• 7
Top Mathematicians
• Shape and Space
• 7.SS.1
Demonstrate an understanding of circles by:
describing the relationships among radius, diameter and circumference of circles;
relating circumference to π;
determining the sum of the central angles;
constructing circles with a given radius or diameter;
solving problems involving the radii, diameters and circumferences of circles.

Students who have achieved this outcome should be able to:
A. Illustrate and explain that the diameter is twice the radius in a given circle.
B. Illustrate and explain that the circumference is approximately three times the diameter in a given circle.
C. Explain that, for all circles, π is the ratio of the circumference to the diameter, (C/d), and its value is approximately 3.14.
D. Explain, using an illustration, that the sum of the central angles of a circle is 360°.
E. Draw a circle with a given radius or diameter with and without a compass.
F. Solve a given contextual problem involving circles.
• 7.SS.2
Develop and apply a formula for determining the area of:
triangles;
parallelograms;
circles.

Students who have achieved this outcome should be able to:
A. Illustrate and explain how the area of a rectangle can be used to determine the area of a triangle.
B. Generalize a rule to create a formula for determining the area of triangles.
C. Illustrate and explain how the area of a rectangle can be used to determine the area of a parallelogram.
D. Generalize a rule to create a formula for determining the area of parallelograms.
E. Illustrate and explain how to estimate the area of a circle without the use of a formula.
F. Apply a formula for determining the area of a given circle.
G. Solve a given problem involving the area of triangles, parallelograms and/or circles.
• 7.SS.3
Perform geometric constructions, including:
perpendicular line segments;
parallel line segments;
perpendicular bisectors;
angle bisectors.

Students who have achieved this outcome should be able to:
A. Describe examples of parallel line segments, perpendicular line segments, perpendicular bisectors and angle bisectors in the environment.
B. Identify line segments on a given diagram that are parallel or perpendicular.
C. Draw a line segment perpendicular to another line segment and explain why they are perpendicular.
D. Draw a line segment parallel to another line segment and explain why they are parallel.
E. Draw the bisector of a given angle using more than one method and verify that the resulting angles are equal.
F. Draw the perpendicular bisector of a line segment using more than one method and verify the construction.
• 7.SS.4
Identify and plot points in the four quadrants of a Cartesian plane using integral ordered pairs.
Students who have achieved this outcome should be able to:
A. Label the axes of a four quadrant Cartesian plane and identify the origin.
B. Identify the location of a given point in any quadrant of a Cartesian plane using an integral ordered pair.
C. Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5 or 10 on its axes.
D. Draw shapes and designs, using given integral ordered pairs, in a Cartesian plane.
E. Create shapes and designs, and identify the points used to produce the shapes and designs in any quadrant of a Cartesian plane.
• 7.SS.5
Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).
Students who have achieved this outcome should be able to:
A. Identify the coordinates of the vertices of a given 2-D shape on a Cartesian plane.
B. Describe the horizontal and vertical movement required to move from a given point to another point on a Cartesian plane.
C. Describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation or successive transformations on a Cartesian plane.
D. Determine the distance between points along horizontal and vertical lines in a Cartesian plane.
E. Perform a transformation or consecutive transformations on a given 2-D shape and identify coordinates of the vertices of the image.
F. Describe the positional change of the vertices of a 2-D shape to the corresponding vertices of its image as a result of a transformation or a combination of successive transformations.
G. Describe the image resulting from the transformations of a given 2-D shape on a Cartesian plane by identifying the coordinates of the vertices of the image.
• Number
• Patterns and Relations
• Statistics & Probability