(C)  create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons;

(D)  identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language;

(E)  identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language;

(F)  compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible;

(G)  partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words; and

(H)  identify examples and non-examples of halves and fourths.

(B)  compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference.

(C)  measure the same object/distance with units of two different lengths and describe how and why the measurements differ;

(D)  describe a length to the nearest whole unit using a number and a unit; and

(E)  tell time to the hour and half hour using analog and digital clocks.

(C)  represent whole numbers as distances from any given location on a number line;

(D)  determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes;

(E)  determine a solution to a problem involving length, including estimating lengths;

(F)  use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit; and

(G)  read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.

(C)  classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices;

(D)  compose two-dimensional shapes and three-dimensional solids with given properties or attributes; and

(E)  decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical trianglesand identify the resulting geometric parts.

(C)  determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row;

(D)  decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area; and

(E)  decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape.

(C)  determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes;

(D)  determine when it is appropriate to use measurements of liquid volume (capacity) or weight; and

(E)  determine liquid volume (capacity) or weight using appropriate units and tools.

(C)  apply knowledge of right angles to identify acute, right, and obtuse triangles; and
(D)  classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.

(D)  draw an angle with a given measure; and
(E)  determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.

(C)  solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.

(B)  determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base.

(B)  describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane; and

(C)  graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table.

(B)  use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution;

(C)  summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution; and

(D)  summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.

(B)  distinguish between situations that yield data with and without variability.

(B)  use data from a random sample to make inferences about a population; and

(C)  compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations.

(B)  determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points; and

(C)  simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected.

(C)  identify whether two events are independent and compute the probability of the two events occurring together with or without replacement;

(D)  apply conditional probability in contextual problems; and

(E)  apply independence in contextual problems.

(B)  derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines; and

(C)  determine an equation of a line parallel or perpendicular to a given line that passes through a given point.

(C)  identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane; and

(D)  identify and distinguish between reflectional and rotational symmetry in a plane figure.

(B)  apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems;

(C)  apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems;

(D)  describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle; and

(E)  show that the equation of a circle with center at the origin and radius r is x2 +y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)2 + (y - k)2 =r2.

(B)  determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure;

(C)  apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure; and

(D)  apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solveproblems using appropriate units of measure.

(B)  determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change.

(B)  apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.

(B)  identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.

(B)  apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.

(B)  prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions;

(C)  apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles;

(D)  verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems; and

(E)  prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.

(B)  construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge;

(C)  use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships; and

(D)  verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.

(B)  identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse;

(C)  verify that a conjecture is false using a counterexample; and

(D)  compare geometric relationships between Euclidean and spherical geometries,including parallel lines and the sum of the angles in a triangle.