High School Geometry. Correlation of the ALEKS course High School Geometry to the ACT College Readiness Standards for Mathematics

Transcription

1 High School Geometry Correlation of the ALEKS course High School Geometry to the ACT College Readiness Standards for Mathematics Standard 5 : Graphical Representations = ALEKS course topic that addresses the standard = Teacher Directed 5.1: Identify the location of a point with a positive coordinate on the number line 5.2: Locate points on the number line and in the first quadrant 5.3: Locate points in the coordinate plane Plotting a point in the coordinate plane 5.4: Comprehend the concept of length on the number line Computing distances on the number line 5.5: Exhibit knowledge of slope Graphing a line through a given point with a given slope 5.6: Identify the graph of a linear inequality on the number line Graphing a linear inequality on the number line 5.7: Determine the slope of a line from points or equations Determining the slope of a line given its graph Finding the slope of a line given its equation 5.8: Match linear graphs with their equations Graphing a line given its x- and y-intercepts Graphing a line given its equation in slope-intercept form Graphing a line given its equation in standard form Writing an equation of a line given the y-intercept and another point Writing the equation of a line given the slope and a point on the line Writing the equation of the line through two given points 5.9: Find the midpoint of a line segment Midpoint of a number line segment Midpoint of a line segment in the plane 5.10: Interpret and use information from graphs in the coordinate plane ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/6

2 Determining the slope of a line given its graph Writing an equation of a line given the y-intercept and another point Writing the equation of the line through two given points 5.11: Match number line graphs with solution sets of linear inequalities Graphing a linear inequality on the number line 5.12: Use the distance formula Distance between two points in the plane 5.13: Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point Writing equations of lines parallel and perpendicular to a given line through a point 5.14: Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) Graphing a circle given its equation in standard form 5.15: Match number line graphs with solution sets of simple quadratic inequalities 5.16: Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax 2 + c Finding x- and y-intercepts of a line given the equation: Advanced Finding the slope of a line given its equation 5.17: Solve problems integrating multiple algebraic and/or geometric concepts Finding slopes of lines parallel and perpendicular to a line given in the form Ax + By = C Writing equations of lines parallel and perpendicular to a given line through a point Writing an equation of a circle given its center and a point on the circle Writing an equation of a circle given the endpoints of a diameter 5.18: Analyze and draw conclusions based on information from graphs in the coordinate plane Determining the slope of a line given its graph Writing an equation of a line given the y-intercept and another point Writing the equation of the line through two given points Standard 6 : Properties of Plane Figures = ALEKS course topic that addresses the standard = Teacher Directed 6.1: Exhibit some knowledge of the angles associated with parallel lines Corresponding and alternate angles 6.2: Find the measure of an angle using properties of parallel lines ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/6

3 Angles and parallel lines 6.3: Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90, 180, and 360 ) Introduction to proofs involving parallel lines Supplementary and complementary angles Identifying linear pairs and vertical angles Solving equations involving vertical angles and linear pairs Angles and parallel lines Finding an angle measure of a triangle given two angles Finding an angle measure given extended triangles Finding an angle measure for a triangle with an extended side 6.4: Use several angle properties to find an unknown angle measure Solving equations involving vertical angles and linear pairs Angles and parallel lines Finding an angle measure given extended triangles Finding an angle measure for a triangle with an extended side Finding an angle measure for a triangle sharing a side with another triangle 6.5: Recognize Pythagorean triples 6.6: Use properties of isosceles triangles Scalene, isosceles, and equilateral triangles Finding angle measures of a right or isosceles triangle given angles with variables Finding an angle measure for a triangle sharing a side with another triangle 6.7: Apply properties of , , similar, and congruent triangles Identifying and naming congruent triangles Special right triangles Triangles and parallel lines Similar right triangles Right triangles and geometric mean Indirect measurement 6.8: Use the Pythagorean theorem Pythagorean Theorem Computing an area using the Pythagorean Theorem 6.9: Draw conclusions based on a set of conditions Triangle inequality: Problem type 1 Triangle inequality: Problem type 2 Relationship between angle measures and side lengths in a triangle: Problem type 1 Relationship between angle measures and side lengths in a triangle: Problem type 2 Classifying quadrilaterals Classifying quadrilaterals: Advanced problem ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/6

4 Classifying parallelograms Properties of parallelograms: Problem type : Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas Finding an angle measure given extended triangles Finding angle measures of a right or isosceles triangle given angles with variables Finding an angle measure for a triangle with an extended side Finding an angle measure for a triangle sharing a side with another triangle Triangle inequality: Problem type 1 Triangle inequality: Problem type 2 Relationship between angle measures and side lengths in a triangle: Problem type 1 Relationship between angle measures and side lengths in a triangle: Problem type 2 Computing an area using the Pythagorean Theorem Properties of parallelograms: Problem type 1 Properties of rectangles Properties of rhombi The sum of interior angle measures in a convex polygon Interior and exterior angle measures in a regular polygon Perimeter of a piecewise rectangular figure Finding a side length given the perimeter and side lengths with variables Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Finding the side length of a rectangle given its perimeter or area Finding the perimeter or area of a rectangle given one of these values Area between two rectangles Area involving rectangles and triangles Finding the radius or the diameter of a circle given its circumference Perimeter involving rectangles and circles Circumference ratios Area between two concentric circles Area involving rectangles and circles Area involving rectangles and circles: Advanced problem Similar polygons Finding coordinates of vertices of polygons Finding the coordinates of a point to make a parallelogram Area of quadrilaterals in the coordinate plane 6.11: Use relationships among angles, arcs, and distances in a circle Identifying central angles, inscribed angles, arcs, chords, and tangents of a circle Inscribed angles of a circle Central angles and inscribed angles of a circle Angles of intersecting secants and tangents Arc length and area of a sector of a circle Standard 7 : Measurement = ALEKS course topic that addresses the standard = Teacher Directed ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/6

5 7.1: Estimate or calculate the length of a line segment based on other lengths given on a geometric figure 7.2: Compute the perimeter of polygons when all side lengths are given Perimeter of a polygon Perimeter of a square or a rectangle 7.3: Compute the area of rectangles when whole number dimensions are given Area of a square or a rectangle 7.4: Compute the area and perimeter of triangles and rectangles in simple problems Area of a triangle Perimeter of a square or a rectangle Area of a square or a rectangle Distinguishing between area and perimeter 7.5: Use geometric formulas when all necessary information is given Area of a triangle Area of a square or a rectangle Area of a parallelogram Area of a trapezoid Area of a regular polygon Circumference and area of a circle Volume of a rectangular prism Volume of a triangular prism Volume of a pyramid Volume of a cylinder Volume of a cone Volume of a sphere 7.6: Compute the area of triangles and rectangles when one or more additional simple steps are required 7.7: Compute the area and circumference of circles after identifying necessary information Circumference and area of a circle 7.8: Compute the perimeter of simple composite geometric figures with unknown side lengths Perimeter of a piecewise rectangular figure 7.9: Use relationships involving area, perimeter, and volume of geometric figures to compute another measure Sides of polygons having the same perimeter Finding the side length of a rectangle given its perimeter or area Finding the perimeter or area of a rectangle given one of these values ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/6

6 Finding the radius or the diameter of a circle given its circumference 7.10: Use scale factors to determine the magnitude of a size change Similar solids: Problem type 1 Similar solids: Problem type 2 Dilation 7.11: Compute the area of composite geometric figures when planning or visualization is required Area of a piecewise rectangular figure Area between two rectangles Area involving rectangles and triangles Area between two concentric circles Area involving rectangles and circles Area involving rectangles and circles: Advanced problem Note: Standards 1, 2, 3, 4, and 8 are not covered in the ALEKS course High School Geometry. Online reporting with all Standards is available with the ALEKS courses Algebra 1, Integrated Mathematics I, and Algebra 2. ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/6