This activity shows how reading a mathematics problem three times, with a different focus question each time, can help students make sense of a problem.

## Comparing Figurate Numbers

Investigate, make conjectures, and develop proofs about triangular and square numbers. Compare numbers whose corresponding figures have similar base lengths.

## Cuisenaire Rods

Look at patterns of solids made with Cuisenaire rods. Make a table of the surface area and volume for each term of this sequence and view graphs of your data. Find the rule for the nth term.

## Enveloping Functions

Investigate the characteristics of functions. How do graphs of functions change when coefficients are changed?

## Falling Objects

Explore the mathematics of a ball dropped from a height of 10 feet. Collect data on the height of the ball with respect to time and plot the curve representing the data.

## Ferris Wheel

Observe as the students diagram the facts of the problem. They then identify and graph the relevant functions to represent the motion around a Ferris wheel.

## Figurate Numbers

Observe the geometric structure of numbers. Play with square and triangular figurate numbers on a graph and see the shapes that representative dot patterns can take.

## Fish Derby

Students have to calculate the optimal number of bass and carp that a pond can support. They determine and graph information about feeding and breeding areas and solve an algebraic equation to get optimal numbers.

## From Corner to Corner

Measure the lengths and diagonals of three squares with a ruler. Look over your measurements and try to come up with a rule of thumb for estimating the length of a diagonal if you know the length of a side.

## Galton Board

Use the Galton board to validate the Law of Large Numbers. Compare experimental and theoretical results to illustrate the Central Limit Theorem.

## Graphing Lab -- Moose Synthesizer Co.

To price his product and maximize his profit, Albert Moose needs to know all his costs and revenue. Assist Albert with his decision.

## Graphing Lab -- Skiing

Michael and friends are planning a skiing weekend. Show them how to afford it.

## Group Test Parabola

Graph the sequence and find the equation of the curve. Solve the equation to determine the value of the 100th term of the sequence.

## Guess My Button

Practice classification/pattern recognition skills by guessing which button out of sixteen the computer has chosen. Go through a series of online questions about the buttons that differ in size, color, shape and number of holes to determine the answer.

## How Many Valentines?

How many valentines are exchanged if each of five friends gives a valentine to each of their other friends? Reflect on your solution, compare it with some others listed, and think about how you would solve a similar problem for more people.

## Hypercube

Discover a fourth spatial dimension by using analogies (point, line and plane) from lower dimensions. Model objects of lower dimensions to gain understanding of a hypercube, which exists in the fourth dimension.

## I Took a Trip on a Train

You took four snapshots of some geometric shapes that you saw on your train trip around a circular track. You dropped the pictures and got them mixed up, and now you must imagine your trip to put them back in order.

## Interest Rate Calculator

The bank is offering four special savings plans for new customers. Use the interest rate calculator to determine the best offer, taking variables like principal and compounding into account.

## Journal

Answer the journal prompts, including reflections from the workshops and your own classroom. The journal (requires a login) will save your entries for 120 days after you register. However, you can print or transfer your entries to your own computer.

## Limerick Factory

A limerick is a very funny piece of nonsense verse with its own special pattern of rhyme and rhythm. Use this tool to choose phrases to create your own limerick that follows the pattern.