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Standard 4.3A: Math
Standard: Patterns and Algebra
Strand: Patterns and Relationships
Cumulative Progress Indicator: The student will develop an informal notion of limit.
Grade: 12
Framework Activities
· Students explore the value of .99 ... (or 4.999... or 3.2999...) as an infinite series (9/10 + 9/100 + ... ), and conclude that its value is exactly 1 (or 5 or 3.3).
· Students informally find the limits of real-world series such as the total vertical distance traveled by a ball dropped from a height of 10 meters which always bounces back to 3/4 of its original height.
· Students estimate the area of a circle with radius of 10 by informally judging the limiting value of the sequence produced by the areas of inscribed regular polygons as their sides increase by 1; that is, they calculate the area of an inscribed equilateral triangle, an inscribed square, an inscribed pentagon, and so on.
· Students discuss pyramid schemes and create a mathematical model to determine how many people would have to participate in the scheme for everyone at the fifth level to be paid, for everyone at the tenth level to be paid, and then for everyone who participated at any level to be paid. For example, if each person pays four others, then there are 4n people at the nth level.
· Additional Framework Activities
Other NJDOE Activities
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