Major MatheMatICal theMeS In eaCh Grade Band | 15exponential models. Then they contextualize their work so that they can compare sets of
data, make predictions, and evaluate claims. Similar opportunities are provided in Algebra
II, where students decontextualize real-world situations to represent them with function
equations. In Precalculus, students decontextualize data, representing it in matrix format,
performing operations with matrices, and then interpreting the results in context.
In Geometry, students work with figures and their transformed images using symbolic
representations and need to attend to the meaning of the symbolic notation to
contextualize problems.
Quantitative reasoning is demonstrated explicitly in the statistics modules throughout A
Story of Functions. For instance, in Algebra I Module 2, students use conditional relative
frequencies to determine whether variables are associated, and they compare conditional
probabilities in Algebra II Module 4 to determine whether two events are independent.mp.3. Construct viable arguments and critique the reasoning of others.
Partner sharing is woven throughout lessons to create ongoing, frequent opportunities
for students to develop this mathematical practice. Students use drawings, models and
numeric representations, and precise language to make their learning and thinking
understood by others. Discussions are also woven into the lessons, and these portions
of the lessons include questions that require students to construct arguments, form
conjectures, and use established properties to test them. The discussion times also allow
students to present counterexamples to arguments generated by others.
An example of how the Algebra I Eureka Math curriculum supports this mathematical
practice is found in Module 1. When students solve equations, they do so in an if-then
format, where they are encouraged to construct arguments that justify how they
progress from one step to another when they isolate a variable. This type of critical
thinking is valuable for students as they progress to solving equations with complex
solutions and where they will perform operations on equations that could introduce
extraneous solutions.
In several modules in the Eureka Math Geometry curriculum, students are required
to construct arguments about properties of objects. In Geometry Module 1, students
construct arguments about unknown angle measures using formal proofs. In Module 2,
they construct arguments to establish the criteria for similar figures in terms of dilations.
Module 5 also requires students to construct arguments that justify constructions and to
develop proofs related to circles.
In Algebra I Module 2, students examine the shape, center, and variability of a data
distribution and use characteristics of the data distribution to communicate, in the
form of a poster presentation, the answer to a statistical question. Students also have
an opportunity to critique poster presentations made by other students. In Algebra II,
students are required to construct viable arguments throughout Module 4 as they
carry out hypothesis testing to compare a treatment group to a control group. This is
continued in Precalculus, where students use laws of probability to justify decisions in a
variety of real-world contexts, such as sports, financial investments, and medical care.
Throughout Module 1 in the Precalculus course, students critically analyze conjectures
commonly formed by algebra students, and they are required to determine the validity
of those arguments. Deciding on the validity of an argument focuses students on
justification and argumentation as they work to decide when purported algebraic