Okla. Admin. Code § 210:15-3-64

Current through Vol. 42, No. 8, January 2, 2025

Section 210:15-3-64 - Standard Three: Geometry and Measurement

(a)Statement of the standard. Students will focus on number and operations to develop fluency with an importance of understanding numbers, ways of representing numbers, relationships among numbers, relationships among number systems, and meanings of operations and how they relate to one another. Students will place an emphasis on the development of estimation to determine the reasonableness of solutions and answers and to compute efficiently and proficiently.

(b)Standard Three objectives for Pre-Kindergarten. The following objectives apply for students in Pre-Kindergarten:

(1) Identify common shapes.

(A)Objective 1. Identify circles, squares, rectangles, and triangles by pointing to the shape when given the name.

(2) Describe and compare measureable attributes.

(A)Objective 1. Identify measureable attributes of objects. Describe them using age appropriate vocabulary (i.e. little, big, long, short, tall, heavy, light). Explain verbally what the objects have in common.

(B)Objective 2. Directly compare two objects with a common measureable attribute using age-appropriate vocabulary (e.g., longer/shorter; heavier/lighter; or taller/shorter.)

(C)Objective 3. Sort objects into sets by one or more attributes.

(c)Standard Three objectives for Kindergarten. The following objectives apply for students in Kindergarten:

(1) Recognize and sort basic two-dimensional shapes; use two-dimensional and three-dimensional shapes to represent real-world objects.

(A)Objective 1. Recognize squares, circles, triangles, and rectangles.

(B)Objective 2. Sort two-dimensional objects using characteristics such as shape and size.

(C)Objective 3. Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably, such as the number of corners/vertices and the number of sides/edges.

(D)Objective 4. Use smaller two-dimensional shapes to fill in the outline of a larger two-dimensional shape.

(E)Objective 5. Compose larger, undefined shapes and structures using three-dimensional objects.

(F)Objective 6. Use basic shapes and spatial reasoning to represent objects in the real world.

(2) Compare and order objects according to location and measurable attributes.

(A)Objective 1. Use words to compare objects according to length, size, weight, position, and location.

(B)Objective 2. Order up to 6 objects using measureable attributes, such as length and weight.

(C)Objective 3. Identify more than one shared attribute between objects, and sort objects into sets.

(D)Objective 4. Compare the number of objects needed to fill two different containers.

(3) Tell time as it relates to daily life.

(A)Objective 1. Develop an awareness of simple time concepts within daily life, using age-appropriate vocabulary (e.g., yesterday, today, tomorrow, morning, afternoon, and night).

(d)Standard Three objectives for Grade 1. The following objectives apply for students in Grade 1:

(1) Recognize and compose two- and three-dimensional shapes.

(A)Objective 1. Identify regular and irregular trapezoids and hexagons by pointing to the shape when given the name.

(B)Objective 2. Compose larger, defined shapes using smaller two-dimensional shapes.

(C)Objective 3. Compose structures with three-dimensional shapes.

(D)Objective 4. Recognize three-dimensional shapes such as cubes, cones, cylinders, pyramids, and spheres.

(2) Select and use nonstandard and standard units to describe length and volume/capacity.

(A)Objective 1. Use nonstandard and standard measuring tools to measure the length of objects.

(B)Objective 2. 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)Objective 3. Measure the same object/distance with units of two different lengths and describe how and why the measurements differ.

(D)Objective 4. Describe a length to the nearest whole unit using a number with standard and nonstandard units.

(E)Objective 5. Use standard and nonstandard tools to identify volume/capacity. Compare and sort containers that hold more, less, or the same amount.

(3) Describe and measure concepts of time.

(A)Objective 1. Tell time to the hour and half-hour (analog and digital).

(B)Objective 2. Describe and measure calendar time by days, weeks, months, and years.

(e)Standard Three objectives for Grade 2. The following objectives apply for students in Grade 2:

(1) Analyze attributes of two- and three- dimensional figures and develop generalizations about their properties.

(A)Objective 1. Recognize regular and irregular trapezoids and hexagons.

(B)Objective 2. Describe, compare, and classify two-dimensional figures according to their geometric attributes.

(C)Objective 3. Compose and decompose two-dimensional shapes using triangles, squares, hexagons, trapezoids, and rhombi.

(D)Objective 4. Sort three-dimensional shapes based on attributes such as number of faces, vertices, and edges.

(E)Objective 4. Recognize right angles and classify angles as smaller or larger than a right angle.

(2) Understand length as a measurable attribute and explore capacity.

(A)Objective 1. Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object.

(B)Objective 2. Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit.

(C)Objective 3. Explore how varying shapes and styles of containers can have the same capacity.

(3) Tell time to the quarter hour.

(A)Objective 1. Distinguish between a.m. and p.m.

(B)Objective 2. Read and write time to the quarter hour on an analog and digital clock.

(f)Standard Three objectives for Grade 3. The following objectives apply for students in Grade 3:

(1) Analyze and use geometric attributes to describe and create polygons and three-dimensional figures in various contexts.

(A)Objective 1. Sort three-dimensional shapes based on attributes.

(B)Objective 2. Build a three-dimensional figure using unit cubes when shown a picture of a three-dimensional shape.

(C)Objective 3. Classify angles within a polygon as acute, right, obtuse, and straight.

(2) Understand measurable attributes of real-world and mathematical objects using various tools.

(A)Objective 1. Find the perimeter of a polygon, given whole number lengths of the sides, using a variety of models.

(B)Objective 2. Analyze why length and width are multiplied to find the area of a rectangle by decomposing the rectangle into one unit by one unit squares and viewing these as rows and columns to determine the area.

(C)Objective 3. Counts cubes systematically to identify the number of cubes needed to pack the whole or half of a three-dimensional structure.

(D)Objective 4. Find the area of two-dimensional figures by counting the total number of same size unit squares that fill the shape without gaps or overlaps.

(E)Objective 5. Choose an appropriate measurement instrument and measure the length of objects to the nearest whole centimeter or meter.

(F)Objective 6. Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch.

(G)Objective 7. Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius.

(3) Solve problems by telling time to the nearest five-minute interval.

(A)Objective 1. Read and write time to the nearest five-minute interval.(analog and digital).

(B)Objective 2. Determine the solutions to problems involving addition and subtraction of time in intervals of five minutes, up to one hour, using pictorial models, number line diagrams, or other tools.

(g)Standard Three objectives for Grade 4. The following objectives apply for students in Grade 4:

(1) Name, describe, classify and construct polygons, and three- dimensional figures based on their attributes; recognize polygons and three-dimensional figures in real life and mathematical situations.

(A)Objective 1. Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various models.

(B)Objective 2. Describe, classify, and construct quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various models.

(C)Objective 3. Given two three-dimensional shapes, identify each shape. Compare and contrast their similarities and differences based on their attributes.

(2) Recognize and measure attributes in real-world and mathematical situations using various tools.

(A)Objective 1. Measure angles in geometric figures and real-world objects with a protractor or angle ruler.

(B)Objective 2. Find the area of polygons by determining if they can be decomposed into rectangles.

(C)Objective 3. Develop the concept that the volume of rectangular prisms with whole-number edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use a variety of tools and create mathematical models to determine the volume using appropriate measurements (e.g., cm³).

(D)Objective 4. Choose an appropriate instrument to measure the length of an object to the nearest whole centimeter or quarter-inch.

(E)Objective 5. Recognize and use the relationship between inches, feet, and yards to measure and compare objects.

(F)Objective 6. Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects.

(G)Objective 7. Determine and justify the best use of customary and metric measurements in a variety of situations (liquid volumes, mass vs. weight, temperatures above 0 (zero) degrees, and length).

(3) Determine elapsed time and convert between units of time.

(A)Objective 1. Determine elapsed time.

(B)Objective 2. Convert one measure of time to another including seconds to minutes, minutes to hours, hours to days, and vice versa, using various models..

(h)Standard Three objectives for Grade 5. The following objectives apply for students in Grade 5:

(1) Describe, identify, classify, and construct two- and three-dimensional figures using their geometric attributes.

(A)Objective 1. Describe, identify, classify and construct triangles (equilateral, right, scalene, isosceles) by their attributes, using various mathematical models.

(B)Objective 2. Describe, identify, and classify three-dimensional figures (cubes, rectangular prisms, and pyramids) and their attributes (number of edges, faces, vertices, shapes of faces), given various mathematical models.

(C)Objective 3. Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid).

(2) Determine volume using the object's dimensions. Compare and analyze rectangular prisms with equivalent volume to recognize their different dimensions.

(A)Objective 1. Determine the volume of rectangular prisms by the number of unit cubes (n) used to construct the shape and by the product of the dimensions of the prism (a.b.c = n). Understand rectangular prisms of different dimensions (p, q, and r) can have the same volume if a*b*c = p*q*r = n.

(B)Objective 2. Estimate the perimeter of polygons and create arguments for reasonable perimeter values of shapes that may include curves.

(3) Understand angle, length, weight, and capacity as measurable attributes of real-world and mathematical objects, using various tools to measure them. Solve real-world problems of length.

(A)Objective 1. Measure and compare angles according to size using various tools.

(B)Objective 2. Measure the length of an object to the nearest whole centimeter or 1/16-inch using an appropriate instrument.

(C)Objective 3. Apply the relationship between inches, feet, and yards to measure, convert, and compare objects to solve problems.

(D)Objective 4. Apply the relationship between millimeters, centimeters, and meters to measure, convert, and compare objects to solve problems.

(E)Objective 5. Estimate lengths and geometric measurements to the nearest whole unit, using benchmarks in customary and metric measurement systems.

(i)Standard Three objectives for Grade 6. The following objectives apply for students in Grade 6:

(1) Use translations, reflections, and rotations to establish congruence and understand symmetry (not on a coordinate plane).

(A)Objective 1. Predict, describe and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.

(B)Objective 2. Recognize that translations, reflections, and rotations preserve congruence and use them to show that two figures are congruent.

(C)Objective 4. Identify and describe the line(s) of symmetry in two-dimensional shapes.

(2) Use mathematical modeling to calculate the area of squares, parallelograms, and triangles to solve problems.

(A)Objective 1. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures.

(B)Objective 2. Develop and use formulas to determine the area of triangles and find unknown measures.

(C)Objective 3. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes.

(3) Understand and use relationships between angles in geometric figures.

(A)Objective 1. Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.

(B)Objective 2. Develop and use the fact that the sum of the interior angles of a triangle is 180° to determine missing angle measures in a triangle.

(4) Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

(A)Objective 1. Estimate weights and capacities using benchmarks in customary and metric measurement systems with appropriate units.

(B)Objective 2. Solve problems that require the conversion of lengths within the same measurement systems using appropriate units.

(j)Standard Three objectives for Grade 7. The following objectives apply for students in Grade 7:

(1) Develop and understand the concept of surface area and volume of rectangular prisms with rational-valued edge lengths.

(A)Objective 1. Recognize that the surface area of a rectangular prism can be found by finding the area of each component of the net of that figure. Know that rectangular prisms of different dimensions can have the same surface area.

(B)Objective 2. Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements (e.g., cm².).

(C)Objective 3. Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements (e.g., cm³.).

(2) Use mathematical models and problems to calculate and justify the area of trapezoids and the area and perimeter of composite figures with rational measurements.

(A)Objective 1. Develop and use the formula to determine the area of a trapezoid.

(B)Objective 2. Find the area and perimeter of composite figures.

(3) Use mathematical models and reasoning with proportions and ratios to determine measurements, justify formulas, and solve problems.

(A)Objective 1. Solve problems that require the conversion of weights and capacities within the same measurement systems using appropriate units.

(B)Objective 2. Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi ([PI]) and can be approximated by rational numbers such as 22/7 and 3.14.

(C)Objective 3. Calculate the circumference and area of circles to solve problems in various contexts, in terms of pi ([PI]) and using approximations for pi ([PI]).

(4) Analyze the effect of translations, reflections, rotations, and dilations on the attributes of two-dimensional figures on and off the coordinate plane.

(A)Objective 1. Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.

(B)Objective 2. Apply proportions, ratios, and scale factors to solve problems involving scale drawings and to determine side lengths and areas of similar triangles and rectangles.

(C)Objective 3. Graph and describe translations (with directional and algebraic instructions), reflections across the x- and y-axes, and rotations in 90^o increments about the origin of figures on a coordinate plane, and determine the coordinates of the vertices of the figure after the transformation.

(k)Standard Three objectives for Pre-Algebra. The following objectives apply for students in Pre-Algebra:

(1) Apply the Pythagorean Theorem to solve problems involving triangles.

(A)Objective 1. IJustify the Pythagorean Theorem using measurements, diagrams, or dynamic software to solve problems in two dimensions involving right triangles.

(B)Objective 2. Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.

(2) Justify and use formulas to calculate surface area and volume of three-dimensional figures.

(A)Objective 1. Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm².).

(B)Objective 2. Calculate the surface area of a cylinder, in terms of pi ([PI]) and using approximations for pi ([PI]), using decomposition or nets. Use appropriate units (e.g., cm².).

(C)Objective 3. Justify why base area (B) and height (h) in the formula V=Bh are multiplied to find the volume of a rectangular prism. Use appropriate units (e.g., cm³.).

(D)Objective 4. Develop and use the formulas V= [PI] r² h and V=Bh to determine the volume of right cylinders, in terms of [PI] and using approximations for [PI]. Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate units (e.g., cm³.).

(m)Standard Three objectives for Geometry. The following objectives apply for students in Geometry:

(1)Reasoning & Logic. Use appropriate tools and logic, including algebraic methods, to evaluate mathematical arguments.

(A)Objective 1. Use undefined terms, definitions, postulates, and theorems in logical arguments/proofs.

(B)Objective 2. Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive.

(C)Objective 3. Assess the validity of a logical argument and give counterexamples to disprove a statement.

(2)Two-Dimensional Shapes. Discover, evaluate and analyze the relationships between lines, angles, and polygons to solve real-world and mathematical problems; express proofs in a form that clearly justifies the reasoning (e.g., two-column proofs, paragraph proofs, flowcharts).

(A)Objective 1. Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems.

(B)Objective 2. Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs.

(C)Objective 3. Apply the properties of angles, (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs.

(D)Objective 4. Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs.

(E)Objective 5. Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs.

(F)Objective 6. Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.

(G)Objective 7. Apply the properties of polygons and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).

(H)Objective 8. Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning.

(I)Objective 9. Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL).

(J)Objective 10. Construct logical arguments to prove triangle similarity (AA, SSS, SAS).

(K)Objective 11. Use numeric, graphic and algebraic representations of transformations in two dimensions (reflections, translations, dilations, rotations about the origin by multiples of 90 °) to solve problems involving figures on a coordinate plane and identify types of symmetry.

(3)Three-Dimensional Shapes. Solve real-world and mathematical problems involving three-dimensional figures.

(A)Objective 1. Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, and composites of these figures).

(B)Objective 2. Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter and circumference of a face, area of a face, and volume.

(4)Circles. Solve real-world and mathematical problems using the properties of circles.

(A)Objective 1. Apply the properties of circles to solve problems involving circumference and area, using approximate values and in terms of pi, using algebraic and logical reasoning.

(B)Objective 2. Use the distance and midpoint formula, where appropriate, to recognize and write the radius r, center (h,k), and standard form of the equation of a circle (x - h)² + (y - k)² = r² with and without graphs.

(C)Objective 3. Apply the properties of circles and relationships among angles; arcs; and distances in a circle among radii, chords, secants and tangents to solve problems using algebraic reasoning.

(5)Right Triangle Trigonometry. Apply mathematical relationships of right triangles and trigonometric ratios to solve real-world and mathematical problems.

(A)Objective 1. Apply the distance formula, the Pythagorean theorem, and the Pythagorean theorem converse (approximate and exact values, including Pythagorean triples) to solve problems, using algebraic and logical reasoning and mathematical models.

(B)Objective 2. Verify and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems using algebraic and logical reasoning.

(C)Objective 3. Use the definition of the trigonometric functions to determine the sine, cosine, and tangent ratio of an acute angle in a right triangle. Apply the inverse trigonometric functions to find the measure of an acute angle in right triangles.

(D)Objective 4. Apply the trigonometric functions as ratios (sine, cosine, and tangent) to find side lengths in right triangles in mathematical models, including the coordinate plane.

(b)Standard Three objectives for Pre Calculus and Trigonometry. The following objectives apply for students in Pre Calculus and Trigonometry:

(1) Investigate conic sections.

(A)Objective 1. Model real-world situations which involve conic sections.

(B)Objective 2. Identify key features of conic sections (foci, directrix, radii, axes, asymptotes, center) graphically and algebraically.

(C)Objective 3. Sketch a graph of a conic section using its key features.

(D)Objective 4. Write the equation of a conic section given key features.

(E)Objective 5. Given the equation ax² + by² + cx + dy + e = 0, determine if the equation is a circle, ellipse, parabola, or hyperbola.

(2) Make sense of the unit circle and its relationship to the graphs of trigonometric functions.

(A)Objective 1. Draw and recognize angles in standard position using radian measure, and determine the quadrant of the terminal side.

(B)Objective 2. Convert radian measure to degree measure and vice-versa.

(C)Objective 3. Find the length of an arc and the area of a sector on a circle.

(D)Objective 4. Use special triangles to determine geometrically the values of sine, cosine, tangent for [PI]/3, [PI]/4 and [PI]/6, and use the unit circle to express the values of sine, cosine, and tangent for [PI]-x, [PI]+x, and 2[PI]-x in terms of their values for x, where x is any real number.

(E)Objective 5. Use reference angles to determine the terminal point P(x,y) on the unit circle for a given angle.

(F)Objective 6. Estimate trigonometric values of any angle.

(G)Objective 7. Apply the properties of a unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

(H)Objective 8. Graph of all six trigonometric functions, identifying key features.

(I)Objective 9. Describe and analyze the relationships of the properties of a unit circle.

(3) Apply trigonometric concepts beyond the right triangle.

(A)Objective 1. Create models for situations involving trigonometry.

(B)Objective 2. Apply the Law of Sines and Law of Cosines to solve problems.

(C)Objective 3. Use trigonometry to find the area of triangles.

(D)Objective 4. Use inverse functions to solve trigonometric; evaluate the solution and interpret them in terms of context.

(4) Verify trigonometric identities and solve equations.

(A)Objective 1. Algebraically manipulate the structure of a trigonometric expression to identify ways to rewrite it.

(B)Objective 2. Choose and produce an equivalent form of an expression to explain the properties of the quantity represented by the expression.

(C)Objective 3. Graphically and algebraically verify solutions to trigonometric equations.

Okla. Admin. Code § 210:15-3-64

Adopted by Oklahoma Register, Volume 40, Issue 5, November 15, 2022, eff. 12/11/2022