GRADE BAND: HS ALGEBRA
Domain: Seeing Structure in Expressions
Why this domain is a priority for
professional development
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Many teachers will look at the standards and
declare they already teach these. In fact, they
address similar content procedurally without
attending to structure. It is new content for teachers
to look at familiar-seeming expressions and
equations and address questions that get at
structure.
Why this domain is a priority for
professional development

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To start working with teachers, one can present
familiar-looking problems but ask unfamiliar
questions. One might even start with a particular
expression and ask, “Tell me all you can about this.”
For example, 460 (1.93)t
Why this domain is a priority for
professional development

The content of this strand is the upper-grade version
of what we were talking about this morning.
Students need to work back and forth between
symbols and a variety of representations and/or
contexts expressions might be drawn from. They
need to be able to look at the components of an
expression and think about the behavior of the
operations involved to see how the expression
changes with the change of a variable.
Key standards in this domain that pd
should focus on

1. Interpret expressions that represent a quantity in terms of its context.
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a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a
single entity. For example, interpret P(1+r)n as the product of P and a factor not
depending on P.
2. Use the structure of an expression to identify ways to rewrite it. For
example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference
of squares that can be factored as (x2 – y2)(x2 + y2).
3. Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
(These standards are of a larger grain size than the others in this section.)
Key standards in this domain that pd
should focus on

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“Write expressions in equivalent forms to solve
problems”—This should be interpreted with a sense
of purpose. Why should expressions be written in
different forms? What benefits do you get from
each form? Once why is addressed, then get at
how—that is, develop skills of symbolic manipulation.
This cluster needs lots of good examples to get
somewhere with groups of students. Simplification is
a basic category of this statement, but the statement
covers much more.
Domains and standards that are in
need of new resources

In addition to working on the content, PD needs to
support teachers with techniques for asking students
to do something new. Teachers need help in
facilitating purposeful discussion.