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Problem Corner

Browse all rich problems in mathematics:
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Discipline(s): Mathematics
Grade(s): 7
Resource Type(s): Content Supports — Activities and rich problems
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1
Volumes Mathematically
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ORC# 9750
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 7–12
Professional Commentary: How does one go about finding the volume of an irregular shape? Students get a preview of integral calculus as they compute volume of a solid as the sum of volumes of slices of the solid....
2
Volumes Experimentally
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ORC# 9749
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 6–8
Professional Commentary: The purpose of this activity is to discover relationships among the volumes of simple solids such as cones, cylinders, pyramids, cubes, and spheres. A discussion of the underlying mathematical ideas is included....
3
The 3x+1 Problem
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ORC# 9748
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 5–8
Professional Commentary: Start with any whole number. Call it A. Find the next integer B in the following way: If A is odd, then B = 3A + 1; if A is even, then B = A/2....
4
Target Game
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ORC# 9747
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 5–8
Professional Commentary: Starting at 0, students take turns adding 1 or 2 until they reach 21; whoever hits 21 exactly is the winner. Students play this game and several variations, with a goal of discovering winning strategies....
5
Statistics Using Dice
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ORC# 9746
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 6–8
Professional Commentary: What happens if you roll two dice many times? How can you analyze the results?...
6
Similar Triangles
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ORC# 9743
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 7–11
Professional Commentary: What would be a reasonable definition of similarity? What are sufficient conditions that two triangles be similar?...
7
Round Robin Tournament
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ORC# 9742
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 6–10
Professional Commentary: Malabar Middle School is scheduling a round-robin tournament for six softball teams. In a round-robin tournament each team plays each other team exactly once....
8
Representation of Data -- The U.S. Census
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ORC# 9741
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 7–12
Professional Commentary: The object of this activity is to study an excellent example of the presentation of data. Students analyze an illustration of the 1930 U.S....
9
Rainy Lake, aka Mirror Lake
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ORC# 9739
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 6–8
Professional Commentary: Students use a topographical map featuring a body of water, such as a lake, pond, or river, to figure out how much the level of the water would rise after a one-inch rainfall the previous night. An extension of the problem and a discussion of the underlying mathematical ideas are included....
10
Pythagorean Theorem
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ORC# 9738
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Resource Type: Content Supports -- Activities and rich problems
Discipline: Mathematics
Grades: Grades 6–10
Professional Commentary: This activity shows how cutting geometric shapes and rearranging the pieces leads to some standard area formulas and to the Pythagorean Theorem. Complete proofs are included....
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