Explore the number line and its elements through a graphic representation of an equation. Move along the curve of the graph of xy=12 to see how the values change as you vary x or y and consider what happens for negative values of x and y.
For a given set of data points, the line that minimizes the sum of the squared errors is the least squares line. Find the least squares line that best represents the height and foot length of 17 people in a scatter plot.
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.
Imagine a cake shaped like a cube that is frosted on all six sides and will be cut into smaller cube-shaped pieces. Make predictions about the number of pieces and the amount of frosting on each piece of cake using the table to check your predictions.
Test your knowledge of polyhedra, prisms, pyramids, volume, surface area, Euler’s Theorem and platonic solids. Take this 39-question test, review your correct and incorrect answers, and print out your assessment.
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.
Try to judge when you think a minute has passed without counting in your head or watching a clock. Use the online stopwatch to record your guesses, get some friends to guess as well and try to come up with reasons for the variations in responses.
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.