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Ohio's Academic Content Standards in Mathematics

Benchmark Resources

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Ohio Standard: Mathematical Processes Standard
Benchmark: (Grades: 11-12) B. Construct logical verifications or counter-examples to test conjectures and to justify or refute algorithms and solutions to problems.
1
Squares Inside Squares: Sequences
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ORC# 123
Resource Information
Resource URL: http://www.pbs.org/teachers/mathline/lessonplans/pdf/hsmp/square...
Resource Type: Lessons
Discipline: Mathematics
Grades: Grades 9–12
Professional Commentary: Students investigate the pattern determined by the areas of squares inscribed in squares formed by joining the midpoints of the sides of the previous square. The sequence generated is a simple geometric sequence....
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2
Circle Packing 2: Soda Rack
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ORC# 7610
Resource Information
Resource URL: http://illuminations.nctm.org/LessonDetail.aspx?ID=L691
Resource Type: Lessons
Discipline: Mathematics
Grades: Grades 9–12
Professional Commentary: In this second lesson (in a unit of three), students consider the arrangement of soda cans placed in a bin with two vertical sides, discover an interesting result, and prove that the result is true. This lesson utilizes an on-site applet....
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3
Red and Blue Points
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ORC# 10180
Resource Information
Resource URL: http://www.ohiorc.org/pm/math/richproblemmath.aspx?pmrid=80
Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 8–12
Professional Commentary: We assume that all the points in the plane have been colored either red or blue. It is then required, without knowing anything further about the distribution of the colors, that we find: (a) a line segment whose endpoints and midpoint are the same color, (b) three points of the same color that determine a right...
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4
Knights and Knaves
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ORC# 10135
Resource Information
Resource URL: http://www.ohiorc.org/pm/math/richproblemmath.aspx?pmrid=29
Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 8–12
Professional Commentary: This problem is the best-known simple example of a knight-knave problem, in which you come to a fork in the road and you do not know which way to go. In one direction lies happiness; in the other, disaster....
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5
Sums of Consecutive Whole Numbers: A Number Series Investigation
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ORC# 10175
Resource Information
Resource URL: http://www.ohiorc.org/pm/math/richproblemmath.aspx?pmrid=60
Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 8–12
Professional Commentary: Students investigate sums of consecutive whole numbers with the aim of answering these questions: Can any whole number greater than 2 be written as a sum of consecutive whole numbers? If not, which can (cannot)?...
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