By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.

• 1.0 Students understand perimeter and area:

  1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm²), square meter (m²), square kilometer (km²), square inch (in²), square yard (yd²), or square mile (mi²).

  1.2 Recognize that rectangles that have the same area can have different perimeters.

  1.3 Understand that rectangles that have the same perimeter can have different areas.

  1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

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• 2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures:

  2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line).

  2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates.

  2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates.

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• 3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:

  3.1 Identify lines that are parallel and perpendicular.

  3.2 Identify the radius and diameter of a circle.

  3.3 Identify congruent figures.

  3.4 Identify figures that have bilateral and rotational symmetry.

  3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, 3/4, and full turns.

  3.6 Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.

  3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.

  3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

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