Power Skills for Honors Algebra II with Statistics

Power Skills are those required/mandatory/vital abilities/competencies/expertise that the student should be able to demonstrate PRIOR to the course.

Everything from Honors Geometry with Data Analysis and:

1. Operations with rational expressions

   1. Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals. (ACC 7, #8)

2. Simplifying radical expressions / operations with radicals

   1. Extend understanding of irrational and rational numbers by rewriting expressions involving radicals, including addition, subtraction, multiplication, and division, in order to recognize geometric patterns. (Geometry with Data Analysis, #1)

      1. Simplify radicals and justify simplification of radicals using visual representations.

      2. Use the operations of addition, subtraction, division, and multiplication, with radicals.

      3. Demonstrate an understanding of radicals as they apply to problems involving squares, perfect squares, and square roots (e.g., the Pythagorean Theorem, circle geometry, volume, and area).

3. Properties of exponents

   1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.. (ACC 7, #12)

   2. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. (ACC 7, #14)

   3. Explain how the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for an additional notation for radicals in terms of rational exponents. (ACC 8, #1)

   4. Rewrite expressions involving radicals and rational exponents using the properties of exponents. (ACC 8, #2)

4. Understand formulas

   1. Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle. (ACC 7, #36)

   2. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms. (ACC 7, #39)

   3. Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions. (ACC 7, #40)

   4. Use formulas to calculate the volumes of three-dimensional figures to solve real-world problems. (ACC 7, #41)

   5. Discover and apply relationships in similar right triangles. (Geometry with Data Analysis, #35)

      1. Derive and apply the constant ratios of the sides in special right triangles (45°-45°-90° and 30°-60°-90°).

      2. Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.

      3. Explain and use the relationship between the sine and cosine of complementary angles.

      4. Demonstrate the converse of the Pythagorean Theorem.

      5. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons.

5. Factor algebraic expressions

   1. Use the structure of an expression to identify ways to rewrite it. (ACC 8, #5)

      1. GCF

      2. Difference of squares

      3. Trinomials

      4. Factoring by grouping

6. Solve / graph equations

   1. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms. (ACC 7, #21)

   2. Create equations in two variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. (ACC 7, #19)

7. Solve application problems

   1. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. (ACC 7, #9)

   2. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies. (ACC 7, #17)

   3. Use variables to represent quantities in a real-world or mathematical problem and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities. (ACC 7, #18)

   4. Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications. (ACC 8, #50)

   5. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. (Alg. I with Probability, #31)

   6. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Geometry with Data Analysis, #4)

   7. Use the mathematical modeling cycle involving geometric methods to solve design problems. (Geometry with Data Analysis, #38)

      1. Accurately model and solve a design problem.

      2. Justify how their model is an accurate representation of the given situation.

8. Function fluency

   1. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. (ACC 8, #16)

      1. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

      2. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

   2. Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (ACC 8, #23)