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Assessments
NAEP Assessment Item, Grade 4: Assemble Pieces to Form Shape
Discipline
Mathematics
Grades
Prekindergarten, Kindergarten, 1, 2, 3, 4, 5
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Professional Commentary

Students are asked to form a 4-sided shape that is not a square using two figures that appear to be isosceles right triangles and to draw a line where the two pieces meet. This constructed-response question is a sample test item used in grades 4, 8, and 12 in the 1996 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring guide, sample student responses, and a discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 1996-4M10, No. 4. (sw)


Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (K–2)
A.
Describe and create plane figures: circle, rectangle, square, triangle, hexagon, trapezoid, parallelogram and rhombus, and identify them in the environment.
Benchmarks (3–4)
E.
Use attributes to describe, classify and sketch plane figures and build solid objects.
F.
Develop definitions of classes of shapes.
I.
Describe, identify and model reflections, rotations and translations, using physical materials.
Grade Level Indicators (Grade Prekindergarten)
3.
Identify, name, create and describe common two-dimensional shapes in the environment and play situations (e.g., circles, triangles, rectangles, and squares).
Grade Level Indicators (Grade 1)
2.
Create new shapes by combining or cutting apart existing shapes.
5.
Copy figures and draw simple two-dimensional shapes from memory.
Grade Level Indicators (Grade 2)
2.
Predict what new shapes will be formed by combining or cutting apart existing shapes.
Grade Level Indicators (Grade 3)
1.
Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face.
Grade Level Indicators (Grade 4)
2.
Describe, classify, compare and model two- and three-dimensional objects using their attributes.
3.
Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.
7.
Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if two shapes are congruent.
Mathematical Processes Standard
Benchmarks (K–2)
F.
Draw pictures and use physical models to represent problem situations and solutions.
Principles and Standards for School Mathematics
Geometry Standard
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Expectations (Pre-K–2)
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
Expectations (3–5)
identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;
classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;
investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
Apply transformations and use symmetry to analyze mathematical situations
Expectations (Pre-K–2)
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
Expectations (3–5)
identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;
classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;
investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
predict and describe the results of sliding, flipping, and turning two-dimensional shapes;
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (Pre-K–2)
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
Expectations (3–5)
identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;
classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;
investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
predict and describe the results of sliding, flipping, and turning two-dimensional shapes;
build and draw geometric objects;
Problem Solving Standard
Solve problems that arise in mathematics and in other contexts