Common Core 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.
Standards:
- 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).
Technology-enhanced investigations:
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.
Purple Math:
Special
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,
integer polynomial
-
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:
Multiple Choice:
Constructed-response:
Khan Academy: HSA-A-SSE
includes HSA-SSE.A.1 and HSA-SSE.A.2 Common Core aligned problems.
Also see:
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:
Performance tasks:
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SSE-B: Write expressions in equivalent
forms to solve problems
Standards:
- 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
payments.
Technology-enhanced investigations:
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,
IF-C.8.a, BF-B.3.
- 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
MD-A.1.
- 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.
NCTM Illuminations:
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."
National Library of Virtual Manipulatives:
Grapher:
A tool for graphing and exploring functions
Imagine Learning Classroom (formerly LearnZillion) subscription
needed:
Khan Academy:
Finite geometric series
formula: video lesson. Aligns
with SSE-B.4.
Purple Math: Aligns with SSE-B.4:
Saltire Software: Common Core Nuggets: There are three
Quadratic Zeroes Applets, which align with SSE-B.3.a.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player to interact with the following
manipulatives:
-
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.
Multiple Choice:
Khan Academy:
Sequences, series intro includes a section on finite geometric
series. Practice questions with videos.
Constructed-response:
Khan Academy: HSA-A-SSE
includes HSA-SSE.B.3 and HSA-SSE.B.4 Common Core aligned problems.
Also see:
MathWarehouse:
Performance tasks:
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:
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Common Core Math:
Intro | HS Algebra Domain: SSE | APR | CED | REI |
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