A collection of work samples will be gathered that address the following standards. 

Number Sense and Operations

10.N.1

10.N.2

 

Patterns, Relations, and Algebra

10.P.2

10.P.4

10.P.5

10.P.7

 

Geometry (Choose any three)

10.G.1

10.G.2

10.G.3

10.G.4

10.G.5

10.G.6

10.G.7

10.G.8

10.G.9

10.G.10

10.G.11

 

Measurement

10.M.1

10.M.2

10.M.3

 

Data Analysis, Statistics, and Probability

10.D.1

10.D.2

 

Number Sense and Operations

At least one work sample documenting all aspects of both learning standards identified below (a total of at least two work samples, each with at least four examples or problems solved correctly):

 

10.N.1

Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties [do not simply define these properties; show how they are applied and demonstrate that students can identify each property; e.g., use the distributive property to multiply 7(23)=7(20+3)=7(20)+7(3)=140+21=161]; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number.

10.N.2

Simplify numerical expressions, including those involving positive integer exponents or the absolute value [e.g., 3(24 - 1) = 45; 4|3 - 5| + 6 = 14]; apply such simplifications in the solution of problems. [Note: Both exponents and absolute value must be shown.]

 

 

 

 

Patterns, Relations, and Algebra

 

At least one work sample documenting all aspects of each of the four learning standards identified below (a total of at least four work samples, each with at least four examples or problems solved correctly):

 

10.P.2	Demonstrate an understanding of the relationship between various representations of a line. Determine a line’s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line (e.g., by using the “point-slope” or “slope y-intercept” formulas). Explain the significance of a positive, negative, zero, or undefined slope.
10.P.4	Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring [e.g., a2 - b2 = (a + b)(a - b); x2 + 10x + 21 = (x + 3)(x + 7); 5x4 + 10x3 - 5x2 = 5x2 (x2 + 2x - 1)]; identifying and canceling common factors in rational expressions; and applying the properties of positive integer exponents. [This standard does not include simple addition, subtraction, and multiplication of polynomials, as covered in 10.P.3]
10.P.5	Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods. [Note: In order to demonstrate an understanding of the equivalence of the methods, at least two methods must be shown.]
10.P.7	Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest [i.e., exponential], and direct [i.e., linear] and inverse [i.e., reciprocal] variation problems. Use technology when appropriate.

 

 

 

 

Geometry

 

At least one work sample documenting all aspects of each standard for any three learning standards identified below (a total of at least three work samples, each with at least four examples or problems solved correctly):

10.G.1	Identify figures using properties of sides, angles, and diagonals. Identify the figures’ type(s) of symmetry.
10.G.2	Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments.
10.G.3	Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle.
10.G.4	Apply congruence and similarity correspondences (e.g., ΔABC ΔXYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.
10.G.5	Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. [Note: Both must be shown]
10.G.6	Use the properties of special triangles (e.g., isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems. [Note: must show at least 30°-60°-90° and 45°-45°-90°]
10.G.7	Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems.
10.G.8	Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the “point-slope” form of the equation.
10.G.9	Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems.
10.G.10	Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.
10.G.11	Use vertex-edge graphs to model and solve problems (i.e., network).

 

 

 

 

Measurement

 

At least one work sample documenting all aspects of each of the three learning standards identified below (a total of at least three work samples, each with at least four examples or problems solved correctly):

10.M.1	Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles. [Note: Include a variety of figures.]
10.M.2	Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones (e.g., find the volume of a sphere with a specified surface area). [Note: All of the above must be shown for all forms listed.]
10.M.3	Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing radius or height of a cylinder affects its surface area or volume.

 

 

 

 

Data Analysis, Statistics, and Probability

At least one work sample documenting all aspects of each learning standard identified below (a total of at least two work samples); the 10.D.1 work sample should include at least four examples or problems solved correctly; one trend line is sufficient for 10.D.2):

 

10.D.1

Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plot, box-and-whisker plot, circle graph, line graph, line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, mode) to communicate information about the data. Use these notions to compare different sets of data. [Note: Include at least four examples or problems solved correctly.]

10.D.2

Approximate a line of best fit (i.e., draw a trend line) given a set of data (e.g., scatter- plot). Use technology when appropriate. [Note: One trend line is sufficient.]