If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Can you find the values at the vertices when you know the values on the edges?
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?
What's the largest volume of box you can make from a square of paper?
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?
Charlie and Abi 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?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.
This article explores the process of making and testing hypotheses.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
Can you decode the mysterious markings on this ancient bone tool?
Can you make a hypothesis to explain these ancient numbers?
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .