Common Core Math
High School Algebra Teaching and Learning Resources
Domain: SSE: Seeing Structure in Expressions
Select the cluster for resources on this page:
SSE-A: Interpret the structure of expressions.
- SSE-A.1. Interpret expressions that represent a quantity in terms of its context.
- SSE-A.1.a. Interpret parts of an expression, such as terms, factors, and coefficients.
- SSE-A.1.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.
- SSE-A.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).
Mathwords.com: Math Dictionary:
Key vocabulary for this domain. Use with SSE-A, SSE-B:
National Library of Virtual Manipulatives:
Algebra Tiles: Visualize multiplying and factoring algebraic
expressions using tiles. Several activities are provided.
Factoring: Factoring differences of squares, sums and
differences of cubes, recognizing patterns. Use with SSE-A.2.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives:
US Common Core State Standard Math HSA-SSE.A.1: 3
manipulatives: Binomial cube, sums of consecutive integers,
US Common Core State Standard Math HSA-SSE.A.2: 9 manipulatives: Binomial cube, sums of consecutive integers, integer
polynomial, multiplying a monomial and a linear polynomial, squaring a
binomial, square of the sum of two numbers, multiplying
binomials, difference of cubes, difference of squares
YouTube video lessons:
Basics: Quadratics and Polynomials: Practice questions with videos.
Use the following with SSE-A.2:
L. Spector: The Math Page: Skill in Algebra. Students see
worked examples of concepts and following the presentation within each
section, students are presented problems in constructed response form.
They would solve using paper-pencil and then by using their mouse to
roll over a box, they see the solution to problems presented. Use
the following with SSE-A.2:
Interpret expressions: 5 questions that combine free
response and multiple choice. Includes related review
resources. Aligns with SSE-A.1.
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SSE-B: Write expressions in equivalent
forms to solve problems
- SSE-B.3. Choose and produce an equivalent
form of an expression to reveal and explain properties of the
quantity represented by the expression.
- SSE-B.3a. Factor a quadratic expression
to reveal the zeros of the function it defines.
- SSE-B.3b. Complete the square in a
quadratic expression to reveal the maximum or minimum value of
the function it defines.
- SSE-B.3c. Use the properties of
exponents to transform expressions for exponential functions.
For example the expression 1.15t can be rewritten as
(1.151/12)12t ≈ 1.01212t to
reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.
- SSE-B.4 Derive the formula for the sum of
a finite geometric series (when the common ratio is not 1), and use
the formula to solve problems. For example, calculate mortgage
Annenberg Learner: Lesson Plan 1:
The X Factor - Trinomials and Algebra Tiles: The activities use a variety of techniques to help students understand
concepts of factoring quadratic trinomials of the form ax2 + bx + c
Glencoe/McGraw-Hill e-Book Assets: Choose
Algebra Tiles under Manipulatives. This virtual
manipulative allows learners to interact with virtual algebra tiles.
MIT BLOSSOMS: Video lessons with additional teacher
and learner resources. Descriptions are from the video summaries.
- The Quadratic Equation: It’s Hip to Be Squared: "The lesson begins with three
quadratics and their graphs (three parabolas): y = x2 -
2x + (0 or 1 or 2). The prerequisite or co-requisite is some working
experience with algebra, like factoring x2 -2x into
x(x-2). The objective is to connect four things: the formula for
y, the graph of y (a parabola), the roots of y and the minimum
or maximum of y." Aligns with Algebra standards SSE-B.3.a,
CED-A.2, and REI-B.4.b and Function standards IF-B.4, IF-C.7.a,
- Flu Math Games:
"This video lesson shows students that math can play a role in
understanding how an infectious disease spreads and how it can
be controlled." Additional simulations are included.
Aligns with Algebra standards SSE-B.3.c and REI-A.1; Function
standards IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics
and Probability standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and
- The Power of Exponentials, Big and Small:
"Exponential growth is keenly applicable to a variety of
different fields ranging from cell growth in biology, nuclear
chain reactions in physics to computational complexity in
computer science. In this lesson, through various examples and
activities, [the presenters] have tried to compare exponential
growth to polynomial growth and to develop an insight about how
quickly the number can grow or decay in exponentials."
Aligns with Algebra standards SSE-B.3.c and CED-A.2 and Function
standards IF-A.3, IF-C.7.(a, c, e), IF-C.8.b, and LE-A.1.(a, c).
- The Towers of Hanoi: Experiential Recursive Thinking:
"This lesson is about the Towers of Hanoi problem, a classic
famous problem involving recursive thinking to reduce what
appears to be a very large and difficult problem into a series
of simpler ones. The learning objective is for students to
begin to understand recursive logic and thinking, relevant to
computer scientists, mathematicians and engineers."
Aligns with Algebra standard SSE-B.3.c, and Function standards
IF-C.8.b and LE-A.1.a.
- Tragedy of the Commons:
"This lesson introduces students to the “Tragedy of the
Commons,” an extended metaphor for problems of shared
environmental or man-made resources that are overused and
eventually depleted. In this metaphor, shared resources are
compared to a common grazing pasture, or “commons,” on which any
dairy farmer can graze as many cows as he/she wishes. If too
many cows are added to the commons, they will overeat the grass
in the pasture and the shared resource will become depleted – a
disadvantage to everyone. In this lesson, students will be
inspired to think about possible solutions to this problem."
Aligns with Algebra standard SSE-B.3.c and Function standards
IF-B.4, IF-C.8.b, LE-A.1.a, LE-A.3, and LE-B.5.
- Algebra Tiles: Use virtual manipulative algebra tiles "to represent
variables and constants, learn how to represent and solve algebra
problems. Solve equations, substitute in variable expressions, and
expand and factor."
- Difference of Squares:
In this activity, students explore arithmetic statements leading to
a result that is the factoring pattern for the difference of two
squares. A geometric interpretation of the familiar formula is also
This interactive manipulative helps learners to explore geometric
series. They can see a representation of several geometric
series and their limits. Use with SSE-B.4.
Compound Interest Simulator: This manipulative will allow learners to
investigate savings account earnings, credit card debt, and a stock
market simulation. Use with SSE-B.4.
National Library of Virtual Manipulatives:
A tool for graphing and exploring functions
Formula for a finite geometric series: video lesson. Aligns
Purple Math: Aligns with SSE-B.4:
Wolfram Demonstrations Project:
Download the free Wolfram CDF player to interact with the following
US Common Core State Standard Math HSA-SSE.B.3: 17
manipulatives. Among those: Completing the square,
continuous exponential growth, exponential decay, investment
returns, simple versus compound interest, half-life of a radio
active element, Newton's law of cooling, carbon dating,
geometric series, and more.
US Common Core State Standard Math HSA-SSE.B.4: 7
manipulatives. Among those: Plot of a geometric sequence
and its partial sums, sum of a geometric series, geometric
series, graphical representation of geometric series, visual
computation of three geometric sums, and more.
Glencoe Online Learning Center, Algebra 1 (2010) self-check quiz:
Ch. 9, lesson 1:
Graphing the Quadratic Equation: Students will encounter questions
requiring completing the square of a quadratic, and identifying maximum
or minimum values of the function.
Glencoe Online Learning Center, Algebra 2 (2010) self-check quiz,
Chapter 5, Lesson 3:
Solving Quadratic Equations by Factoring
Sequences, series intro includes a section on finite geometric
series. Practice questions
Illustrative Mathematics: Algebra:
Inside Mathematics: MARS Task:
Two Solutions: This task addresses standard SSE-B.3. Students
find solutions to equations and inequalities. Some problems
involve factoring a quadratic expression to reveal the zeros of the
function it defines.
Mathematics Assessment Project: Standards: High School: Algebra:
Choose from the following:
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Intro | HS Algebra Domain: SSE | APR | CED | REI |