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.

It is important to understand polynomials and to be able to classify them based on the number of terms, as well as recognize the coefficients, and degrees. You must also understand how to perform mathematical operations on them. This seminar will focus on combining polynomials using addition and subtraction. It will be important to understand the rules to make sure you are combining only like terms. You will apply techniques you have learned involving exponents and general addition and subtraction rules. You will use the techniques learned in this seminar to verify solutions to various other types of polynomial problems as you move forward. When adding and subtracting polynomials, you will first identify the like terms to combine polynomials to their simplest form.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

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.

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.

In this unit, the student will learn about transformational geometry. The student will learn about congruence transformations, such as reflections, translations, and rotations, and will also learn about geometric patterns
such as symmetry and tessellations.

The purpose of this task is to give students practice writing a constraint equation for a given context. Instruction accompanying this task should introduce the notion of a constraint equation as an equation governing the possible values of the variables in question.

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. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.

In this seminar you will learn when quadratic equations can be solved using square root techniques, and when they can be solved by factoring and using the zero product property. You will apply techniques you have learned involving radical expressions and factoring. You will use the techniques learned in this seminar to verify solutions to various other types of problems as you move forward. When solving quadratic equations using this method, you will identify the patterns found in the solutions which will allow you to make graphic interpretations of the solutions, as well as allow you to identify when a quadratic function may (or may not) be solved using these techniques.StandardsCC.2.2.HS.C.5Construct and compare linear, quadratic, and exponential models to solve problems.

This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

This 10-minute video lesson shows that three points uniquely define a circle and that the center of a circle is the circumcenter for any triangle that the circle is circumscribed about.

This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.

Parts (d) and (e) of this task constitute a very advanced application of the skill of making use of structure: in (d) students are being asked to use the defining property of even and odd functions to manipulate expressions involving function notation. In (e) they are asked to see the structure in the system of two equations involving functions.

This is a remix of Pre-Algebra/Beginning Algebra Concepts - Computer Resources with some additions to the Integers activities. https://www.oercommons.org/authoring/28963-pre-algebra-beginning-algebra-concepts-computer

The intention of this curriculum guide is to provide teachers with supplemental materials to use to support students in strengthening their skills in various concept areas that are crucial for understanding beginning algebra. The activities are broken down by skill with links provided below. This is intended as a way to provide students with engaging, primarily computer-based activities to get extra practice with material that is covered elsewhere in the curriculum. This collection focuses on simulations and games using the computer—some resources may be ripe for teachers to develop unique activities to accompany the simulation and some possible suggestions are included with the descriptions. This series is intended to be pick-and-choose.

In this Curriculum Guide:

Activities and practice with: Integers, Exponents, Order of Operations, Distributive Property, Expressions, Equations and Basic Graphing

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

This task is designed to make students think about the meaning of the quantities presented in the context and choose which ones are appropriate for the two different constraints presented. In particular, note that the purpose of the task is to have students generate the constraint equations for each part (though the problem statements avoid using this particular terminology), and not to have students solve said equations.

The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.

This 7-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 39.