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Common Core Math

High School Algebra Teaching and Learning Resources

Domain: SSE: Seeing Structure in Expressions

Common Core Math

Select the cluster for resources on this page:

  • SSE-A: Interpret the structure of expressions.

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

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SSE-A: Interpret the structure of expressions.

Standards:

 

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:

YouTube video lessons:

Multiple Choice:

Glencoe Online Learning Center, Algebra 1 (2010) self-check quizzes:

Khan Academy: see Algebra 1: Seeing Structure in Expressions: Practice questions with videos.  Use the following with SSE-A.1:

Constructed-response:

Khan Academy: Algebra 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:

OpenEd:

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

Performance tasks:

Illustrative Mathematics: Algebra:

Mathematics Assessment Project: Standards: High School: Algebra: http://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.

 

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SSE-B: Write expressions in equivalent forms to solve problems

Standards:

Technology-enhanced investigations:

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 where a=1.

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, 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:

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:

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

Khan Academy: Sequences, series intro includes a section on finite geometric series.  Practice questions with videos.

Constructed-response:

Khan Academy: Quadratic Equations: Practice questions with videos.

MathWarehouse:

OpenEd: Produce an equivalent expression: 5 questions that combine free response and multiple choice.  Includes related review resources.  Aligns with SSE-B.3.

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: http://map.mathshell.org/stds.php?standardid=1190   Choose from the following:

 

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