Alg+1+-+Unit+1

**A-APR.1**. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
 * ===**Common Core Standard(s)**===


 * G-GMD.1.** Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. //Use dissection arguments, Cavalieri’s principle, and informal limit arguments.//


 * N-RN.1.** Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. //For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.//


 * N-RN.2**. Rewrite expressions involving radicals and rational exponents using the properties of exponents. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Mathematical Practice(s)**

 * 1. Makes sense of problems and perseveres in solving them.**
 * 2. Reason abstractly and quantitatively.**
 * 3. Construct viable arguments and critique the reasoning of others.**
 * 4. Model with mathematics (G.GMD.1 only)**
 * 5. Use appropriately tools strategically (G.GMD.1 only)**
 * 6. Attend to precision (G.GMD.1 only)**
 * 7. Look for and make use of structure**
 * 8. Look for and express regularity in repeated reasoning.** ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Information Technology Standard**

 * HS.TT.1.3 Use technology for an appropriate task** || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Revised Bloom's Level of thinking**
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 * Remembering**
 * Applying**
 * Creating (see instructional resources)** ||

**Learning Target/Task Analysis**

 * Linking prior knowledge: Students should be familiar with adding/subtracting polynomials from middle school as well as should be familiar with geometric formulas.**

**A-APR.1/G-GMD.1 I can add and subtract polynomials.**

 * I can multiply polynomials.**
 * I can use the rules of adding, subtracting and multiplying polynomials with geometric formulas.**


 * N-RN.1/N-RN.2 I can convert rational exponents to radical form.**

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Essential Vocabulary**

 * sum, difference, product, exponents, constants, coefficients, variables, rational exponents, radicals, distributive property, like terms, cylinders, cones, pyramid, circle(geometric definition), circumference, area(squared units), volume(cubic units), Cavaleri's principle, expression**

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**Sample Assessments**

 * Mini cumulative quizzes focused on student needs**
 * Thumbs up/thumbs down/thumbs sides ways formative assessment**
 * Exit tickets**
 * Mini projects**
 * Weekly cumulative tests**

**Differentiation:**

 * Basic tasks:**


 * Extension:**

**Video for combining like terms:**
http://www.khanacademy.org/math/algebra/polynomials/v/simply-a-polynomial

http://www.khanacademy.org/math/algebra/polynomials/v/adding-polynomials http://www.khanacademy.org/math/algebra/polynomials/v/subtracting-polynomials
 * Videos for adding and subtracting polynomials:**

http://www.khanacademy.org/math/algebra/polynomials/v/multiplication-of-polynomials
 * Video that explains and links the distributive property to FOIL:**

**Video explaining the common mistake made when simplifying (7x + 3) to the power of 2.**
http://www.khanacademy.org/math/algebra/polynomials/v/square-a-binomial

http://www.khanacademy.org/math/algebra/exponents-radicals/v/exponent-properties-involving-products
 * Video outlining the basic concept behind power of a product:**

http://www.khanacademy.org/math/algebra/exponents-radicals/v/rational-exponents-and-exponent-laws
 * Video that explains rational exponents:**

http://www.khanacademy.org/math/algebra/exponents-radicals/v/simplifying-square-roots
 * Video that explains simplifying square roots:**

http://www.khanacademy.org/math/algebra/exponents-radicals/v/simplifying-cube-roots
 * Video that explains simplifying cube roots:**

http://www.khanacademy.org/math/algebra/exponents-radicals/v/radical-equivalent-to-rational-exponents-2
 * Video that links rational exponents to roots:**

See instructional resources
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**Instructional Resources:**
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html

http://www.khanacademy.org/math/algebra/polynomials-and-quadratics/e/adding_and_subtracting_polynomials
 * Practice Problems courtesy of Khan Academy:**
 * Adding and subtracting polynomials:**

Multiplying polynomials: http://www.khanacademy.org/math/algebra/polynomials-and-quadratics/e/multiplying_polynomials

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**Notes and Additional Information:**

 * Content should be spiraled throughout the semester.**