# data[].attributes.headline
(4)  Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships.

# data[].attributes.subject
(4)  Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships.

# data[].attributes.body
(A)  distinguish between undefined terms, definitions, postulates, conjectures, and theorems;

(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.

# data[].attributes.headline
(5)  Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.

# data[].attributes.subject
(5)  Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.

# data[].attributes.body
(A)  investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circleschoosing from a variety of tools;

(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.

# data[].attributes.headline
(6)  Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

# data[].attributes.subject
(6)  Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

# data[].attributes.body
(A)  verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships 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.

# data[].attributes.headline
(7)  Similarity, proof, and trigonometry. The student uses the process skills in applying similarity to solve problems.

# data[].attributes.subject
(7)  Similarity, proof, and trigonometry. The student uses the process skills in applying similarity to solve problems.

# data[].attributes.body
A)  apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles; and

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

# data[].attributes.headline
(8)  Similarity, proof, and trigonometry. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. 

# data[].attributes.subject
(8)  Similarity, proof, and trigonometry. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. 

# data[].attributes.body
(A)  prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems; and

(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.

# data[].attributes.headline
(9)  Similarity, proof, and trigonometry. The student uses the process skills to understand and apply relationships in right triangles.

# data[].attributes.subject
(9)  Similarity, proof, and trigonometry. The student uses the process skills to understand and apply relationships in right triangles.

# data[].attributes.body
(A)  determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems; and

(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.

# data[].attributes.headline
(10)  Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. 

# data[].attributes.subject
(10)  Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. 

# data[].attributes.body
(A)  identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes; and

(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.

# data[].attributes.headline
(11)  Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.

# data[].attributes.subject
(11)  Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.

# data[].attributes.body
(A)  apply the formula for the area of regular polygons to solve problems using appropriate units of measure;

(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.

# data[].attributes.headline
(12)  Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. 

# data[].attributes.subject
(12)  Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. 

# data[].attributes.body
(A)  apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;

(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.

# data[].attributes.headline
(3)  Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity)

# data[].attributes.subject
(3)  Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity)

# data[].attributes.body
(A)  describe and perform transformations of figures in a plane using coordinate notation;
(B)  determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane;

(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.

# data[].attributes.headline
2)  Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures

# data[].attributes.subject
2)  Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures

# data[].attributes.body
(A)  determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint;

(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.

# data[].attributes.headline
(13)  Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.

# data[].attributes.subject
(13)  Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.

# data[].attributes.body
(A)  develop strategies to use permutations and combinations to solve contextual problems;
(B)  determine probabilities based on area to solve contextual problems;

(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.

# data[].attributes.headline
8 (11)  Measurement and data. The student applies mathematical process standards to use statistical procedures to describe data.

# data[].attributes.subject
8 (11)  Measurement and data. The student applies mathematical process standards to use statistical procedures to describe data.

# data[].attributes.body
(A)  construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data;

(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.

# data[].attributes.headline
7 (12)Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data.

# data[].attributes.subject
7 (12)Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data.

# data[].attributes.body
(A)  compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads;

(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.

# data[].attributes.headline
6(13)  Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems.

# data[].attributes.subject
6(13)  Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems.

# data[].attributes.body
(A)  interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots; and

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

# data[].attributes.body
(A)  represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots;

(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.

# data[].attributes.headline
6(11)  Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers.

# data[].attributes.subject
6(11)  Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers.

# data[].attributes.headline
5(8)  Geometry and measurement. The student applies mathematical process standards to identify locations on a coordinate plane.

# data[].attributes.subject
5(8)  Geometry and measurement. The student applies mathematical process standards to identify locations on a coordinate plane.

# data[].attributes.body
(A)  describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to they-axis starting at the origin;

(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.

# data[].attributes.headline
5(7)  Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving measurement. The student is expected to solve problems by calculating conversions within a measurement system, customary or metric.

# data[].attributes.subject
5(7)  Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving measurement. The student is expected to solve problems by calculating conversions within a measurement system, customary or metric.

# data[].attributes.headline
5(6)  Geometry and measurement. The student applies mathematical process standards to understand, recognize, and quantify volume.

# data[].attributes.subject
5(6)  Geometry and measurement. The student applies mathematical process standards to understand, recognize, and quantify volume.

# data[].attributes.body
(A)  recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible; and

(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.

# data[].attributes.headline
5(5)  Geometry and measurement. The student applies mathematical process standards to classify two-dimensional figures by attributes and properties. The student is expected to classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

# data[].attributes.subject
5(5)  Geometry and measurement. The student applies mathematical process standards to classify two-dimensional figures by attributes and properties. The student is expected to classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

# data[].attributes.headline
4(8)  Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement.

# data[].attributes.subject
4(8)  Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement.

# data[].attributes.body
(A)  identify relative sizes of measurement units within the customary and metric systems;
(B)  convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table; and

(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.

# data[].attributes.headline
4(7)  Geometry and measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees.

# data[].attributes.subject
4(7)  Geometry and measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees.

# data[].attributes.body
(A)  illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers;
(B)  illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers;
(C)  determine the approximate measures of angles in degrees to the nearest whole number using a protractor;

(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.

# data[].attributes.headline
4(6)  Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties.

# data[].attributes.subject
4(6)  Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties.

# data[].attributes.body
(A)  identify points, lines, line segments, rays, angles, and perpendicular and parallel lines;
(B)  identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure;

(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.

# data[].attributes.headline
3(7)  Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement.

# data[].attributes.subject
3(7)  Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement.

# data[].attributes.body
(A)  represent fractions of halves, fourths, and eighths as distances from zero on a number line;
(B)  determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems;

(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.

# data[].attributes.headline
3(6)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties.

# data[].attributes.subject
3(6)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties.

# data[].attributes.body
(A)  classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language;
(B)  use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories;

(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.

# data[].attributes.headline
2(8)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties.

# data[].attributes.subject
2(8)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties.

# data[].attributes.body
(A)  create two-dimensional shapes based on given attributes, including number of sides and vertices;
(B)  classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language;

(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.

# data[].attributes.headline
2(9)  Geometry and measurement. The student applies mathematical process standards to select and use units to describe length, area, and time.

# data[].attributes.subject
2(9)  Geometry and measurement. The student applies mathematical process standards to select and use units to describe length, area, and time.

# data[].attributes.body
(A)  find the length of objects using concrete models for standard units of length;
B)  describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object;

(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.

# data[].attributes.headline
1(7)  Geometry and measurement. The student applies mathematical process standards to select and use units to describe length and time.

# data[].attributes.subject
1(7)  Geometry and measurement. The student applies mathematical process standards to select and use units to describe length and time.

# data[].attributes.body
(A)  use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement;
(B)  illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other;

(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.

# data[].attributes.headline
K(7)  Geometry and measurement. The student applies mathematical process standards to directly compare measurable attributes. The student is expected to:

# data[].attributes.subject
K(7)  Geometry and measurement. The student applies mathematical process standards to directly compare measurable attributes. The student is expected to:

# data[].attributes.body
(A)  give an example of a measurable attribute of a given object, including length, capacity, and weight; and

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

# data[].attributes.headline
1 (6)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties.

# data[].attributes.subject
1 (6)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties.

# data[].attributes.body
(A)  classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language;
(B)  distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape;

(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.

# data[].attributes.headline
K(6)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:

# data[].attributes.subject
K(6)  Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:

# data[].attributes.body
(A)identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangle
(B) identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world
(C) identify two-dimensional components of three-dimensional objects
(D)  identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably
(E)  classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size
(F)  create two-dimensional shapes using a variety of materials and drawings