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Recommended investigations

Consecutive Odds and Evens: Determine a rule that relates arithmetic operations on four consecutive odd and even numbers.

Patterns in a Table: Investigate numeric relationships in a two dimensional matrix generated by a polynomial function with two variables.

Fractions into Whole Numbers: Find three whole numbers that can be substituted into a fractional expression so that the expression evaluates to a whole number.

McNugget Numbers: Find combinations of McDonald's Chicken McNugget orders that will and will not generate different natural numbers.

Multiplying Rabbits: Examine how the family tree of a rabbit forms the Fibonacci sequence and the golden ratio.

Fibonacci Extended: Identify an explicit pattern between terms in a group of numbers that are generated recursively.

Going Fishing: Determine the terms of an arithmetic sequence given its constant difference, number of terms, and sum.

Infinite Series: Determine the sum of various infinite series and investigate how to tell if a series will converge.

Pascal's Patterns: Identify patterns in a triangular array of numbers.

Hot Air Balloons: Determine the height of a hot air balloon over time based on a recursive condition.

Half-Sums: Consider the infinite sums of some numbers.

Arranging Toothpicks: What is the total number of toothpicks used to build a rectangular grid?

Almost a Square: What rectangle can you construct so that its area and dimensions are close to those of a specific square?

Choose an Elevator: Based on certain criteria, determine which of two elevators reaches the lobby first.

Hypatia's Triumph: Take on the Egyptian Hypatia's challenge about sums of squares.

Raised to the 100th: Use patterns to determine the units digit for numbers raised to the 100th power.

Summing Multiples: Find a pattern in the sum of multiples.

Gretel's Goldfish: When will Hansel and Gretel have the same number of goldfish?

Tri-Square Trios: Explore whether the sum of two triangular numbers can equal a square number.

Sum of Infinite Fractions: Determine the sum of an infinite geometric series that begins with the number one.

Partial Sum of Consecutive Integers: Can a partial sum of consecutive positive integers equal a number with identical digits?

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