Secondary Mathematics II

Strand: ALGEBRA - Seeing Structure in Expression (A.SSE)

Interpret the structure of expressions (Standards A.SSE.1–2). Write expressions in equivalent forms to solve problems, balancing conceptual understanding and procedural fluency in work with equivalent expressions (Standard A.SSE.3).
• A Cubic Identity
This Illustrative Mathematics task presents a challenging exercise in both algebraic manipulations and seeing structure in algebraic expressions.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Adding and Subtracting Polynomials video
This video introduces and explains the topic.
• Adding and Subtracting Rational Expressions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Adding and Subtracting Rational Expressions video
This video introduces and explains the topic.
• ALGEBRA - Seeing Structure in Expression (A.SSE) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Seeing Structure in Expression (A.SSE)
• Algebra Team: Overview of Teaching Styles
This Teaching Channel video illustrates how two teachers' collaboration impacted their algebra program. This site provides a lesson plan and student handouts. (10 min.)
• Animal Populations
This Illustrative Mathematics task students have to interpret expressions involving two variables in the context of a real world situation.
• Comparing Investments
This lesson unit is intended to help you assess how well students are able to interpret exponential and linear functions.
• Equivalent Expressions
This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure.
• Factoring Special Products
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Factoring Special Products video
This video introduces and explains the concept.
• Factoring Trinomials by Grouping 1
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Factoring Trinomials by Grouping 1 video
This is a video introducing and explaining the concept.
• Factoring Trinomials by Grouping 2
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Factoring Trinomials by Grouping 2 video
This video introduces and explains this concept.
• Forms of exponential expressions
There are many different ways to write exponential expressions that describe the same quantity, in this task the amount of a radioactive substance after t years. Depending on what aspect of the context we need to investigate, one expression of the quantity may be more useful than another. This task contrasts the usefulness of four equivalent expressions. Students first have to confirm that the given expressions for the radioactive substance are equivalent. Then they have to explain the significance of each expression in the context of the situation.
• Horseshoes in Flight (pdf)
Students analyze the structure of algebraic expressions and a graph to determine what information each expression readily contributes about the flight of a horseshoe. This task is particularly relevant to students who are studying (or have studied) various quadratic expressions (or functions). The task also illustrates a step in the mathematical modeling process that involves interpreting mathematical results in a real-world context.
• Ice Cream
This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents, precisely the language being used in standard A-SSE.B.3. Students are provided with an expression giving the temperature of a container at a time t, and have to use simple inequalities (e.g., that 2t>0 for all t) to reduce the complexity of an expression to a form where bounds on the temperature of a container of ice cream are made apparent.
• Identifying Quadratic Functions (Standard Form)
This task has students explore the relationship between the three parameters a, b, and c in the equation f(x)=ax2+bx+c and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part.
• Introduction to the Materials (Math 2)
Introduction to the Materials in the Mathematics Two of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
Math Task Overview: Students will analyze quadratic patterns related to the difference of squares and use patterns with the number line. They will then prove the general rule with a sequence of calculations that model inductive reasoning.
• Module 1: Quadratic Functions - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 1, Quadratic Functions, picks up where students left off with linear and exponential functions, using the same types of diagrams and representations to introduce quadratic functions. The entire module focuses on the features of quadratic functions, comparing quadratics to other functions, and representing quadratic functions.
• Module 1: Quadratic Functions - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 1, Quadratic Functions, picks up where students left off with linear and exponential functions, using the same types of diagrams and representations to introduce quadratic functions. The entire module focuses on the features of quadratic functions, comparing quadratics to other functions, and representing quadratic functions.
• Module 2: Structures of Expressions - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 2, Structures of Expressions is both a functions module and an algebra module. It is designed to extend students knowledge of quadratic functions and to reinforce two big ideas of functions, Functions can be transformed in the same, predictable way and Different algebraic forms have purpose in different situations.
• Module 2: Structures of Expressions - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 2, Structures of Expressions is both a functions module and an algebra module. It is designed to extend students knowledge of quadratic functions and to reinforce two big ideas of functions, Functions can be transformed in the same, predictable way and Different algebraic forms have purpose in different situations.
• Module 3: Solving Quadratics & Other Equations - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable.
• Module 3: Solving Quadratics & Other Equations - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable.
• Multiplying and Dividing Monomials
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Multiplying and Dividing Monomials video
This video introduces and explains the topic.
• Multiplying and Dividing Rational Expressions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Multiplying and Dividing Rational Expressions video
This video introduces and explains the topic.
• Multiplying Polynomials
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Multiplying Polynomials video
This video introduces and explains the concept.
• Non-linear Functions video
This video introduces non-linear functions.
• Polynomials
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Polynomials video
The video introduces and explains the topic.
• Profit of a company
This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.
• Representing Conditional Probabilities 2
This lesson unit is intended to help educators assess how well students understand conditional probability.
This lesson unit is intended to help educators assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation.
The goal of this task is to complete the square in a quadratic expression in order to find its minimum or maximum value.
• Sectors of Circles
This lesson unit is intended to help you assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic.
• Seeing Dots
The purpose of this Illustrative Mathematics task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context.
• Simplifying Expressions with Exponents
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Simplifying Expressions with Exponents video
This is a video introduction and explanation of the topic.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
• Solving Quadratic Equations by Completing the Square
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Quadratic Equations by Factoring
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Quadratic Functions by Completing the Square video
This video introduces and explains the topic.
• Sorting Equations and Identities
This lesson unit is intended to help educators assess how well students are able to recognize the differences between equations and identities, as well as substitute numbers into algebraic statements in order to test their validity in special cases.
• Special Products of Polynomials
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Special Products of Polynomials video
This video introduces and explains the concept.
• Sum of Even and Odd
An Illustrative Mathematics task that supports A.SSE.2.
• Taxes and Sales
This task is not about computing the final price of the shirt but about using the structure in the computation to make a general argument.
• Vertex of a parabola with complex roots
The goal of this Illustrative Mathematics task is to study the relationship between the roots of a quadratic function and its graph.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.