

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

1. Extend understanding of irrational and rational numbers by rewriting expressions involving radicals, including addition, subtraction, multiplication, and division, in order to recognize geometric patterns. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

2. Use units as a way to understand problems and to guide the solution of multistep problems.
a. Choose and interpret units consistently in formulas.
b. Choose and interpret the scale and the origin in graphs and data displays.
c. Define appropriate quantities for the purpose of descriptive modeling.
d. Choose a level of accuracy appropriate to limitations of measurements when reporting quantities. Unpacked Content
Alabama Alternate Achievement Standards




Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

3. Find the coordinates of the vertices of a polygon determined by a set of lines, given their equations, by setting their function rules equal and solving, or by using their graphs. Unpacked Content


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Example: Rearrange the formula for the area of a trapezoid to highlight one of the bases. Unpacked Content
Alabama Alternate Achievement Standards



Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

5. Verify that the graph of a linear equation in two variables is the set of all its solutions plotted in the coordinate plane, which forms a line. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
1 
Classroom Resources: 
1 

6. Derive the equation of a circle of given center and radius using the Pythagorean Theorem.
a. Given the endpoints of the diameter of a circle, use the midpoint formula to find its center and then use the Pythagorean Theorem to find its equation.
b. Derive the distance formula from the Pythagorean Theorem. Unpacked Content
Alabama Alternate Achievement Standards




Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

7. Use mathematical and statistical reasoning with quantitative data, both univariate data (set of values) and bivariate data (set of pairs of values) that suggest a linear association, in order to draw conclusions and assess risk.
Example: Estimate the typical age at which a lung cancer patient is diagnosed, and estimate how the typical age differs depending on the number of cigarettes smoked per day. Unpacked Content



Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

8. Use technology to organize data, including very large data sets, into a useful and manageable structure.
Unpacked Content


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

9. Represent the distribution of univariate quantitative data with plots on the real number line, choosing a format (dot plot, histogram, or box plot) most appropriate to the data set, and represent the distribution of bivariate quantitative data with a scatter plot. Extend from simple cases by hand to more complex cases involving large data sets using technology. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

10. Use statistics appropriate to the shape of the data distribution to compare and contrast two or more data sets, utilizing the mean and median for center and the interquartile range and standard deviation for variability.
a. Explain how standard deviation develops from mean absolute deviation.
b. Calculate the standard deviation for a data set, using technology where appropriate. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

11. Interpret differences in shape, center, and spread in the context of data sets, accounting for possible effects of extreme data points (outliers) on mean and standard deviation. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

12. Represent data of two quantitative variables on a scatter plot, and describe how the variables are related.
a. Find a linear function for a scatter plot that suggests a linear association and informally assess its fit by plotting and analyzing residuals, including the squares of the residuals, in order to improve its fit.
b. Use technology to find the leastsquares line of best fit for two quantitative variables. Unpacked Content


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

13. Compute (using technology) and interpret the correlation coefficient of a linear relationship. Unpacked Content

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

14. Distinguish between correlation and causation. Unpacked Content


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

15. Evaluate possible solutions to reallife problems by developing linear models of contextual situations and using them to predict unknown values.
a. Use the linear model to solve problems in the context of the given data.
b. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the given data. Unpacked Content
Alabama Alternate Achievement Standards




Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
3 
Classroom Resources: 
3 

16. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
10 
Classroom Resources: 
10 

17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.
a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.
b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
5 
Learning Activities: 
3 
Classroom Resources: 
2 

18. Given the coordinates of the vertices of a polygon, compute its perimeter and area using a variety of methods, including the distance formula and dynamic geometry software, and evaluate the accuracy of the results. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

19. Derive and apply the relationships between the lengths, perimeters, areas, and volumes of similar figures in relation to their scale factor. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
1 
Classroom Resources: 
1 

20. Derive and apply the formula for the length of an arc and the formula for the area of a sector. Unpacked Content



Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
2 
Classroom Resources: 
2 

21. Represent transformations and compositions of transformations in the plane (coordinate and otherwise) using tools such as tracing paper and geometry software.
a. Describe transformations and compositions of transformations as functions that take points in the plane as inputs and give other points as outputs, using informal and formal notation.
b. Compare transformations which preserve distance and angle measure to those that do not. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
3 
Classroom Resources: 
3 

22. Explore rotations, reflections, and translations using graph paper, tracing paper, and geometry software.
a. Given a geometric figure and a rotation, reflection, or translation, draw the image of the transformed figure using graph paper, tracing paper, or geometry software.
b. Specify a sequence of rotations, reflections, or translations that will carry a given figure onto another.
c. Draw figures with different types of symmetries and describe their attributes. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
5 
Classroom Resources: 
5 

23. Develop definitions of rotation, reflection, and translation in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
1 
Classroom Resources: 
1 

24. Define congruence of two figures in terms of rigid motions (a sequence of translations, rotations, and reflections); show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other.
Example: â–³ABC is congruent to â–³XYZ since a reflection followed by a translation maps â–³ABC onto â–³XYZ.
Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
3 
Lesson Plans: 
1 
Classroom Resources: 
2 

25. Verify criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another.
a. Verify that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
b. Verify that two triangles are congruent if (but not only if) the following groups of corresponding parts are congruent: anglesideangle (ASA), sideangleside (SAS), sidesideside (SSS), and angleangleside (AAS).
Example: Given two triangles with two pairs of congruent corresponding sides and a pair of congruent included angles, show that there must be a sequence of rigid motions will map one onto the other. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
2 
Classroom Resources: 
2 

26. Verify experimentally the properties of dilations given by a center and a scale factor.
a. Verify that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b. Verify that the dilation of a line segment is longer or shorter in the ratio given by the scale factor. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
1 
Classroom Resources: 
1 

27. Given two figures, determine whether they are similar by identifying a similarity transformation (sequence of rigid motions and dilations) that maps one figure to the other. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

28. Verify criteria for showing triangles are similar using a similarity transformation (sequence of rigid motions and dilations) that maps one triangle to another.
a. Verify that two triangles are similar if and only if corresponding pairs of sides are proportional and corresponding pairs of angles are congruent.
b. Verify that two triangles are similar if (but not only if) two pairs of corresponding angles are congruent (AA), the corresponding sides are proportional (SSS), or two pairs of corresponding sides are proportional and the pair of included angles is congruent (SAS).
Example: Given two triangles with two pairs of congruent corresponding sides and a pair of congruent included angles, show there must be a set of rigid motions that maps one onto the other. Unpacked Content
Alabama Alternate Achievement Standards



Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
0 

29. Find patterns and relationships in figures including lines, triangles, quadrilaterals, and circles, using technology and other tools.
a. Construct figures, using technology and other tools, in order to make and test conjectures about their properties.
b. Identify different sets of properties necessary to define and construct figures.
Unpacked Content


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
3 
Classroom Resources: 
3 

30. Develop and use precise definitions of figures such as angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
4 
Classroom Resources: 
4 

31. Justify whether conjectures are true or false in order to prove theorems and then apply those theorems in solving problems, communicating proofs in a variety of ways, including flow chart, twocolumn, and paragraph formats.
a. Investigate, prove, and apply theorems about lines and angles, including but not limited to: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; the points on the perpendicular bisector of a line segment are those equidistant from the segment's endpoints.
b. Investigate, prove, and apply theorems about triangles, including but not limited to: the sum of the measures of the interior angles of a triangle is 180?; the base angles of isosceles triangles are congruent; the segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length; a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem using triangle similarity.
c. Investigate, prove, and apply theorems about parallelograms and other quadrilaterals, including but not limited to both necessary and sufficient conditions for parallelograms and other quadrilaterals, as well as relationships among kinds of quadrilaterals.
Example: Prove that rectangles are parallelograms with congruent diagonals.
Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
4 
Classroom Resources: 
4 

32. Use coordinates to prove simple geometric theorems algebraically. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
3 
Lesson Plans: 
2 
Classroom Resources: 
1 

33. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
Example: Find the equation of a line parallel or perpendicular to a given line that passes through a given point. Unpacked Content
Alabama Alternate Achievement Standards



Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
2 
Classroom Resources: 
2 

34. Use congruence and similarity criteria for triangles to solve problems in realworld contexts. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
5 
Learning Activities: 
3 
Lesson Plans: 
1 
Classroom Resources: 
1 

35. Discover and apply relationships in similar right triangles.
a. Derive and apply the constant ratios of the sides in special right triangles (45^{o}45^{o}90^{o} and 30^{o}60^{o}90^{o}).
b. Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.
c. Explain and use the relationship between the sine and cosine of complementary angles.
d. Demonstrate the converse of the Pythagorean Theorem.
e. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
6 
Learning Activities: 
3 
Classroom Resources: 
3 

36. Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems. Unpacked Content
Alabama Alternate Achievement Standards

Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
3 
Classroom Resources: 
3 

37. Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Unpacked Content
Alabama Alternate Achievement Standards


Mathematics (2019) 
Grade(s): 9  12 
Geometry with Data Analysis 
All Resources: 
2 
Classroom Resources: 
2 

38. Use the mathematical modeling cycle involving geometric methods to solve design problems.
Examples: Design an object or structure to satisfy physical constraints or minimize cost; work with typographic grid systems based on ratios; apply concepts of density based on area and volume. Unpacked Content
Alabama Alternate Achievement Standards
