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Additional investigations

Squares on a Checkerboard: Determine how may squares are on a given checkerboard.

Completing the Sequence: Find the next numbers in the sequences.

Sum of Consecutive Integers: Use the sum of consecutive integers to form certain numbers.

Triangular Numbers: Form triangular numbers and look for patterns.

Triangles inside Triangles: Extend the given table and determine a relationship between the numbers in the triangle.

Sum of Natural Numbers: Find a way to add a set of natural numbers.

Repeating Patterns: Find the pattern to count numbers.

Fractal Iterations: Explore the idea of fractals.

Tessellating a Plane: Determine why some polygons tessellate the plane and why others do not.

The Next Row: Complete the row using a pattern.

What Time is It?: Determine the next value in the sequence.

Foil Frenzy: Simplify an expression.

Horizontal Inquisition: Draw the next figure in the sequence.

Playing for Sticks: Devise a strategy so that you will always win the game.

Theater Seating: How many seats are in the Mathematics Theater?

Units of Seven: Find the units digit of a large number.

Spreading Rumors: It is important for 8000 people to hear a rumor by May 14. Is this outcome likely to occur if the pattern for spreading the rumor continues as started?

Adding Places: How many times will the digits of each number in a set add to equal 8?

Counting Stones: Following the counting pattern described, which of the original nine stones is counted as stone #599?

Add, Add, Subtract: What is the value of the expression?

Triangular Array: What numeral will be listed directly beneath 125 when the triangular array is continued?

Alpha Numeric: Fill in the next letter of the alphabet, using the logic established to list the first eight.

Row Sum: In the given arrangement of numbers, investigate the sum of all the numbers in a row.

Laying Bricks: How many ways are there to lay bricks to form different patio patterns?

Not So Good Partitions: Find all positive whole numbers that are not "good" numbers.

Even Factors: Find numbers whose factors are all even (excluding the number 1 as a factor).

Number Machine: What will the number machine give me if I put in 100?

Missing Letters: Find the next two letters in the given sequence.

Sprinting Around: When will Sonic the Hedgehog, the Road Runner, and the Tasmanian Devil meet if they are running on a circular track following the patterns described?

Average Patterns: Use the average of four 26's and four 34's to determine the average of four of another number.

Counting Terms: How many terms are in the given sequence?

Breaking the Code: Use what you know or what you can find out about common letters to help you decode this message.

The Middle Digit: Investigate the pattern(s) involving the middle digit in the square of numbers whose digits are all 1's.

Squaring Legs: Using information about how a scroboscopus squares its number of legs, can you tell how many scroboscopi Tom bought?

Proper Patterns: Given some of the proper factors of a number, what could the number be?

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