Understanding adding and subtracting polynomials.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.

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.

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.

Mathematics involves many different types of numbers. It is important that you can classify and name numbers and expressions. In this seminar you will go beyond the basics and learn about various types of expressions called polynomials. You will explore terminology affiliated with polynomials and classify them based on their degree.  You will also use past knowledge on how to simplify and combine like terms. You will use the techniques learned in this seminar to then perform operations on various types of polynomials such as adding, subtracting, and multiplying moving forward.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.CC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.  

Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers.
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Students play an Expressions Game in which they describe expressions to their partners using the vocabulary of expressions: term, coefficient, exponent, constant, and variable. Their partners try to write the correct expressions based on the descriptions.Key ConceptsMathematical expressions have parts, and these parts have names. These names allow us to communicate with others in a precise way.A variable is a symbol (usually a letter) in an expression that can be replaced by a number.A term is a number, a variable, or a product of numbers and variables. Terms are separated by the operator symbols + (plus) and – (minus).A coefficient is a symbol (usually a number) that multiplies the variable in an algebraic expression.An exponent tells how many copies of a number or variable are multiplied together.A constant is a number. In an expression, it can be a constant term or a constant coefficient. In the expression 2x + 3, 2 is a constant coefficient and 3 is a constant term.Goals and Learning ObjectivesIdentify parts of an expression using appropriate mathematical vocabulary.Write expressions that fit specific descriptions (for example, the expression is the sum of two terms each with a different variable).

In this lesson you will learn how to convert between decimal, percent and fraction; calculate percent of change; and apply percents to real-world situations.  You will be able to discuss the importance of writing numbers in different formats; how to determine a percent increase or decrease; and how percents are an integral part of daily living.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.MP.1. Make sense of problems and persevere in solving them.MP.4. Model with mathematics.MP.5. Use appropriate tools strategically.

Students use a simple seesaw to visualize solving a two- or three-step mathematics equation, while solving a basic structural engineering weight balance problem in the process. They solve two-step equations on a worksheet and attempt to solve the challenge of "balancing a beam" through hands-on problems. The use of sensor equipment for correct position monitoring aids students in balancing the structure, as well as balancing the equation as they solve it on paper.