Subject: Algebra 1
Subject: Algebra 1
Grade Level: 8th/9th
Unit Title: Radicals, Exponents and Polynomials |Timeframe Needed for Completion:
Grading Period: 1st 9 weeks (22 days) | |
|Big Idea/Theme: Analyze This |
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|Understandings: rules of exponents, perform operations with polynomials, factor binomials and trinomials; simplify radicals involving products and quotients, use Pythagorean theorem to solve right triangles, |
|distance and midpoint formulas, use perimeter and area to solve equations, |
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|Essential Questions: |Curriculum Goals/Objectives (to be assessed at the end of the unit/quarter) |
|Why are exponents used in multiplication and in equations? |Find the length and midpoints or segments to solve problems (2.01). |
|How is multiplying two binomials similar to multiplying two digit numbers? |N.RN.1 |
|How is simplifying radical expressions similar to simplifying monomial expressions? |Explain how the definition of the meaning of rational exponents follows from extending the properties of|
|Describe situations where the Pythagorean Theorem is used in construction. |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. *** |
| |A.SSE.1a Identify the parts of the expression and explain their meaning within the context of the |
| |problem.*** |
| |A.SSE.1b Decompose expressions and make sense of the multiple factors and terms by explaining the |
| |meaning of the individual parts.*** |
| |A.SSE.2 Rewrite algebraic expressions in different equivalent forms such as factoring or combining like |
| |terms.(1.01c) |
| |A.SSE.3c Use properties of exponents (such as power of a power, product of powers, power of a product |
| |and rational exponents, etc) *** |
| |A.APR.1 Understand the definition of a polynomial, the concepts of combining like terms and closure, and|
| |add, subtract, and multiply polynomials and understand how closure applies under these operations. |
| |(1.01b) |
|Essential Skills/Vocabulary: |Assessment Tasks: |
|Vocabulary: | |
|exponent, scientific notation, base, power, binomial, monomial, polynomial, trinomial, degree, factor, |Quick writes |
|perfect square, standard form of polynomials, square root., radical, simplify, hypotenuse, leg, |Teacher made tests and quizzes |
|Pythagorean triple, distance and midpoint formula |Find the error |
| |Cornell notes |
| |Groupwork |
|Essential skills: |Projects |
|multiply and divide monomials using rules of exponents, including negative exponents and zero exponents |Graphic organizers |
|operate with scientific notation |Anticipation/prediction guides |
|factor binomials using GCF, difference of squares | |
|factor trinomials using perfect squares, with the leading coefficient 1, and other numbers | |
|simplify radical expressions using the product and quotient properties of square roots, and | |
|rationalizing the denominator | |
|solve problems using the Pythagorean theorem | |
|determine whether a triangle is a right triangle | |
|find the distance between points on the coordinate plane | |
|find a point a given distance from another point in a plane | |
|find the midpoint of a line segment | |
|find the endpoint of a line segment given the midpoint and one endpoint | |
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|Guiding questions: | |
|1. How are the GCF and the Distributive property used to factor polynomials? | |
|How are monomials factored? | |
|How are binomials factored? | |
|How are trinomials factored? | |
|How can you find the other factor of a polynomial if you know the product and one of the factors? | |
|How are adding and multiplying polynomials different? | |
|What does FOIL stand for? | |
|How is factoring a polynomial connected to the FOIL method? | |
|What do you do differently when finding the degree of a monomial versus finding the degree of a binomial| |
|or trinomial? | |
|If the base and height of a rectangular prism are binomials, how is the volume computed? | |
|How are powers multiplied? Divided? | |
|What is the difference between multiplying and dividing monomials with exponents? | |
|How is a problem simplified with a negative exponent? | |
|How is a number written in scientific notation? | |
|What is the square root of a number? The cube root? | |
|What is the relationship between the square root of a number and the square of a number? | |
|What is an exponential function? | |
|How can we find the factors of polynomials?? | |
|The Pythagorean Theorem involves what geometric figure? | |
|What is meant by the legs and hypotenuse of a triangle and what is their relationship to the Pythagorean| |
|Theorem? | |
|Materials Suggestions: |
|Prentice Hall Mathematics Algebra 1: Chapters 11 (sections 1, 2, 3, 4) , 8 (sections 1, 2, 3, 4, 5), 9 (operations on polynomials 1-3, factor polynomials 2,5-7) |
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|Use applications and open-ended questions throughout topics. |
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