 # Common Core High School Algebra Teaching and Learning Resources

## Domain: SSE: Seeing Structure in Expressions • SSE-A: Interpret the structure of expressions.

• SSE-B: Write expressions in equivalent forms to solve problems ### 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 x– 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:

 coefficient factoring rules maximum of a function term exponent rules factor of a polynomial minimum of a function zero of a function expression geometric series

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:

Multiple Choice:

• Interpret expressions: 5 questions that combine free response and multiple choice.  Includes related review resources.  Aligns with SSE-A.1.
• Expression structure SSE.2: 5 multiple choice questions.  Includes related review resources.  Aligns with SSE-A.2.

Khan Academy: Practice questions with videos.  Use the following with SSE-A.1:

Khan Academy: see Algebra 1: Polynomial Factorization and Algebra 2: Polynomial Expressions, Equations, and Functions: Practice questions with videos.  Use the following with SSE-A.2:

Constructed-response:

Khan Academy: Algebra 1: Polynomial Factorization and Algebra 2: Polynomial Expressions, Equations, and Functions: 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:

Illustrative Mathematics: Algebra:

Mathematics Assessment Project: Standards: High School: Algebra: https://www.map.mathshell.org/stds.php?standardid=1190 Choose from the following:

Mathematics Vision Project, Secondary 1 Student Edition:

• Getting Ready Module: This module contains 10 classroom tasks.  Task 1: Checkerboard Borders; Task 2: Building More Checkerboard Borders, and Task 3: Serving Up Symbols align to algebra standard SSE-A.1.
• Module 3: Linear and Exponential Functions: This module contains 10 classroom tasks.  Task 7: Making My Point, Task 8: Efficiency Experts, and Task 9: Up a Little, Down a Little align to algebra standard SSE-A.1.

### 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."
• 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 included.
• Limits: 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: Grapher: A tool for graphing and exploring functions

LearnZillion:

Khan Academy: Formula for a finite geometric series: 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:see Algebra 1: Quadratic Equations and Functions and Sequences: Practice questions with videos.

MathWarehouse: 