Standards - Mathematics

• Functions are used to create equations representative of ordered pairs of data.
• Residuals may be examined to analyze how well a function fits the data.
• When a linear association is suggested, a linear function can be fit to the scatter plot to aid in modeling the relationship.

• using technology to graph some data and look at the regression line that technology can generate for a scatter plot.

• Functions are used to create equations representative of ordered pairs of data.
• Residuals may be examined to analyze how well a function fits the data.
• When a linear association is suggested, a linear function can be fit to the scatter plot to aid in modeling the relationship.
• Linear functions are used to model data that have a relationship that closely resembles a linear relationship.
• The slope and intercept of a linear function may be interpreted as the rate of change and the zero point (starting point).

• Geometric shapes may be decomposed into other shapes which may be useful in creating formulas.
• Geometric shapes may be divided into an infinite number of smaller geometric shapes, and the combination of those shapes maintain the area and volume of the original shape.

• Geometric shapes may be decomposed into other shapes which may be useful in creating formulas.
• Geometric shapes may be divided into an infinite number of smaller geometric shapes, and the combination of those shapes maintain the area and volume of the original shape.

• Contextual situations may be modeled in a Cartesian coordinate system.
• Coordinate modeling is frequently useful to visualize a situation and to aid in solving contextual problems.

• Just as their corresponding sides are in the same proportion, perimeters and areas of similar polygons have a special relationship. Perimeters: The ratio of the perimeters is the same as the scale factor. If the scale factor of the sides of two similar polygons is m/n, then the ratio of the areas is (m/n)²

• Radians measure the ratio of the arc length to the radius for an intercepted arc.
• The ratio of the area of a sector to the area of a circle is proportional to the ratio of the central angle to a complete revolution.

• Mapping one point to another through a series of transformations can be recorded as a function.
• Some transformations (translations, rotations, and reflections) preserve distance and angle measure, and the image is then congruent to the pre-image, while dilations preserve angle but not distance, and the pre-image is similar to the image.
• Distortions, such as only a horizontal stretch, preserve neither.

Students understand that:

• Mapping one point to another through a series of transformations can be recorded as a function.
• Since translations, rotations and reflections preserve distance and angle measure, the image is then congruent.
• The same transformation may be produced using a variety of tools, but the geometric sequence of steps that describe the transformation is consistent.

• Geometric definitions are developed from a few undefined notions by a logical sequence of connections that lead to a precise definition.
• A precise definition should allow for the inclusion of all examples of the concept and require the exclusion of all non-examples.

• Any distance preserving transformation is a combination of rotations, reflections, and translations.
• If a series of translations, rotations, and reflections can be described that transforms one object exactly to a second object, the objects are congruent.

• If a series of translations, rotations, and reflections can be described that transforms one object exactly to a second object, the objects are congruent.
• It is beneficial to have minimal sets of requirements to justify geometric results (e.g., use ASA, SAS, or SSS instead of all sides and all angles for congruence).

• A dilation uses a center and line segments through vertex points to create an image which is similar to the original image but in a ratio specified by the scale factor.
• The ratio of the line segment formed from the center of dilation to a vertex in the new image and the corresponding vertex in the original image is equal to the scale factor.

• A figure that may be obtained from another through a dilation and a combination of translations, reflections, and rotations is similar to the original.
• When a figure is similar to another the measures of all corresponding angles are equal, and all of the corresponding sides are in the same proportion.

• A figure that may be obtained from another through a dilation and a combination of translations, reflections, and rotations is similar to the original.
• When a figure is similar to another the measures of all corresponding angles are equal, and all of the corresponding sides are in the same proportion.

• Many of the constructions build on the relationships among the objects and are justified by the properties used during the construction. Technology can be used as a means to explain the properties and definitions by developing procedures to carry out the construction.