing parameters in function equations
affects the graphs of parent functions for quadratic functions, as well as cubic, square
root, and cubed root functions.
The Algebra II curriculum provides expanded opportunities for students to recognize
structure. Students apply their understanding of transformations of parent graphs
from Algebra I to the graphs of exponential and logarithmic functions in Module 3 and
graphs of trigonometric functions in Module 2. In Module 3, students extend the laws of
exponents from integer exponents to rational and real number exponents. They connect
how these laws are related to the properties of logarithms and understand how to
rearrange an exponential equation into logarithmic form.