## Proper Patterns

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

## Squaring Legs

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

## The Middle Digit

Investigate the pattern(s) involving the middle digit in the square of numbers whose digits are all 1’s.

## Breaking the Code

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

## Counting Terms

How many terms are in the given sequence?

## Average Patterns

Use the average of four 26’s and four 34’s to determine the average of four of another number.

## 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?

## Missing Letters

Find the next two letters in the given sequence.

## Number Machine

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

## Even Factors

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

## Not So Good Partitions

Find all positive whole numbers that are not “good” numbers.

## Laying Bricks

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

## Row Sum

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

## Alpha Numeric

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

## Triangular Array

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

What is the value of the expression?

## Counting Stones

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

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

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?

## Units of Seven

Find the units digit of a large number.

## Theater Seating

How many seats are in the Mathematics Theater?

## Playing for Sticks

Devise a strategy so that you will always win the game.

## Horizontal Inquisition

Draw the next figure in the sequence. Explain how you determined the result.

## Foil Frenzy

Simplify an expression.

## What Time is It?

Determine the next value in the sequence.

## The Next Row

Complete the row using a pattern.

## Tessellating a Plane

Determine why some polygons tessellate the plane and why others do not.

## Fractal Iterations

Explore the idea of fractals.

## Repeating Patterns

Find the pattern to count numbers.

## Sum of Natural Numbers

Find a way to add a set of natural numbers.

## Triangles inside Triangles

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

## Triangular Numbers

Form triangular numbers and look for patterns.

## Sum of Consecutive Integers

Use the sum of consecutive integers to form certain numbers.

## Completing the Sequence

Find the next numbers in the sequences.

## Squares on a Checkerboard

Determine how may squares are on a given checkerboard.