Standards - Mathematics

• Simplify radicals and justify simplification of radicals using visual representations.
• Use the operations of addition, subtraction, division, and multiplication, with radicals.
• Demonstrate an understanding of radicals as they apply to problems involving squares, perfect squares, and square roots (e.g., the Pythagorean Theorem, circle geometry, volume, and area).

• Choose the appropriate known conversions to perform dimensional analysis to convert units.
• Correctly use graphing window and other technology features to precisely determine features of interest in a graph.
• Determine when a descriptive model accurately portrays the phenomenon it was chosen to model.
• Justify their selection of model and choice of quantities in the context of the situation modeled and critique the arguments of others concerning the same situation.
• Determine and distinguish the accuracy and precision of measurements.

• Find the coordinates of the vertices of a polygon given a set of lines and their equations by setting their function rules equal and solving or by using their graph.

• Accurately rearrange equations or inequalities to produce equivalent forms for use in resolving situations of interest.

• Accurately find ordered pairs that satisfy the equation.
• Accurately graph the ordered pairs and form a line

• Create a right triangle in a circle using the horizontal and vertical shifts from the center as the legs and the radius of the circle as the hypotenuse.
• Write the equation of the circle in standard form when given the endpoints of the diameter of a circle, using the midpoint formula to find the circle's center, and then use the Pythagorean Theorem to find the equation of the circle.
• Find the distance between two points when using the Pythagorean Theorem and use that process to create the Distance Formula.

• Construct a scatter plot to represent a set of bivariate data.
• Use mathematical vocabulary to describe and interpret patterns in bivariate data.
• Use logical reasoning and appropriate strategies to draw a straight line to fit data that suggest a linear association.
• Use mathematical vocabulary, logical reasoning, and closeness of data points to a line to judge the fit of the line to the data.
• Find a central value using mean, median and mode.
• Find how spread out the univariate data is using range, quartiles and standard deviation.
• Make plots like Bar Graphs, Pie Charts and Histograms.

Students are able to:

• recognize patterns, trends, clusters, and gaps in the organized data.

• Choose from among data display (dot plots, histograms, box plots, scatter plots) to convey significant features of data.
• Accurately construct dot plots, histograms, and box plots.
• Accurately construct scatter plots using technology to organize and analyze the data.

• Accurately find the center (median and mean) and spread (interquartile range and standard deviation) of data sets.
• -Present viable arguments and critique arguments of others from the comparison of the center and spread of multiple data sets.
• Explain their reasoning on how standard deviation develops from the mean absolute deviation.

Students are able to:

• Accurately identify differences in shape, center, and spread when comparing two or more data sets.
• Accurately identify outliers for the mean and standard deviation.
• Explain, with justification, why there are differences in the shape, center, and spread of data sets.

• Accurately create a scatter plot of data.
• Make reasonable assessments on the fit of the function to the data by examining residuals.
• Accurately fit a function to data when there is evidence of a linear association.
• Use technology to find the least-squares line of best fit for two quantitative variable.

• use technology to graph different data sets
• Use the correlation coefficient to assess the strength and direction of the relationship between two data sets.

Students are able to:

• distinguish between correlation and causation

• Accurately create a scatter plot of data.
• Correctly choose a function to fit the scatter plot.
• Make reasonable assessments on the fit of the function to the data by examining residuals.
• Accurately fit a linear function to data when there is evidence of a linear association.
• Accurately fit linear functions to scatter plots.
• Correctly find the slope and intercept of linear functions.
• Justify and explain the relevant connections slope and intercept of the linear function to the data.

• Accurately decompose circles, cylinders, pyramids, and cones into other geometric shapes.
• Explain and justify how the formulas for circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone may be created from the use of other geometric shapes.

• Accurately decompose circles, spheres, cylinders, pyramids, and cones into other geometric shapes.
• Explain and justify how the formulas for surface area, and volume of a sphere, cylinder, pyramid, and cone may be created from the use of other geometric shapes.

• Create geometric figures on a coordinate system from a contextual situation.
• Accurately find the perimeter of polygons and the area of polygons such as triangles and rectangles from the coordinates of the shapes.
• Explain and justify solutions in the original context of the situation.

• Find the scale factor of any given set of similar figures.
• Find the ratios of perimeter, area, and volume

• Reason from progressive examples using dynamic geometry software to form conjectures about relationships among arc length, central angles, and the radius.
• Use logical reasoning to justify (or deny) these conjectures and critique the reasoning presented by others.
• Interpret a sector as a portion of a circle, and use the ratio of the portion to the whole circle to create a formula for the area of a sector.

• Accurately perform dilations, rotations, reflections, and translations on objects in the coordinate plane with and without technology.
• Communicate the results of performing transformations on objects and their corresponding coordinates in the coordinate plane, including when the transformation preserves distance and angle.
• Use the language and notation of functions as mappings to describe transformations.