
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
This article explores the process of making and testing hypotheses.

Charlie and Lynne put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

Can you find the value of the circles when you know what's in the squares?

Can you make a hypothesis to explain these ancient numbers?

Can you decode the mysterious markings on this ancient bone tool?

Can you find rectangles where the value of the area is the same as the value of the perimeter?