Appendix A4: Pennsylvania State Standards5

Grades K-3 (Pennsylvania Academic Standards for Mathematics, 2.9.3, Geometry)

A. Name and label geometric shapes in two and three dimensions (e.g., circle/sphere, square/cube, triangle/pyramid, rectangle/prism).

B. Build geometric shapes using concrete objects (e.g., manipulatives).

C. Draw two- and three-dimensional geometric shapes and construct rectangles, squares and triangles on the geoboard and on graph paper satisfying specific criteria.

D. Find and describe geometric figures in real life.

I. Predict how shapes can be changed by combining or dividing them.

Grades 4-5 (Pennsylvania Academic Standards for Mathematics, 2.9.5, Geometry)

D. Describe in words how geometric shapes are constructed.

E. Construct two- and three-dimensional shapes and figures using manipulatives, geoboards and computer software.

F. Find familiar solids in the environment and describe them.

H. Describe the relationship between the perimeter and area of triangles, quadrilaterals and circles.

I. Represent and use the concepts of line, point and plane.

J. Define the basic properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres and cylinders.

L. Identify properties of geometric figures (e.g., parallel, perpendicular, similar, congruent, symmetrical).

Grades K-3 (Pennsylvania Academic Standards for Mathematics, 2.9.3, Geometry)

A. Name and label geometric shapes in two and three dimensions (e.g., circle/sphere, square/cube, triangle/pyramid, rectangle/prism).

B. Build geometric shapes using concrete objects (e.g., manipulatives).

C. Draw two- and three-dimensional geometric shapes and construct rectangles, squares and triangles on the geoboard and on graph paper satisfying specific criteria.

D. Find and describe geometric figures in real life.

I. Predict how shapes can be changed by combining or dividing them.

Grades 4-5 (Pennsylvania Academic Standards for Mathematics, 2.9.5, Geometry)

A. Give formal definitions of geometric figures.

B. Classify and compare triangles and quadrilaterals according to sides or angles.

C. Identify and measure circles, their diameters and their radii.

D. Describe in words how geometric shapes are constructed.

E. Construct two- and three-dimensional shapes and figures using manipulatives, geoboards and computer software.

F. Find familiar solids in the environment and describe them.

I. Represent and use the concepts of line, point and plane.

J. Define the basic properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres and cylinders.

L. Identify properties of geometric figures (e.g., parallel, perpendicular, similar, congruent, symmetrical).

Grades 4-5 (Pennsylvania Academic Standards for Mathematics, 2.8.5, Algebra and Functions)

H. Locate and identify points on a coordinate system.

Grades K-3 (Pennsylvania Academic Standards for Mathematics, 2.9.3, Geometry)

A. Name and label geometric shapes in two and three dimensions (e.g., circle/sphere, square/cube, triangle/pyramid, rectangle/prism).

B. Build geometric shapes using concrete objects (e.g., manipulatives).

D. Find and describe geometric figures in real life.

E. Identify and draw lines of symmetry in geometric figures.

F. Identify symmetry in nature.

G. Fold paper to demonstrate the reflections about a line.

H. Show relationships between and among figures using reflections.

Grades 4-5 (Pennsylvania Academic Standards for Mathematics, 2.9.5, Geometry)

E. Construct two- and three-dimensional shapes and figures using manipulatives, geoboards and computer software.

G. Create an original tessellation.

K. Analyze simple transformations of geometric figures and rotations of line segments.

L. Identify properties of geometric figures (e.g., parallel, perpendicular, similar, congruent, symmetrical).

Grades K-3 (Pennsylvania Academic Standards for Mathematics, 2.3.3, Measurement and Estimation)

A. Compare measurable characteristics of different objects on the same dimensions (e.g., time, temperature, area, length, weight, capacity, perimeter).

B. Determine the measurement of objects with non-standard and standard units (e.g., U.S. customary and metric).

C. Determine and compare elapsed times.

D. Tell time (analog and digital) to the minute.

E. Determine the appropriate unit of measure.

F. Use concrete objects to determine area and perimeter.

G. Estimate and verify measurements.

H. Demonstrate that a single object has different attributes that can be measured i. different ways (e.g., length, mass, weight, time, area, temperature, capacity. perimeter).

Grades 4-5 (Pennsylvania Academic Standards for Mathematics, 2.3.5, Measurement and Estimation)

A. Select and use appropriate instruments and units for measuring quantities (e.g., perimeter, volume, area, weight, time, temperature).

B. Select and use standard tools to measure the size of figures with specified accuracy, including length, width, perimeter and area.

C. Estimate, refine and verify specified measurement of objects.

D. Convert linear measurements within the same system.

E. Add and subtract measurements.