Develop an understanding of infinite sequences that arise in natural situations. The students decide that the Fibonacci sequence shows how many pairs of rabbits there are each month. The students explore other patterns in this sequence, noting that each term is the sum of the two preceding terms. Students look for infinite sequences in Pascal's triangle. Investigate, represent, and use non-terminating decimals.
Students investigate using simple equations to iterate patterns.
The resulting y- value is 1 . Using this as the new x yields a 2 for y . Students explore the question of which fractions have terminating decimal equivalents and which have repeating decimal equivalents. They discover that the only fractions in lowest terms which correspond to terminating decimals are those whose denominators have only 2 and 5 as prime factors. Represent, analyze, and predict relations between quantities, especially quantities changing over time.