 # GEOMETRY STRAND

 GRADE STANDARDS COMMENTS k MKG1 Students will correctly name simple two and three -dimensional figures, and recognize them in the environment. a. Recognize and name the following basic two-dimensional figures: triangles, rectangles, squares, and circles. b. Recognize and name the following three-dimensional figures: spheres (balls) and cubes. c. Observe concrete objects in the environment and represent the objects using basic shapes, such as drawing a representation of a house using a square together with a triangle for the roof. d. Combine basic shapes into basic and more complicated shapes, and decompose basic shapes into combinations of basic shapes. e. Compare geometric shapes and identify similarities and differences of the following two and three-dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes. MKG2. Students will understand basic spatial relationships. MKG3 Students will identify, create, extend, and transfer patterns from one representation to another using actions, objects, and geometric shapes. a. Identify a missing shape within a given pattern of geometric shapes. b. Extend a given pattern, and recognize similarities (such as color, shape, texture, or number) in different patterns . 1st M1G1 Students will study and create various two and three-dimensional figures and identify basic figures (squares, circles, triangles, and rectangles) within them. a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons. b. Build, represent, name, and describe cylinders, cones, and rectangular prisms (objects that have the shape of a box). c. Create pictures and designs using shapes, including overlapping shapes. M1G2 Students will compare, contrast, and/or classify geometric shapes by the common attributes of position, shape, size, number of sides, and number of corners. 2nd M2G1 Students will describe and classify plane figures (triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, hexagons, and irregular polygonal shapes) according to the number of edges and vertices and the sizes of angles (right angle, obtuse, acute). M2G2 Students will describe and classify solid geometric figures (prisms, cylinders, cones, and spheres) according to such things as the number of edges and vertices and the number and shape of faces and angles. 3rd M3G1 Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. a. Draw and classify previously learned fundamental geometric figures as well as scalene, isosceles, and equilateral triangles. b. Identify and explain the properties of fundamental geometric figures. c. Examine and compare angles of fundamental geometric figures. d. Identify the center, diameter, and radius of a circle. 4th M4G1 Students will define and identify the characteristics of geometric figures through examination and construction. a. Examine and compare angles in order to classify and identify triangles by their angles. b. Describe parallel and perpendicular lines in plane geometric figures. c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi). d. Compare and contrast the relationships among quadrilaterals. M4G2 Students will understand fundamental solid figures. a. Compare and contrast a cube and a rectangular prism in terms of the number and shape of their faces, edges, and vertices. b. Describe parallel and perpendicular lines and planes in connection with rectangular prisms. c. Construct/collect models for solid geometric figures (cubes, prisms, cylinders, etc.) M4G3 Students will use the coordinate system . a. Understand and apply ordered pairs in the first quadrant of the coordinate system. b. Locate a point in the first quadrant in the coordinate plane and name the ordered pair. c. Graph ordered pairs in the first quadrant. 5th M5M1. Students will extend their understanding of area of fundamental geometric plane figures. a. Estimate the area of fundamental geometric plane figures. b. Derive the formula for the area of a parallelogram (e.g., cut the parallelogram apart and rearrange it into a rectangle of the same area). c. Derive the formula for the area of a triangle (e.g. demonstrate and explain its relationship to the area of a rectangle with the same base and height). d. Find the areas of triangles and parallelograms using formulae. e. Estimate the area of a circle through partitioning and tiling and then with formula (let pi = 3.14). (Discuss square units as they apply to circles.) f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes. M5M4. Students will understand and compute the volume of a simple geometric solid. a. Understand a cubic unit (u3) is represented by a cube in which each edge has the length of 1 unit. b. Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3). c. Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives. d. Compute the volume of a cube and a rectangular prism using formulae. e. Estimate the volume of a simple geometric solid. f. Understand the similarities and differences between volume and capacity. M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles. M5G2. Students will understand the relationship of the circumference of a circle to its diameter is pi (π ≈ 3.14). 6th M6M2. Students will use appropriate units of measure for finding length, perimeter, area and volume and will express each quantity using the appropriate unit. a. Measure length to the nearest half, fourth, eighth and sixteenth of an inch. b. Select and use units of appropriate size and type to measure length, perimeter, area and volume. c. Compare and contrast units of measure for perimeter, area, and volume. M6M3. Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids and cones). a. Determine the formula for finding the volume of fundamental solid figures. b. Compute the volumes of fundamental solid figures, using appropriate units of measure. c. Estimate the volumes of simple geometric solids. d. Solve application problems involving the volume of fundamental solid figures. M6M4. Students will determine the surface area of solid figures (right rectangular prisms and cylinders). a. Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets. b. Compute the surface area of right rectangular prisms and cylinders using formulae. c. Estimate the surface areas of simple geometric solids. d. Solve application problems involving surface area of right rectangular prisms and cylinders. M6M4. Students will determine the surface area of solid figures (right rectangular prisms and cylinders). a. Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets. b. Compute the surface area of right rectangular prisms and cylinders using formulae. c. Estimate the surface areas of simple geometric solids. d. Solve application problems involving surface area of right rectangular prisms and cylinders. M6G1. Students will further develop their understanding of plane figures. a. Determine and use lines of symmetry. b. Investigate rotational symmetry, including degree of rotation. c. Use the concepts of ratio , proportion and scale factor to demonstrate the relationships between similar plane figures. d. Interpret and sketch simple scale drawings. e. Solve problems involving scale drawings. M6G2. Students will further develop their understanding of solid figures. a. Compare and contrast right prisms and pyramids. b. Compare and contrast cylinders and cones. c. Interpret and sketch front, back, top, bottom and side views of solid figures. d. Construct nets for prisms, cylinders, pyramids, and cones.
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