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56 | eUreka Math algebra I StUdy gUIde
Focus Standards: N-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step
problems; choose and interpret units consistently in formulas; and choose and interpret
the scale and the origin in graphs and data displays.★
N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.★
N-Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities.★
A-CED.A.2 Create equations in two or more variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales.★
Instructional Days: 5Student Outcomes
Lesson 1: Graphs of Piecewise Linear Functions
● (^) Students define appropriate quantities from a situation (a graphing story), choose and
interpret the scale and the origin for the graph, and graph the piecewise linear
function described in the video. They understand the relationship between physical
measurements and their representation on a graph.
Lesson 2: Graphs of Quadratic Functions
● (^) Students represent graphically a nonlinear relationship between two quantities and
interpret features of the graph. They understand the relationship between physical
quantities via the graph.
Lesson 3: Graphs of Exponential Functions
● (^) Students choose and interpret the scale on a graph to appropriately represent an
exponential function. Students plot points representing the number of bacteria over
time, given that bacteria grow by a constant factor over evenly spaced time intervals.
Lesson 4: Analyzing Graphs—Water Usage During a Typical Day at School
● (^) Students develop the tools necessary to discern units for quantities in real-world
situations and choose levels of accuracy appropriate to limitations on measurement.
They refine their skills in interpreting the meaning of features appearing in graphs.
Lesson 5: Two Graphing Stories
● (^) Students interpret the meaning of the point of intersection of two graphs and use
analytic tools to find its coordinates.
Topic B: The Structure of Expressions
In Lessons 6 and 7 of this topic, students develop a precise understanding of what it
means for expressions to be algebraically equivalent. By exploring geometric representations
of the distributive, associative, and commutative properties for positive whole numbers and
variable expressions assumed to represent positive whole numbers, students confirm their
understanding of these properties and expand them to apply to all real numbers. Students
use the properties to generate equivalent expressions and formalize that two algebraic
expressions are equivalent if we can convert one expression into the other by repeatedly
applying the commutative, associative, and distributive properties and the properties of
rational exponents to components of the first expression. A goal of this topic is to address a
fundamental, underlying question: Why are the commutative, associative, and distributive
properties so important in mathematics?^4 The answer to the question is, of course, that these
three properties help generate all equivalent algebraic expressions discussed in Algebra I.